HIGH THEMAL ENERGY STORAGE DENSITY MOLTEN SALTS FOR PARABOLIC
TROUGH SOLAR POWER GENERATION
by
TAO WANG
RAMANA G. REDDY, COMMITTEE CHAIR
NITIN CHOPRA
YANG-KI HONG
A THESIS
Submitted in partial fulfillment of the requirements
for the degree of Master of Science
in the Department of Metallurgical and Materials Engineering
in the Graduate School of
The University of Alabama
TUSCALOOSA, ALABAMA
2011
Copyright Tao Wang 2011
ALL RIGHTS RESERVED
ABSTRACT
New alkali nitrate-nitrite systems were developed by using thermodynamic modeling and
the eutectic points were predicted based on the change of Gibbs energy of fusion. Those systems
with melting point lower than 130oC were selected for further analysis. The new compounds
were synthesized and the melting point and heat capacity were determined using Differential
Scanning Calorimetry (DSC). The experimentally determined melting points agree well with the
predicted results of modeling. It was found that the lithium nitrate amount and heating rate have
significant effects on the melting point value and the endothermic peaks. Heat capacity data as a
function of temperature are fit to polynomial equation and thermodynamic properties like
enthalpies, entropies and Gibbs energies of the systems as function of temperature are
subsequently induced. The densities for the selected systems were experimentally determined
and found in a very close range due to the similar composition. In liquid state, the density values
decrease linearly as temperature increases with small slope. Moreover, addition of lithium nitrate
generally decreases the density. On the basis of density, heat capacity and the melting point,
thermal energy storage was calculated. Among all the new molten salt systems, LiNO3-NaNO3KNO3-Mg(NO3)2-MgKN quinary system presents the largest thermal energy storage density as
well as the gravimetric density values. Compared to the KNO3-NaNO3 binary solar salt, all the
new molten salts present larger thermal energy storage as well as the gravimetric storage density
values, which indicate the better thermal energy storage capacity for solar power generation
systems.
ii
DEDICATION
This thesis is dedicated to everyone who helped me and guided me through the trials and
tribulations of creating this manuscript. In particular, my family and close friends who stood by
me throughout the time taken to complete this masterpiece.
iii
ACKNOWLEDGEMENTS
I am pleased to express my gratitude and appreciation to my advisor, Professor Ramana
G. Reddy, for his patience and guidance during my graduate study and the entire research work. I
am greatly benefited from his experience, knowledge and enthusiasm for scientific research.
I would like to express my sincere thanks to Dr. Nitin Chopra and Dr. Yang-Ki Hong for
serving on my committee. Their valuable suggestions and comments are very insightful for my
research work.
I would like to thank all the research colleagues of Dr. Reddy‟s research group, special
thanks to Dr. Divakar Mantha for his valuable suggestions and comments. I would like to extend
my gratitude to U.S Department of Energy for the financial support.
Finally, I would like to thank my parents and my fiancée, whose invaluable
understanding and loving support helped me through the difficult times.
iv
TABLE OF CONTENTS
ABSTRACT
ii
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
LIST OF TABLES
viii
LIST OF FIGURES
x
CHAPTER 1. INTRODUCTION
1
CHAPTER 2. LITERATURE REVIEW
11
2.1 Melting point
11
2.2 Density
15
2.3 Heat capacity
18
CHAPTER 3. OBJECTIVES
22
CHAPTER 4. THERMODYNAMIC MODELING OF SALT SYSTEMS
24
4.1 Thermodynamic modeling
24
4.2 Calculations
27
v
CHAPTER 5. EXPERIMENTAL PROCEDURE
30
5.1 Melting point determination of molten salt mixtures
30
5.1.1 Materials
30
5.1.2 Apparatus and Procedure
30
5.2 Heat Capacity determination of molten salt mixtures
32
5.3 Density determination of molten salt mixtures
33
CHAPTER 6. RESULT AND DISCUSSION
34
6.1 Melting point determination
34
6.1.1 DSC equipment calibration
34
6.1.2 Results
35
6.1.3. Discussion
41
6.2 Heat capacity determination
51
6.2.1 Heat capacity calibration
51
6.2.2 Results
52
6.2.3 Thermodynamic properties
55
6.2.4 Discussion of Gibbs energy change for molten salts
84
6.3 Density determination
86
vi
6.3.1 Density calibration
86
6.3.2 Results and discussions
82
6.4 Thermal energy storage density of molten salts
90
CHAPTER 7. CONCLUSION
94
REFERENCES
96
APPENDIX
104
APPENDIX A
104
APPENDIX B
109
APPENDIX C
114
APPENDIX D
118
APPENDIX E
123
APPENDIX F
128
APPENDIX G
133
APPENDIX H
138
APPENDIX I
143
vii
LIST OF TABLES
2.1. Melting point of various nitrate salt systems
12
2.2. Melting point of various carbonate salt systems
13
2.3 Melting point of various fluoride/chloride salt systems
14
2.4 Melting point of various hydroixde salt systems
15
2.5 Density coefficients A and B of nitrate salts
16
2.6 Density coefficients A and B of carbonate salts
17
2.7 Density coefficients A and B of chloride/fluoride salts
17
2.8 Density coefficients A and B of molten salt mixture with hydroxide salts
18
2.9 Heat capacity of alkali nitrate salt at 500 oC
19
2.10 Heat capacity of alkali carbonate salt at 500 oC
19
2.11 Heat capacity of fluoride/chloride salt at 500oC
20
2.12 Heat capacity of hydroxide salt at 500oC
21
4.1 Calculated composition and melting point for multi-component systems
29
6.1 Calibration data of melting points with different samples
35
6.2 DSC results of melting point, transition point and change of enthalpy
41
viii
6.3 Fusion and solid phase transition temperature for individual salts
42
6.4. Melting points of candidate systems as function of temperatures
51
6.5 Calibration data of heat capacities with different samples
52
6.6 Heat capacity of selected new TES molten salt mixtures
54
6.7 Change of Gibbs energy values at 623.15K for molten salt systems
85
6.8 Calibration of density measurements with different pure nitrate salts
86
6.9 Coefficient of A and B for density determination of salt #1 to salt # 9
87
6.10 Extrapolated value of density and heat capacity at 500 oC of salt #1 to salt #9
91
6.11 Energy density of salt #1 to salt #9 compare to solar salt
92
6.12 Gravimetric storage densities for solar salt and new molten salts
93
ix
LIST OF FIGURES
1.1 Theoretical and engineering energy conversion efficiency as function of temperature
6
1.2 Gravimetric storage density for different energy storage systems
as function of temperature
8
5.1 Photography of set-up for DSC equipment
31
6.1 Melting point calibration with indium sample
34
6.2 Melting point calibration with KNO3 sample
35
6.3 DSC endothermic peaks of LiNO3-NaNO3-KNO3 salt.
36
6.4 DSC endothermic peaks of NaNO3-NaNO2-KNO3 salt.
37
6.5 DSC endothermic peaks of LiNO3-NaNO3-KNO3-MgK salt.
37
6.6 DSC endothermic peaks of LiNO3-NaNO3-KNO3-NaNO2 salt.
38
6.7 DSC endothermic peaks of LiNO3-NaNO3-NaNO2-KNO3-KNO2 salt.
38
6.8 DSC endothermic peaks of LiNO3-NaNO3-KNO3-KNO2 salt.
39
6.9 DSC endothermic peaks of LiNO3-KNO3-NaNO2-KNO2 salt.
39
6.10 DSC endothermic peaks of LiNO3-KNO3-NaNO2-Mg(NO3)2 salt.
40
6.11 DSC endothermic peaks of LiNO3-NaNO3-KNO3-Mg(NO3)2-MgKN Salt.
40
6.12 DSC plot of 69.8wt% KNO3 -30.2wt% NaNO2 binary system
43
x
6.13 DSC plot of 27.0wt% NaNO3-73.0wt% KNO3 binary system
45
6.14 DSC plot of 45.8wt%LiNO3-54.2wt%KNO3 binary system
45
6.15 DSC plot of 46.0wt% NaNO3-54.0wt% KNO3 binary system
46
6.16(a) DSC endothermic peaks of LiNO3-NaNO3-KNO3-KNO2 salt
for 20oC/min heating rate.
47
6.16(b) DSC endothermic peaks of LiNO3-NaNO3-KNO3-KNO2 salt
for 5oC/min heating rate.
48
6.17(a) DSC endothermic peaks of LiNO3-KNO3-NaNO2-KNO2 salt
for 5oC/min heating rate.
49
6.17(b) DSC endothermic peaks of LiNO3-KNO3-NaNO2-KNO2 salt
for 20oC/min heating rate.
49
6.18 Heat capacity data plot of LiNO3-NaNO3-KNO3 ternary system
as function of temperature
53
6.19 Heat capacity of LiNO3-NaNO3-KNO3 in liquid state from 403.15-623.15K
54
6.20 Change of Gibbs energy as function of temperature for molten salt systems
85
6.21 The densities of the salt #1 to salt #5 as function of temperature
87
6.22 The densities of the salt #6 to salt #9 as function of temperature
89
6.23 Densities of the salt #1, salt #2 as function of temperature compared to
the equimolar NaNO3-KNO3 binary system and pure KNO3.
6.24 Gravimetric storage density comparison of different energy storage
xi
90
systems as function of temperature
93
xii
CHAPTER 1
INTRODUCTION
Renewable energy sources such as wind, solar, water power, geothermal and biomass are
playing more and more significant role in our energy supply. Because the cheap cost and infinite
amount of energy storage inside the resource, solar energy is emphasized since 20th century and
viewed as promising alternative method to satisfy the large energy consumption every day in the
world, reduce the emission of carbon and strengthen the economy.
The wind energy was used as a clean energy to generate electricity back to late 19 th century.
However, this renewable energy source was not emphasized due to the cheap price of fossil fuel.
The re-emergence happened in mid 1950s when the amount of traditional energy source was
found apparently decrease. The development of wind energy usage continued and in 1990 the
first mega-watt wind turbine was launched, which was viewed as a symbol of shift to large scale
wind energy utilization [1-2]. The modern application of wind energy mainly relies on wind
turbine. On the basis of aerodynamic, wind turbine generates certain net positive torque on
rotating shaft and then converts the mechanical power to electrical power. As an electrical power
generator, wind turbine is connected to some electrical network to transport the electricity to
battery charging utilities, residential power systems and large scale energy consuming systems.
In general, most of wind turbines are small scale and can only generate 10KW electrical power.
Only few of the wind turbine systems operate with capacity as large as 5MW. Although the
usage of wind energy can reduce the emission of carbon oxide, the noise pollution and high cost
1
limit its large scale application. Since the wind is not transportable, the electrical energy can only
be generated where the wind blows, which also decrease the flexibility of wind energy.
Water power is another term of alternative power supply and it was used for irrigation,
operating machines like watermill even before the development of electrical power. The modern
application of water power is to generate electricity by using the gravitational force of falling or
flowing water. These days, there are various ways for the water power application. The most
traditional method is to store the water in dam and generate electricity by converting the
potential energy; pump storage is a different way to utilize water power and can change its
output depending on the energy demand by moving water between reservoirs at different
elevations. In the low energy demand period, excess energy is used to lift water to the higher
level, while in the peak period of energy demand, the water is released back to the lower
elevation through water turbine. Water power can also be converted by taking advantage of
naturally raise and fall of tide to satisfy the demand of electrical energy consumption [3].
Although the usage of water power can reduce the emission of carbon dioxide and cost, it will
destroy the ecosystem because of the large land required for construction. There will be methane
emission from the reservoir; the potential failure hazard of dam is also a fatal issue and flow
shortage caused by drought may also create serious problem. As result of that, water power
technique is not a long-term alternative choice.
Geothermal energy is the energy form generated inside the earth. At the very beginning of
the planet formation, a large amount of thermal energy was stored from the radioactive decay of
minerals, volcanic activity and solar energy absorption. Because of the temperature difference
2
between the core and the surface of planet, the thermal energy stored inside the earth is driven to
the outer surface in the form of heat. This form of renewable energy source can be applied to
generate electrical power and heat for industrial, space and agricultural applications.
Theoretically, the deposited amount of geothermal energy is adequate to supply the energy
consumption in the world. However, most of the geothermal energy is stored deeply near the
core of the earth, the deep drilling and exploration of geothermal energy is very expensive and
limits the large-scale use of this renewable energy source [4].
Biomass is a renewable energy source used to generate heat or electricity with living or
recently living organism such as wood, waste, (hydrogen) gas and alcohol fuels. The biomass
energy can be converted to electrical energy by thermal method such as combustion, pyrolysis,
and gasification. Several specific chemical processes may also be able to convert the biomass
energy to other forms. The main problem arise from application of biomass is air pollution which
contains carbon monoxide, NOx (nitrogen oxides), VOCs (volatile organic compounds),
particulates and other pollutants. And the level of air pollution, to some extent, is even above that
of traditional fuel resource. Some other possible issue like transportation and sink of carbon also
limit the wide usage of this type of alternative energy [5].
Among all the renewable energy sources, solar energy is the most suitable alternative
energy for our future life. It is clean, cheap, abundant, without any noise, air pollution, no
transportation issue and easy to be obtained anywhere in the earth. Inside the core of the Sun,
hydrogen fuses into helium with a rate of 7×1011 kg/s and generates very powerful nucleation
power. This type of nucleation explosion creates ultra high temperature in the core of the Sun,
3
which reaches approximately 16 million K degrees. Although the Sun is not perfectly black body,
it still radiates abundant power with the energy density as 1.6×107 watts/m2 [6-7]. Because of the
enough amount of hydrogen underneath the surface of the Sun, the radiation given arise of from
the nucleation explosion can continue at least 5 million years with the same rate and strength.
The energy reaching the earth is vastly reduced mainly caused by the absorption and spreading
of the radiation. It is easily to understand that there are numerous amorphous objects all around
the entire universe which can absorb certain portion of the radiation for the Sun. Moreover, the
light generated from the spherical object such as the Sun fills all the available space between the
origin to the destination. Even though the energy will not be lost in the travelling process, due to
the long distance between the Sun to the earth, the surface area of the sphere which is formed
with the Sun as center and the distance as radius is much larger than that of the earth. As the
result of that, only 1340W/m2 finally reaches the upmost surface of the earth. Even though the
final amount of the received solar energy is very small compared to that is initially radiated from
the Sun, the average daily solar radiation falling on one area in the continental United States is
equivalent in total energy content to 11 barrels of oil. In summary, the solar energy itself is
relatively unlimited, useful, clean and almost unexploited energy and definitely can behave as
the promising mean for the future energy supply [8].
There are several different methods to take advantage of the solar energy and all the
methods can be distinguished into three group: solar parabolic trough, solar tower and solar dish.
Parabolic trough is constructed by silver coated parabolic mirror and there is a Dewar tube going
through the length of the mirror and set on the focal point, all the radiation is concentrated on the
tube and transfer by heat transfer fluid to the thermal energy storage unit. Solar tower are used to
4
capture solar energy with thousands of mirrors and focus the concentrated sunlight to the top of
the tower which is located in the middle of the heliostats. The thermal energy storage medium
within the tower was heated to high temperature and transferred to thermal energy storage tank
and eventually sent to steam pump. The solar dish is built with a large, reflective parabolic dish
which concentrates all the received sunlight to one spot. There is normally a receiver located on
the focal point and transform the solar energy to other forms of useful energy. The working
upper limit temperature of solar parabolic trough system is the lowest among these three systems,
normally its maximum working temperature is within the range from 400-500oC; the solar tower
has higher maximum working temperature which ranges from 500-1000oC; the solar dish has the
highest working upper limit temperature which reaches 700-1200oC [9].
The energy conversion efficiency is the most concerned parameter in the solar energy
storage application and the theoretical and real engineering efficiency are given in fig 1.1 as
function of temperature. The theoretical conversion efficiency can be up to 80% while in real
application, the value is always less than 70% regardless of collectors. The actual efficiency
increases with temperature in the whole working temperature. As a result of that, the thermal
energy storage materials in solar parabolic trough, for instance, should be able to work stably at
the upper limit temperature of this type of collection system which is 500 oC to ensure the highest
efficiency [9, 10].
5
Fig 1.1 Theoretical and engineering energy conversion efficiency as function of
temperature
Solar energy can be stored in three major forms: sensible heat, latent heat and
thermochemical heat. Sensible heat storage was utilized based on the heat capacity and the
change as function of temperature of storage materials in the charging and discharging process
which correspond to the absorbing and withdrawing energy processes, respectively. The sensible
heat stored from the melting point to the maximum working temperature can be expressed by
equation 1 [9].
[1]
Where m is the mass of storage material, Tmp and TH are melting point temperature and high
temperature in the same phase, respectively, Cp(T) is the heat capacity at different temperature.
Because the sensible heat storage materials remain in a single phase in the working temperature
range, the charging and discharging processes are completely reversible for unlimited cycles.
6
Latent heat storage is operated by absorbing and withdrawing energy in the charging and
discharging processes accompanied with fusion of materials [9]. The latent heat collected
throughout the working temperature range can be expressed by equation 2 as following:
[2]
Where T is temperature in solid state, Tmp is melting point temperature of storage material, TH is
the high temperature in liquid state and
is enthalpy of fusion.
Thermochemical heat storage is based on the heat capacity and its change as function of
temperature accompanied with chemical reaction. The thermochemical heat collected throughout
the working temperature range can be expressed by equation 3.
[3]
Where TL is the low temperature before the reaction, TR is the reaction temperature and
is the enthalpy of chemical reaction. Because of the destruction of the chemical bonds
in the reaction process, the charging and discharging process cannot be completely reversible,
which reduces the stability and recyclability of storage operation [10].
Sensible energy storage method is chosen to ensure the efficient usage of solar energy for
parabolic trough system of which the maximum working temperature ranges from 400-500oC.
Different from thermochemical heat storage, the sensible heat storage can achieve completely
reversible working condition under unlimited cycles. Also, fig 1.2 illustrates that the sensible
heat storage materials mainly work in the working temperature range for parabolic trough system,
7
and the gravimetric energy storage densities of sensible heat is higher than that of latent heat
materials [9 -11].
Fig 1.2 Gravimetric storage density for different energy storage systems as function of
temperature
Various materials are chosen to serve as thermal energy storage fluid for sensible heat
such as water, thermal oil, ionic liquid and molten salt [12]. The properties of different heat
transfer fluid determine the performance of solar energy heating system. In these days, the
efficiency and cost of output of electrical power mainly relies on the parabolic trough solar
power plant and the thermal storage fluid [12]. A large investment cost is needed to dispatch
100MW to 200MW energy by consuming the energy transfer fluids. Given by this situation, the
development of new thermal storage fluid with higher thermal energy storage density is
paramount to lower the expense for generating energy and a lot of effect has been put on design
of new systems [13-16].
8
Water is commonly used as heat transfer and thermal energy storage fluid in industry
because of its low cost, high heat capacity and high thermal conductivity. However, the
limitation for using this medium is also obvious that the temperature range within which the
liquid state can be assured is too small. It is well know that, water can only serve as thermal
energy storage liquid above the freezing point 0oC and below the boiling temperature 100oC. In
practical experiment, the actual temperature range is even less than 100 oC because of the large
amount of weight loss near the boiling temperature due to the high vapor pressure. Water is
possible to work above 100oC only if high pressure is also applied to avoid the phase
transformation, but the cost will be highly increased. Accordingly, water is only suitable to work
in low temperature below 100oC.
Thermal oils are also being used in the parabolic trough solar power plant and have very
low melting point as low as 12oC [17, 18]. However, the application of the oil for the thermal
energy storage liquid is limited by some disadvantages from the physic-chemical properties. The
upper limit for this oil is only 300 oC and above that the liquid state cannot be maintained.
Moreover, the low thermal decomposition temperature, low density and low heat capacity result
in limited thermal energy storage capacity. Since the working temperature range is so narrow, the
rankie cycle efficiency is reduced when using the synthetic oil and the cost for generating power
is considered to be very expensive [19, 20].
Ionic liquid is another medium served as thermal energy storage fluid. The liquid
temperature range of ionic liquid is large, which is one of the main advantages of this type of
material. The high heat capacity and density ensure the efficiency of thermal energy storage of
9
ionic liquid. What‟s more, the excellent chemical stability and little vapor pressure increase the
lifetime [21-24]. However, as a result of the very serve corrosion problem to the liquid container
and the high cost, the usage of ionic liquid is still limited.
Considering various relative physic-chemical properties of thermal energy storage system,
molten salts have been proposed as a suitable group for a wide temperature range application.
They are being emphasized in the solar energy applications because of their low melting point
and high upper limit which can increase the stable working range. The high heat capacity
increases the thermal energy storage density of the heat storage system; excellent thermal
stability and negligible vapor pressure ensure the steadiness of cyclic repeating in the lifetime
[25]; low viscosity strengths the mobility and efficiency of the thermal storage liquid; low
utilization cost reduce the investment and protect the economy. The liquidus temperature range
of the molten salt varies from 150-600oC, combination of various salts can bring the melting
down and further increase the working temperature range. Due to these properties, molten salts
can be excellent thermal energy storage fluid in the solar power generation system.
10
CHAPTER 2
LITERATURE REVIEW
Several physical and thermodynamic properties of thermal energy storage fluid play
significant role in determining the efficiency and performance of solar energy storage systems. In
order to evaluate the feasibility of systems, the physic-chemical properties of several molten salts
should be reviewed. The three determining parameter which directly affect the thermal energy
storage capacity in systems are melting point, heat capacity and density.
There are large amount of melting point data available in the literature for various molten
salt system in previous literatures while those with melting point less than 120 oC is very limited.
All the previous study on molten salt system revealed that five group of molten salts are
emphasized and commonly used: alkai or alkaline nitrates, carbonates, sulphates, chloride and
hydroxides. Although most of the systems have the same group of cation, the melting point
varies a lot from one to anther due to the different effect of anions.
2.1 Melting point
The melting points of individual and multi-component nitrate/nitrite systems are listed in
Table 2.1[26-31]. Among those systems, solar salt (NaNO3/KNO3: 60/40) is the thermal energy
storage medium which is currently being used with the freezing point of 221oC [27]. Although
the melting point for this system is highest in all the candidate mixtures in this group, the lowest
11
combined compound cost makes it widely used in solar energy storage field. Another ternary
system HITEC which contains NaNO3, KNO3 and NaNO2 has freezing point of 141 oC [28].
This combination brings the melting point down but the lack of combination of optimum features
limits its further application [29]. Some mixtures such as LiNO3-Ca(NO3)2-KNO3 are not often
utilized because they increase the compound cost at the same time of lowering the melting point
to around 120oC [30], moreover , the decreased melting point is still high compared to the
organic oil. There are also several systems have the melting points less than 100 oC or even 60oC,
they are not used in the parabolic trough solar power plant due to the decomposition of some
components during high temperature [31].
Table 2.1. Melting point of various nitrate salt systems
Compound
Melting Point (ºC)
LiNO3
253
NaNO3
KNO3
Ca(NO3)2
Sr(NO3)2
Ba(NO3)2
NaNO3-NaNO2
NaNO3-NaNO2-KNO3
NaNO3-KNO3-CaNO3
LiNO3-KNO3-NaNO3
KNO3-CaNO3-LiNO3
LiNO3-KNO3-NHNO3
KNO3-NHNO3-AgNO3
307
334
561
570
590
221
141
133
120
117
92
52
The melting points of individual and multi-component carbonate systems are listed in
Table 2.2 [26, 32, 33]. Different from the nitrate salts, the melting points for both the individual
12
and multi-component carbonate systems are on the higher side. The lowest melting point is
achieved with lithium, sodium and potassium carbonate ternary system whose melting point is
still 277oC higher than that of the nitrate ternary system with the same cations [32]. Besides,
because of the thermal decomposition issue, the choice of component involved in the multicomponent carbonate systems is limited. Some salt like CaCO3 doesn‟t have stable form at high
temperature and the lack of multi-component system reduces the chance of the synthesis of low
melting point salt mixtures. Even though this group of salt is not thermally stable and the
working temperature range is relatively small, it is still viewed as possible candidate working at
high temperature due to its low price.
Table 2.2 Melting point of various carbonate salt systems
Compound
Li2CO3
Na2CO3
K2CO3
MgCO3
Na2CO3-K2CO3
Li2CO3-Na2CO3
Li2CO3-K2CO3
Li2CO3-K2CO3-Na2CO3
Melting Point (ºC)
732
858
900
990
710
496
488
397
Alkali and Alkaline fluoride/chloride salts are also selected as one possible choice as the
thermal energy storage fluid and the melting point examined from previous literatures are given
in table 2.3 [34-38]. A lot of study has been done for this group of salt and the melting points
were found in the same range as the carbonate group. And for the pure salt, metal chloride salts
have lower melting point than metal fluoride ones.
13
Table 2.3 Melting point of various fluoride/chloride salt systems
Compound
LiF
NaF
KF
LiCl
NaCl
KCl
LiF-KF
LiF-NaF
LiCl-KF
LiF-NaF-KF
LiF-NaF-KF-MgF2
LiF-KF-BaF2
LiF-KF-CsF-RbF
Melting Point (ºC)
849
996
858
610
801
771
493
652
487
454
449
320
256
Several studies were also conducted to determine the melting point of molten hydroxide
salts and the results are shown in Table.2.4. The data of pure salts and multi-component mixtures
merely in this group were not much determined in the literatures. Generally, they are mixed with
other groups of anion and form some low melting point salt mixtures [39-42]. On the basis of the
previous literature data, alkali hydroxide salts and their mixture with salts in other groups have
relatively lower melting point compared with pure carbonate and fluoride/ chloride group salt
mixtures. Most of the melting points given in Table 4 are lower than 300oC; sodium potassium
hydroxide binary mixture even reaches the melting point below 200oC. Accordingly, relatively
large temperature range can be obtained by using hydroxide salt mixtures or adding them as
additive.
14
Table 2.4 Melting point of various hydroixde salt systems
Compound
LiOH-LiF
NaOH-KOH
LiOH-NaOH
NaOH-NaNO2
NaOH-NaNO3
NaOH-NaCl-NaNO3
NaOH-NaCl-Na2CO3
Melting Point (ºC)
427
170
213
232
237
242
282
2.2 Density
For the solar energy storage system, density for the thermal energy storage fluid is also
essential parameter. The density is needed for the size calculation as function of temperature and
assessing for the thermal stability of thermoclines. Besides, density as function of temperature is
used to evaluate the volume change in the process of freezing which contributes to potential
stress.
Alkali/alkaline nitrate salts were studied very much about their density as function of
temperature. All the results indicate that the density was decreased linearly as temperature
increases and any specific density value in the molten state can be expressed by equation as
equation 4:
 = A-BT
[4]
Where  (g/cm3) is the density of salt, A ( g/cm3) is the initial density value at 0oC and B
(mg/cm3·°C) is the density change slope as function of temperature. The coefficients are shown in
15
Table 2.5 for the nitrate group molten salts. Among these systems, pure sodium nitrate has the
largest value which reveals the high initial density value at low temperature [43]. Conversely,
lithium nitrate has the lowest value while it presents the smallest decrease trend as temperature
increases [44]. The densities and A, B values of multi-component nitrate salts were included in
the range of those two salts discussed above.
Table 2.5 Density coefficients A and B of nitrate salts
Compound
A(g/cm3)
B×103(g/cm3·°C)
LiNO3
1.922
0.556
NaNO3
KNO3
2.334
2.127
0.767
0.760
NaNO3-KNO3
2.134
0.773
KNO3-CaNO3-LiNO3
LiNO3-KNO3-NaNO3
2.172
2.083
0.735
0.715
Several experiments were also conducted to measure the density as function of temperature
for the individual and multi-component carbonate salt systems. The density of the carbonate salt
also follow the same trend as that of nitrate salt and the temperature dependence of density
followed the linear equation as discussed above. It is observed that all the carbonate salts have
higher initial density coefficient A than the nitrate salt. The largest value is reached to 2.511 and
even the lowest value in this group is greater than the maximum A of nitrate group [45-49].
What‟s more, the regression slope coefficient B of carbonate salt is lower compared to that of the
nitrate salt group. Accordingly, the salts in this group present larger density in the molten state
and the density coefficient A and B are given in Table 2.6.
16
Table 2.6 Density coefficients A and B of carbonate salts
Compound
A(g/cm3)
B×103(g/cm3·°C)
Li2CO3
2.303
0.532
Na2CO3
Na2CO3-K2CO3
Li2CO3-K2CO3
Li2CO3-Na2CO3
Li2CO3-Na2CO3-K2CO3
2.350
2.473
2.511
2.456
2.364
0.448
0.483
0.599
0.519
0.544
Density of metal fluoride and chloride molten salt were also examined and present similar
regression trend as temperature increases. The linear temperature dependence is also expressed
by the same equation. On the basis of previous literature data, the pure chloride salt shows lower
density than the fluoride salt with the same cation in the molten state [49]. What‟s more, the
sodium halide salt has the largest density value while the lithium halide salt has the lowest value,
which is very similar to the nitrate group salt. The density determination coefficient A and B are
given in Table.2.7.
Table 2.7 Density coefficients A and B of chloride/fluoride salts
Compound
LiCl
NaCl
KCl
LiF
NaF
KF
LiF-NaF
LiCl-NaF-KCl
LiF-NaF-MgF
A(g/cm3)
1.766
1.991
1.976
2.226
2.581
2.469
2.520
2.436
2.240
17
B×103(g/cm3·°C)
0.432
0.543
0.583
0.490
0.636
0.651
0.818
0.742
0.701
The density measurement of hydroxide was not conducted as much as those three anion
groups discussed above. Only few data of density is available for the alkali hydroxide salt when
added into other salt systems and temperature dependence also follows the linear regression
trend [32, 41]. The density determination coefficient A and B are given in Table 2.8.
Table. 2.8 Density coefficients A and B of molten salt mixture with hydroxide salts
Compound
LiCl-LiOH
LiF-LiOH
A(g/cm3)
1.6
1.65
B×103(g/cm3·°C)
0.443
0.471
2.3 Heat capacity
In the heating process, the temperature of solar energy storage molten salt is increase by
absorbing energy from the solar radiation. Conversely, the same amount of heat is released and
applied to heating system in the process of cooling. Heat capacity is the amount of heat required
to increase the temperature of certain material by 1 oC and can be viewed as the directly relevant
parameter to the energy storage ability. To some extent, the large heat capacity assures the
efficiency of the application of solar energy storage materials
The heat capacity of alkali/alkaline nitrate salt was investigated for both individual and
multi-component system in the previous literature. To simplify the comparison, only the heat
capacity value at 500oC is shown in all the following tables. In the liquid state, the heat capacity
increases with temperature following linear equation and the increasing slope is as small as 10-5
to 10-4 [50, 51]. Among those alkali nitrate salt systems, lithium nitrate has the largest heat
18
capacity at 500oC while potassium nitrate presents the lowest value at that temperature. In table
2.9, the heat capacity results at the selected temperature in literature are given.
Table 2.9 Heat capacity of alkali nitrate salt at 500oC
Compound
LiNO3
NaNO3
KNO3
NaNO3-KNO3
LiNO3-KNO3
LiNO3-KNO3-NaNO3
Heat capacity(J/g·K)
2.175
1.686
1.400
1.533
1.642
1.681
For the carbonate salt systems, in the molten state, the heat capacity is almost constant and
almost independent with temperature [32, 33]. Same as the nitrate group salts, the heat capacity
for pure carbonate salt decreases as the atomic number of the alkali element increases, which
means the value for lithium carbonate is the largest and that of potassium carbonate is the
smallest. Generally, the heat capacity value for carbonate in molten state is larger than that in
solid state. However, the sodium-potassium carbonate binary system is an exception, for which
the heat capacity in solid state is larger than liquid state. In table 2.10, the heat capacity results of
carbonate salts at the selected temperature in literature are given.
Table 2.10 Heat capacity of alkali carbonate salt at 500 oC
Compound
Li2CO3
Na2CO3
Heat Capacity(J/g·K)
2.50
1.78
K2CO3
Na2CO3-K2CO3
1.51
1.57
19
Li2CO3-K2CO3
Li2CO3-Na2CO3
Li2CO3-K2CO3-Na2CO3
1.60
2.09
1.63
The heat capacity of fluoride/chloride salt was measured in several literature and found
that for the pure salt, the lithium halide has the biggest heat capacity data in the molten state
while the potassium halides shows the lowest heat capacity value. Similar to the carbonate group,
the heat capacity value of fluoride/chloride salt varies little with temperature in the liquid state
[32, 33]. The values at 500oC for the alkali/alkaline halides are shown in Table 2.11.
Table 2.11 Heat capacity of fluoride/chloride salt at 500oC
Compound
LiCl
NaCl
KCl
LiF-KF
NaCl-MgCl2
LiF-NaF-KF
KCl-MgCl2-CaCl2
Heat Capacity (J/g·K)
1.48
1.15
0.90
1.63
1.00
1.55
0.92
The heat capacity of pure and multi-component hydroxide salt systems is limited in the
previous literature and the values in the liquid state follow linear equation which is observed for
all the molten salt discussed above [52]. The values at 500oC for the alkali/alkaline halides are
shown in Table 2.12.
20
Table 2.12 Heat capacity of hydroxide salt at 500oC
Compound
NaOH
LiOH-NaOH
NaOH-KOH
Heat Capacity(J/g·K)
1.88
2.21
1.82
In summary, on the basis of comparison of various physic-chemical properties, molten
nitrate slats have relatively low melting point, excellent working temperature range, reasonable
density and high heat capacity. As the result of that, molten nitrate salt is suitable to be applied as
the thermal energy storage fluid in the solar energy storage system.
21
CHAPTER 3
OBJECTIVES
Based on review of previous literature data, it is found that there are several disadvantages
such as the high melting point, relatively low density value or poor heat capacity in liquid state
which limit the application of molten salt in certain groups in solar thermal energy storage
system. Conversely, alkali/alkaline nitrate salt is considered as the suitable choice and proposed
as the thermal energy storage liquid for high temperature.
Currently, the used thermal energy storage liquid is NaNO3 (60mol%)-KNO3 (40mol%)
binary system (solar salt) which has the melting point at 221oC [30]. Although the melting point
for this salt mixture is not the lowest, it is still emphasized because of its low investment cost.
However, there are some drawbacks for this binary nitrate mixture. The main disadvantage is
the high melting point. In evenings or in winter, the molten salt can easily freeze and block the
pipeline. As a result of that, some auxiliary cost should be added to overcome this problem and
the total investment will be increased.
Development and synthesis of newer molten salt mixtures with freezing point lower than
those currently used for thermal energy storage applications is necessary for higher efficiency of
utilization of solar energy and getting rid of any unnecessary cost. The approach to develop
lower freezing point molten salt mixtures is by the prediction of new eutectic mixtures and also
22
by the development of new nitrate compounds. Besides these two most well known systems,
several other mixtures were also studied. Preliminary evaluation of several new molten salt flux
systems based on requirements for thermal energy storage systems, mainly including freezing
point, density, heat capacity, viscosity, and thermal energy storage density. The promising
candidate low melting point molten salt system should satisfy the requirements that eutectic
melting temperatures are lower than 220oC and the thermal energy storage densities are higher
than binary solar salt. It is known that the melting point can be lowered by the addition of one or
more ABNO3 nitrate compounds where A and B are cations. Consequently, several multicomponent systems which have more constituent salts than solar salt were came up with and
studied with little fundamental data on the physic-chemical properties at the required operating
conditions available at present.
In this thesis, the new systems with simulated eutectic compositions were tested for their
experimental melting points, heat capacities using the Differential Scanning Calorimetry (DSC)
technique which is considered to be the accurate instrument for thermodynamic data analysis
[53-59]. Some significant thermodynamic properties such as heat capacity, enthalpy, and entropy
and Gibbs energy were calculated in the thesis to evaluate the energy change of the system in the
phase change process and the potential of being applied in the parabolic trough solar power plant.
The energy density was obtained by using the experimental measured density and heat capacity
of the mixtures in molten state. Finally, 9 down-selected systems were present and discussed.
23
CHAPTER 4
THERMODYNAMIC MODELING OF SALT SYSTEMS
4.1 Thermodynamic modeling
To lower the melting point of solar energy storage system, multi-component system is
applicable. Thermodynamic model was introduced to predict the eutectic temperature of salt
systems based on the Gibbs energies of fusion of individual salt and that of mixing of constituent
binary systems. At the eutectic temperature, the Gibbs energies in the liquid state and solid state
of salt are equal. In thermodynamics, Gibbs energy of fusion can be expressed by the equation
given as follows:
G = H-TS
[5]
Where H is the change of enthalpy of fusion and S is the change of entropy of fusion. Equally,
the entropy change of fusion can be expressed by differentiating G and the equation is given:

[6]
It is known that the change in entropy can be expressed in terms of change in heat capacity in the
melting process as:

24
[7]
If the change of heat capacity is assume to be independent of temperature, the integral of
from Tm to T can be shown as:
[8]
where Sm is the entropy of fusion at the melting point which is equal to
. Accordingly,
Eq.8 can be rewritten as:
[9]
Substituting Eq. 9 in Eq. 6 and integrating the equation from Tm to T we get,
[10]
Eq. 10 illustrates that by using the change of heat capacity, melting point and enthalpy of fusion,
the Gibbs energy change at any temperature can be obtained.
The standard Gibbs energy of fusion of a salt „1‟ can be expressed in terms of the activity
of the salt as:
[11]
where
is the molar excess Gibbs energy and X1 is the molefraction of the salt „1‟. Gibbs
energy of fusion at any give temperature T is expressed by Eq 7 in terms of its molefraction and
partial molar excess Gibbs energy.
25
Take LiNO3-NaNO3-KNO3 as an example in which the integral molar excess Gibbs energy is
composed of the summation of the Gibbs energies of three constituent binary system and one
ternary. The expression of the integral excess Gibbs energy is given by Eq.12.
[12]
Gibbs energies of the three constituent binary systems, LiNO 3-NaNO3, LiNO3-KNO3, and
NaNO3-KNO3 of the LiNO3-NaNO3-KNO3 ternary system are taken from the literature [48, 49].
The Gibbs energies of mixing or the integral excess Gibbs energies of the three constituent
binary systems of the LiNO3-NaNO3-KNO3 ternary system are given below:
LiNO3-NaNO3 Binary System
J/mol
[13]
LiNO3-KNO3 Binary System
J/mol
[14]
J/mol
[15]
NaNO3-KNO3 Binary System
When assume the intergral excess Gibbs energy of
to be zero, the excess Gibbs energy in
the ternary system can be expressed by the summation of three constituent binary systems:
[16]
26
Generally, the partial molar excess Gibbs energies are reduced from the integral molar
excess Gibbs energy and can be expressed by the generalized equation for certain “m”
component salt as:
[17]
In the ternary system, the i value equals to 1,2 and 3, and the partial molar excess Gibbs energy
of mixing for each component can be expressed as follows:
[18]
[19]
[20]
Based on Eq. 7 and the partial molar excess Gibbs energy of individual component, the
Gibbs energy in the fusion can be expressed as Eq.21- 23.
[21]
[22]
[23]
4.2 Calculations
The fusion of the ternary salt system is defined by solutions of Eq. 21-Eq. 23. NewtonRaphson method can be used to solve these three non-linear equations by linearizing the nonlinear equations using the Taylor series and truncating the series to first order derivatives.
27
Consider the three non-linear functions F, G, and H in three variables, x, y, and z. The three
equations that are solved for the three variables are written as:
F(x, y, z) = 0;
G(x, y, z) = 0;
H(x, y, z) = 0;
[24]
The partial derivatives of the function F with respect to x, y and z are given as:
;
;
;
[25]
Similarly, the partials derivatives can be expressed for the other two functions G and H.
Newton-Raphson iterative method of solving the three equations in three variables
essentially deals with the solution of the incremental vector in the matrix equation given below.
[26]
For the initial values of x, y, and z, (say xi, yi, and zi) the right hand side vector contains the
values of the functions at the initial values (xi, yi, and zi). The 3×3 matrix on the left hand side
contains the partial derivatives of the functions with respect to the three variables at the initial
values. Solutions of the matrix equation (Eq. 26) result in the increments of the variables x, y,
and z. The variables for the next iteration will then be xi + x, yi + y, and zi + z. The
process of solving the matrix equation (Eq. 26) is continued until the increments in the variables
x, y, and z is less than a very small quantity. The iteration process is then said to be
28
converged and the values of the variables at convergence of the solution are the roots of the
system of the three fusion equations.
The composition of LiNO3, NaNO3 and KNO3 and the eutectic temperature is solved by
using the Newton-Raphson iterative method. Different from the data in previous literature, the
eutectic temperature for the ternary is 116oC. Besides, the composition for each component is
also different from those published in literatures. The new molten ternary system is composed of
25.92 wt% LiNO3, 20.01 wt% NaNO3, and 54.07 wt% KNO3. The similar method is also applied
to other multi-component systems to determine the composition and eutectic temperature. The
predicted melting points for new solar energy storage system are given Table.4.1.
Table 4.1 Calculated composition and melting point of multi-component molten salts systems
System
Salt #1
Salt #2
Salt #3
Salt #4
Salt #5
Salt #6
Salt #7
Salt #8
Salt #9
LiNO3
25.9
-
17.5
11.5
17.2
9
19.3
19.3
15.4
NaNO3
20
16.1
14.2
10.4
13.9
42.3
-
17.2
Composition (wt%)
KNO3 NaNO2 KNO2
54.1
54.7
29.2
50.5
17.8
27.4
47.6
17.2
4.1
33.6
15.1
54.6
23.7
2.4
55.9
23.9
32.4
-
29
Mg(NO3)2
0.9
8.3
MgKN
50.7
26.7
Calc. Tmp
(°C)
116
123.8
98.6
98.6
95.7
100.0
108.1
100.8
103.6
CHAPTER 5
EXPERIMENTAL PROCEDURE
5.1 Melting point determination of molten salt mixtures
5.1.1 Materials
Ternary, quaternary and quinary nirate and nitrite mixtures were tested in the thesis. Most
components in the mixtures don‟t require any pre-preparation and can be used as received. The
only exception is new developed MgKN which was composed of 66.67 mol% KNO3 and 33.33
mol% Mg(NO3)2. This unique compound is synthesized from magnesium nitrate hexahydrate
(98%, Alfa Aesar) and potassium nitrate (ACS, 99.0% min, Alfa Aesar) and added into the
mixture as one single component. As received magnesium nitrate hexahydrate is dehydrated
before synthesizing MgKN compound. Weighted amount of magnesium nitrate taken in a
stainless steel crucible and placed on a hot plate in an argon atmosphere. Temperature of the salt
is measured with a thermocouple immersed in the salt. The temperature was held at 523.15 K for
2 hours. The salt solidifies to a white mass. The temperature of the salt is then raised to 573.15 K
slowly to remove any traces of moisture and to ensure complete dehydration. The complete
removal of water is ascertained by weight loss.
5.1.2 Apparatus and Procedure
30
Differential scanning calorimetry (DSC) analysis was performed using Perkin Elmer
Diamond DSC instrument and the setup is shown in fig. 5.1. Heat flow and temperature can be
recorded in the instrument with an accuracy of 0.0001 mW and 0.01 K respectively. The
measurements were made under purified nitrogen atmosphere with a flow rate of 20cc/min and at
a heating rate of 5 K/min.
Fig 5.1 Photography of set-up for DSC equipment
After dehydration if necessary, each component was weighed to an accuracy of 0.1mg with
the electrical balance and mixed thoroughly in a stainless steel crucible. Later, the mixture is
heated up to certain temperature at which the entire salt melts. At this temperature the salt
mixture was held for about 30 minutes. The salt mixture is allowed to air cool to ambient
temperature. This procedure is repeated 3 to 4 times to get the well-mixed compound. Standard
aluminum pan with lid used for DSC measurements are weighed before the experiment. Small
amount of the synthesized compound is placed carefully in the aluminum pan and closed with
the lid. The lid is crimped by a sample press and the pan is weighed. The weight of the sample is
31
determined by removing the weight of the pan and lid. For the determination of melting point
and heat capacity (20-25) mg of the sample was used.
Perkin-Elmer Diamond Differential Scanning Calorimeter (DSC) is used to measure the
melting point and heat capacity of compound. The crimped ample pan was immediately put
inside the sample chamber of DSC after preparation and held at 523.15 K for 10 hours to remove
the trace amount of moisture possibly caught in the process of loading sample and also to ensure
a homogeneous mixture. In the experimental procedure, a temperature range from 298.15 K to
523.15 K was set with a heating rate of 5 K min1 followed by a cooling cycle at the same rate.
This cycle is repeated for at least 6 times to ensure good mixture of the sample and
reproducibility of the results.
5.2 Heat Capacity determination of molten salt mixtures
To start Cp measurement, the same procedure as that of melting point determination is
followed with an addition of „iso-scan-iso‟ steps to the program after 5-cycle temperature scan.
Starting from 298.15 K, the temperature was held for 5 minutes before and after each scan step.
Small temperature scan range is chosen to avoid thermal resistance between device and testing
sample except when the temperature is approaching the melting temperature. The upper limit for
the Cp measurement was set to 623.15 K in our experiments. Since the change in the molar heat
capacity of the salt in the liquid state is very small, the Cp data in the liquid state can be easily fit
to an equation and extrapolated to higher temperatures. To get the value of molar heat capacity
of the sample, heat flow curve for the baseline of the empty sample pan also needs to be obtained
immediately following the identical “iso-scan-iso” steps which were used for the actual sample
32
run. The difference of heat flow between the actual crimpled sample and the empty sample pan is
the absolute heat absorbed by the test sample.
5.3 Density determination of molten salt mixtures
Density measurement was carried out with standard densitometer which has fixed volume.
Initial weight of the densitometer is measured and noted. Salt composition, of which the density
is measured, is placed in a beaker on a hot place. The densitometer is also placed on the same hot
plate. The temperature is set to a fixed value above the melting point of the salt and is measured
by a thermocouple. After the salt is melted and when the temperature shows stable reading, the
molten salt is poured in to the densitometer up to the set mark on the sensitometer bottle. The
weight of the densitometer with the molten salt is measured. The weight difference between this
weight and the weight of empty densitometer gives the weight of the molten salt at the fixed set
temperature. By knowing the fixed volume in the densitometer, the density of the salt at that
temperature can be calculated. This procedure is repeated at least three times to accurately
determine the density of the salt.
33
CHAPTER 6
RESULT AND DISCUSSION
6.1 Melting point determination
6.1.1 DSC equipment calibration
Before the actual melting point measurement, pure indium, zinc metal and several
individual salts were used to calibrate the DSC equipment. For metals, only one sharp peak was
observed for each and the heat flow curve for indium metal is shown in fig 6.1. However, larger
and boarder peaks are found for salts, just like the condition illustrated in fig 6.2 for pure
potassium nitrate. Based on the results shown in Table 6.1, the experimental data for melting
points and enthalpies of fusion have excellent agreement with the literature values [60-63]. The
variation of point is within 0.7% and the variation of change of enthalpy is less than 3%.
Figure 6.1 Melting point calibration with indium sample
34
Figure 6.2 Melting point calibration with KNO3 sample
Table 6.1 Calibration data of melting points with different samples
Sample
Indium
Zinc
LiNO3
NaNO3
KNO3
Lit.
Tmp
°C
156.6
419.5
256.7
310.0
337.0
Expt.
Tmp
°C
156.3
418.8
255.0
308.1
337.2
Lit.
Ttrans
°C
277.0
133.0
Expt.
Ttrans
°C
275.3
133.2
Lit.
ΔHfusion
J/g
28.6
108.6
361.7
177.7
99.3
Expt.
ΔHfusion
J/g
27.8
106.8
363.3
175.6
100.5
Lit.
ΔHtrans
J/g
14.7
53.8
Expt.
ΔHtrans
J/g
15.2
52.9
6.1.2 Results
Differential scanning calorimetry (DSC) was used to determine the melting point and any
solid state phase transitions of the salt mixture. A low scanning rate was chosen to record the
heat flow curve as function of temperature in order to improve the sensitivity of detection [64]. It
helps to pick up any small endothermic peaks and also avoids the thermal resistance between the
35
internal furnace and sample. Nine systems were chosen to test and the eutectic composition is
already listed in Table 4.1.
All the selected systems are composed of alkaline nitrate and nitrite and most of them have
three basic components which are lithium, sodium, potassium nitrate or nitrite. All the quaternary
and quinary systems were developed on the basis of the LiNO3-NaNO3-KNO3 baseline ternary.
Figure 6.3-6.11 shows the DSC plot of all the salt systems. DSC plots for each system were
collected for at least five runs (each run with fresh salt preparation) to ensure the reproducibility.
All the onset temperatures, peak temperatures, predicted temperatures, enthalpy of fusion for
melting peaks and the solid phase transformation temperatures are given in Table.6.2.
Figure 6.3 DSC endothermic peaks of LiNO3-NaNO3-KNO3 salt.
36
Figure 6.4 DSC endothermic peaks of NaNO3-NaNO2-KNO3 salt.
Figure 6.5 DSC endothermic peaks of LiNO3-NaNO3-KNO3-MgK salt.
37
Figure 6.6 DSC endothermic peaks of LiNO3-NaNO3-KNO3-NaNO2 salt.
Figure 6.7 DSC endothermic peaks of LiNO3-NaNO3-NaNO2-KNO3-KNO2 salt.
38
Figure 6.8 DSC endothermic peaks of LiNO3-NaNO3-KNO3-KNO2 salt.
Figure 6.9 DSC endothermic peaks of LiNO3-KNO3-NaNO2-KNO2 salt.
39
Figure 6.10 DSC endothermic peaks of LiNO3-KNO3-NaNO2-Mg(NO3)2 salt.
Figure 6.11 DSC endothermic peaks of LiNO3-NaNO3-KNO3-Mg(NO3)2-MgKN salt
Table 6.2 illustrates that the predicted melting point is close to the experimental
determined value and most deviation is within 10% except for system #9. The great agreement
40
between experimental and calculated data verifies the accuracy and feasibility of the
thermodynamic modeling.
Table 6.2 DSC results of melting point, transition point and predicted melting point
System
Salt #1
Salt #2
Salt #3
Salt #4
Salt #5
Salt #6
Salt #7
Salt #8
Salt #9
Calculated, °C
116.0
123.8
98.6
98.6
95.7
100.0
108.1
100.8
103.6
Tmp
Onset, °C
99.4
115.0
94.0
94.0
91.0
93.0
99.2
101.0
83.4
Peak, °C
119.1
124.0
99.9
101.0
95.0
96.0
100.3
101.9
89.2
Ttrans
Peak, °C
104.3
NA
NA
NA
NA
NA
79.3
85.3
NA
ΔHfusion
J/g
60.0
9.7
24.4
6.0
6.2
8.6
6.0
5.9
9.3
6.1.3. Discussion
It is observed that the first curve is different from last ones shown in the DSC plots and
this phenomenon is common for all the melting point measurement with DSC technique. This
happened because in the first cycle, the moisture caught by salt mixture, especially the lithium
nitrate, was removed in the process of heating. Moreover, the partially solidified sample in the
sample loading process can be re-homogenized in the first heating cycle [65-67]. In figure 6.3,
6.9 and 6.10, more than one endothermic peak was found. The first smaller endothermic peak
refers to solid state phase transition of the salt mixture. The second larger endothermic peak
refers to the melting of the salt. Normally, the onset temperature of transition is taken as the
experimental transition point for any metallic sample. However, in case of molten salts mixtures,
since the thermal conductivity is low [68-74], the complete transition is ensured only at the peak
41
transition temperature. The thermal gradient which exists due to the low thermal conductivity of
the salt results in internal heat flow which enhances the mixing in the salt. Thus, the transition
temperature is defined as the peak temperature of phase transition. For salt No.1, the small
endothermic peak happened before and was connected to the main peak which occurred at
390.27K. The first endothermic peaks for salt No. 7 and 8 occurred at almost the same
temperature because of the similar composition for these two compounds. Since the small
amount of magnesium nitrate and potassium nitrite contained in these two compounds, the small
endothermic peak can hardly be related to these two components. Obviously, the rest three major
components must have something to do with the first peaks happened before the melting peaks
for both cases. Each component among the major three ones were tested to find out any possible
solid phase transition peaks of them and the results shown in Table. 6.3, which reveals that
lithium nitrate doesn't have any phase transition peak in solid state while potassium nitrate and
sodium nitrite both own the solid phase transformation peaks before their melting peaks.
Table 6.3 Fusion and solid phase transition temperature for individual salts
System
LiNO3
KNO3
NaNO2
Tmp, °C
255.0
337.2
431.1
ΔHfusion, J/g
363.3
100.5
111.9
Ttrans, °C
133.2
41.70
ΔHtrans, J/g
52.9
8.80
The further investigation was carried out by running the KNO3-NaNO2 (55.0 wt% and 23.8 wt %)
binary compound with the very similar weight percentage as that in salt No. 7 (54.6 wt% and
23.7 wt%) and salt No. 8 (55.9wt% and 23.9wt%). By converting the weight percentage of the
studied binary system into 100% scale, the weight fraction for sodium nitrate and potassium
nitrate can be rewritten as 69.8wt% and 30.2wt%. The DSC plot for this binary system was
42
shown in fig 6.12. Although the solid transition and melting temperature were brought down by
adding lithium nitrate, the shape of the plots in fig. 6.9 and 6.10 are identical to that shown in fig.
6.12. The enthalpy of solid state transformation of the binary salt was also converted to that in
both quaternary systems by using the weight fraction occupied by the binary system and the
comparable change of converted enthalpy between the binary system and two quaternary systems
indicates the relevance of the solid transition peaks in salt #7 and #8 to the combined effect of
potassium nitrate and sodium nitrite.
Figure 6.12 DSC plot of 69.8wt% KNO3- 30.2wt% NaNO2 binary system
The similar analysis was applied to No.1 salt to find out the reason for the presence of a
small peak adherent to the main melting peak before the melting point. Sodium nitrate and
potassium nitrate binary system was synthesized based on the weight fraction of these two
constituent salts in No. 1 salt. DSC plot for the sodium nitrate-potassium nitrate binary system in
Fig. 6.13 with the converted composition which is essentially same as that in the No.1 ternary
system shows smooth heat flow curve before the melting peak, which means the solid transition
peak in ternary is not simply relative to the binary system. Assumption was made that the solid
43
phase transformation peak in the ternary salt is resulted from a multiple effect, i.e. the
combination of one of the eutectic binary system involved in the ternary salt mixture and the
other binary system which is composed of the rest components. The statement is verified that the
small peak in salt #1 is mainly caused by the solid phase transformation peak in lithium nitratepotassium nitrate eutectic binary system given the similar shape of the DSC plots in Fig. 6.14.
Since in salt No.1 there is excess amount of sodium nitrate to form the lithium nitrate-sodium
nitrate binary system, the rest sodium nitrate can interact with potassium nitrate and form new
sodium-potassium nitrate system which is shown in fig.6.15. Besides, a solid phase
transformation peak is observed in fig.6.15 which has a very small area and won‟t change the
shape of phase transformation peak in fig.6.14 when these two binary systems are combined and
form salt #1. The enthalpies of solid state transformation in two binary salts were also converted
to that in salt #1 by using the weight fractions occupied by both binary systems. The difference
of the change of converted enthalpies between the lithium-potassium nitrate eutectic binary and
ternary system is filled by the binary mixture which is composed of the rest components: sodium
nitrate-potassium nitrate. The comparable converted values of enthalpy change between salt #1
and its two constituent binary systems further verify the assumption that the solid phase
transformation happened in salt #1 is mainly due to the combined effect of LiNO 3-KNO3 eutectic
binary system and NaNO3-KNO3 binary system.
44
Figure.6.13 DSC plot of 27.0wt% NaNO3-73.0wt% KNO3 binary system
Figure.6.14 DSC plot of 45.8wt%LiNO3-54.2wt%KNO3 binary system
45
Figure.6.15 DSC plot of 46.0wt% NaNO3-54.0wt% KNO3 binary system
Unlike those discussed mixtures above, salt No.2, Salt No.4, Salt No.5 and Salt No.6 have
only one relatively board melting peak and the heat flow curve before and after are very stable.
Similarly, there is no solid transformation peaks observed in salt No.3, salt No.7 and salt No.8.
However, the heat flow after the melting peak in these cases are not stable and the main
endothermic peak is followed by a small hump which is considered to be the recrystallization
process once the compound entered into the liquid state. When the process is finished, the heat
flow curve returns to steady state.
Heating rate is a significant parameter when collect the heat flow curves by using DSC
technique. Fig 6.16(a) and Fig 6.16(b) illustrate the difference of melting point for salt No.6 due
to the change of heating rate. If the heating rate is 20 oC/min, the peak temperature and onset
temperature for the melting peak is 96.69oC and 92.21oC, respectively. Once the heating rate is
decreased to 5oC/min, these two temperatures will also be lowered to 96.14 oC and 91.90oC. The
difference is resulted from the diverse amount of thermal resistance between the testing sample
and the furnace inside the DSC instrument [75]. Under higher heating rate, the decisive thermal
46
resistance is raised due to the low thermal conductivity medium between the furnace and the
actual sample. The insensitivity of gas heat conduction medium in DSC results each unit of
temperature increase on one side cannot have an immediate response on the other side of the gas.
Consequently, the sample holder which is connected the furnace has a higher temperature than
that inside the sample. In this condition, the value of temperature profile collected as the sample
holder temperature is larger than the actual temperature. The deviation will be much smaller
when the heating rate is reduced. In the case, the thermal resistance will be decreased because of
the lower temperature gradient of the gas medium in the heating process. As a result of that, the
collected temperature from the sensor attached to the sample holder will be very close to the
actual temperature inside the testing sample.
Figure 6.16(a) DSC endothermic peaks of LiNO3-NaNO3-KNO3-KNO2 salt for 20oC/min
heating rate.
47
Figure 6.16(b) DSC endothermic peaks of LiNO3-NaNO3-KNO3-KNO2 salt for 5oC/min
heating rate.
Besides the difference of temperature while using higher and lower heat rate, the solution
of DSC will also be affected by different heating rate. Fig. 6.17(a) shows the DSC plot for salt
No. 7 using the heating rate as 5 oC/min and the DSC plot in Fig. 6.17(b) is collected under the
heating rate as 20oC/min. It can be observed that in the lower heating rate, two small separated
peaks can be viewed as two parts of the solid phase transformation process, while in Fig. 6.17(b)
two small peaks before the melting peak merge and present as a board hump. The qualification
of resolution can be executed by the term named resolution factor RMKE which is calculated as
the ratio of the peak heat flow value of the separated peaks to that of the concave point between
two peaks. The equation for determining RMIKE is given in Eq. 27 [76, 77].
RMIKE =hpeak/hmin
48
[27]
Figure 6.17(a). DSC endothermic peaks of LiNO3-KNO3-NaNO2-KNO2 salt for 5oC/min
heating rate.
Figure 6.17(b). DSC endothermic peaks of LiNO3-KNO3-NaNO2-KNO2 salt for 20oC/min
heating rate.
In the case of lower heating rate, the RMKE is determined to be 1.5 and the value for higher
heating rate is not available because the concave point of heat flow doesn‟t exist from
Fig.6.17(b). Since the higher RMKE value indicates better resolution, it can be stated that the
49
lower heating rate also results in greater sensitivity of the equipment to pick up any small
endothermic peaks.
Besides the down-selected 9 compounds, some more salt mixtures were also tested. Most
of them were not selected to the final candidate for the thermal energy storage application
because of their higher melting point. Table 6.4 gives some of the trial systems measured with
DSC technique. It is illustrated that the melting points of mixtures with lower or even no content
of lithium nitrate turn out to be higher than those with sufficient amount of lithium nitrate. For
most of the mixtures with melting point lower than 120oC, the amount of lithium nitrate should
be larger than 8.1wt%. Also, all of the systems in table 6.4 with lithium nitrate less than 1.5wt%
have melting point higher than 140oC. Based on the observation above, it is concluded that the
lithium nitrate can be used as an additive to bring the melting point down for thermal energy
storage systems.
50
Table 6.4 Melting points of candidate systems as function of temperatures
System
Composition (wt%)
Onset
Temp
Peak
Temp
(oC)
(oC)
LiNO3 – NaNO3 – KNO2
10.7
45.9
43.4
89.0
91.0
LiNO3 - KNO3 - NaNO2
LiNO3 - NaNO3 - KNO3 - KNO2
LiNO3 - NaNO3 - NaNO2 - KNO2
LiNO3 - KNO3 - NaNO2 - KNO2
19.6
9.0
8.1
19.3
56.4
42.3
45.4
54.6
24.1
33.7
6.5
23.7
15.1
40.1
2.4
102.4
93.0
90.0
99.2
104.6
96.0
91.0
100.3
LiNO3 - KNO3 - NaNO2 – Mg(NO3)2
LiNO3 - NaNO3 - KNO3 - Mg(NO3)2
- MgK
LiNO3 - NaNO3 - KNO2 – Ca(NO3)2
NaNO3 - KNO3 - NaNO2 - KNO2
NaNO3 - KNO3 - KNO2 – Mg(NO3)2
19.3
55.9
23.8
0.9
101.0
102.0
15.4
17.2
32.4
8.3
83.4
89.2
1.4
42.5
43.2
39.0
16.3
14.6
33.3
7.1
38.0
26.3
34.1
4.2
125.0
140.7
138.6
147.0
144.7
142.1
NaNO3 - NaNO2 - KNO2 - Ca(NO3)2
LiNO3 - NaNO3 - NaNO2 - KNO2 Ca(NO3)2
LiNO3 - NaNO3 - KNO2 - Ca(NO3)2 Mg(NO3)2
45.1
9.2
41.0
4.8
115.0
139.0
1.5
39.3
3.7
32.3
23.2
138.0
148.0
1.4
37.9
31.3
27.5
2.0
133.9
153.4
26.7
6.2 Heat capacity determination
6.2.1 Heat capacity calibration
DSC was also calibrated for the heat capacity measurement. Lithium nitrate, sodium
nitrate and potassium nitrate were examined for the heat capacities from room temperature to
upper limit temperature for the instrument. In liquid state, the heat capacity values for each salt
can be fit to straight line with trace amount of increasing trend. Since the temperature range from
the onset temperature of liquid state to the upper limit of DSC is relatively small, the heat
capacity values for pure individual salts can be viewed as constants. The comparison between the
theoretical and experimental heat capacity data is given in Table 6.5. Except lithium nitrate, the
51
experimental heat capacities data for the rest two systems are almost same as the literature. Even
for lithium nitrate which demonstrates the biggest difference from the literature data, the 2.8%
vibration is still within a reasonable range
Table 6.5 Calibration data of heat capacities with different samples
Sample
LiNO3
NaNO3
KNO3
Lit. Cp
J/g.K
2.18
1.69
1.40
Expt. Cp
J/g.K
2.12
1.67
1.39
6.2.2 Results
The materials used in the heat capacity measurements are the same as those in the melting
point experiments. Molar heat capacities of the all compound were measured by the DSC
equipment from room temperature to 623.15 K. The heat flow is recorded as a function of
temperature in “iso-scan-iso” steps at intervals of 20 K. The „iso stage‟ refers to isothermal
holding at a particular temperature, „scan stage‟ refers to the heat flow recording at a heating rate
of 5 K min1 up to a an increment of 25 K, followed by another isothermal holding stage. This is
a standard procedure followed in the measurement of heat capacity of materials using the DSC
equipment [63, 64]. This procedure of heat capacity measurement has two advantages; (i) any
heat fluctuations during the recording are avoided by the isothermal steps and (ii) any phase
transition can be highlighted by the choice of temperature range. The absolute heat flow to the
sample is determined by subtracting the heat flow collected by running a baseline curve with an
empty pan. Because the heat capacity measurement in the heating process corresponds to
52
collecting the value of required heat flow at each temperature, all the heat capacity plots have the
same shape with that of heat flow in the melting point measurements. Take the heat capacity plot
of LiNO3-NaNO3-KNO3 ternary system as an instance which is shown in fig 6.18, the heat
capacity curve also has two different peaks. The first little peaks corresponds to one occurs at
390.27K which was observed in fig 6.3, the second large and sharp peak happened right after the
small one is prevalent to the endothermic peak with the peak temperature as 390.27 K. Similarly,
after the phase transformation, the heat capacity in liquid state becomes very stable and increase
with temperature linearly with little slope.
Fig 6.18 Heat capacity data plot of LiNO3-NaNO3-KNO3 ternary system as function of
temperature
The heat capacity change as function of temperature for salt No.1 was illustrated in fig
6.19. Based on the trend of heat capacity in the liquid state, any value for the system in the liquid
can be extrapolated. The expressions for heat capacity in liquid state for the new molten salt
systems were discussed and given in the next section.Table.6.6 shows the specific heat capacity
53
of the all the selective compounds measured at 623.15 K and extrapolated at 773.15K. Besides,
the molar heat capacities at 773.15K are given in Table 6.6 of all the salts.
Fig 6.19 Heat capacity of LiNO3-NaNO3-KNO3 in liquid state from 403.15-623.15K
Table 6.6 Heat capacity of selected new TES molten salt mixtures
System
Salt #1
Salt #2
Salt #3
Salt #4
Salt #5
Salt #6
Salt #7
Salt #8
Salt #9
Expt. (623.15K)
Extrapolated(773.15K)
Extrapolated(773.15K)
Cp, J/g.K
Cp, J/g.K
Molar Cp, J/mol.K
1.53
1.43
1.48
1.53
1.53
1.51
1.56
1.55
1.61
1.70
1.68
1.55
1.66
1.70
1.63
1.67
1.68
1.70
152.1
151.5
218.3
141.1
144.0
143.5
144.3
141.0
193.7
54
6.2.3 Thermodynamic properties
The standard thermodynamic properties such as entropy, enthalpy, and Gibbs energy for
salt mixtures are determined from the experimental data of melting point and heat capacity in the
temperature range of the present study and expression for determining these properties are given
in equation 28-30. In thermodynamics, all these three properties are related to heat capacity and
its variances with temperature. In the studied temperature range (298.15K-623.15K), they can be
described as expression includes heat capacity:
[28]
[29]
[30]
Where Tt is the solid transformation temperature, T mp is the melting point, ΔHt is enthalpy of
solid phase transformation and ΔHfusion is enthalpy of fusion. The standard thermodynamic
properties, entropy, enthalpy and Gibbs energies as function of temperature for each compound
are expressed in the following section.
6.2.3.1 LiNO3-NaNO3-KNO3 (Salt #1)
The heat capacity data can be divided into two sections for LiNO3-NaNO3-KNO3
compound; (i) solid state 1 (323.15-384.15) K (ii) liquid state (403.15-623.15) K. Accordingly,
55
the heat capacity data are fit to two separate polynomial equations corresponding to the three
phases of the compound.
6.2.3.1.1 Heat capacity of solid state 1: (298.15-384.15) K
The heat capacity data for LiNO3-NaNO3-KNO3 compound in the solid state 1 in the
temperature range of 298.15 to 384.15 K is fit to a second order polynomial equation. Eqn. (31)
gives the polynomial equation along with the least square fit parameter (R 2) in the temperature
range for the solid state 1 of the compound.
[31]
(
)K
R2 = 0.982
6.2.3.1.2 Heat capacity of liquid state: (403.15-623.15) K
The heat capacity data for LiNO3-NaNO3-KNO3 compound in the liquid state in the
temperature range of 403.15 to 623.15 K is fit to a linear equation. Eqn. (32) gives the linear
equation along with the least square fit parameter (R 2) in the temperature range for the liquid
state of the compound.
J/K.mol
56
[32]
R2 = 0.947
Heat capacity data of the LiNO3-NaNO3-KNO3 compound in the solid state follows a
second order polynomial curve whereas the heat capacity is linear in the liquid state.
6.2.3.1.3 Thermodynamic properties of solid state 1(298.15-384.15) K:
J/K.mol
J/mol
[33]
[34]
[35]
J/mol
6.2.3.1.4 Thermodynamic properties of liquid state 2(403.15-623.15) K:
[36]
57
J/K·mol
J/mol
[37]
[38]
J/mol
Among the equations above, equation (33)-(35) refer to the thermodynamic properties for
solid state; equations (36)-(38) refer to thermodynamic properties of the liquid. The entropy,
enthalpy and Gibbs energy values in the studied temperature ranges for solid and liquid state are
given in Table A.1 and A.2 in appendix A, respectively, with the corresponding heat capacity as
function of temperature.
6.2.3.2 NaNO3-NaNO2-KNO3 (Salt #2)
The heat capacity data can be divided into two sections for NaNO3-NaNO2-KNO3
compound; (i) solid state 1 (323.15-392.15) K (ii) liquid state (413.15-623.15) K. Accordingly,
the heat capacity data are fit to two separate polynomial equations corresponding to the three
phases of the compound.
6.2.3.2.1 Heat capacity of solid state 1: (298.15-392.15) K
58
The heat capacity data for NaNO3-NaNO2-KNO3 compound in the solid state in the
temperature range of 298.15 to 392.15 K is fit to a second order polynomial equation. Eqn. (39)
gives the polynomial equation along with the least square fit parameter (R 2) in the temperature
range for the solid state 1 of the compound.
·
(
[39]
)K
R2 = 0.978
6.2.3.2.2 Heat capacity of liquid state: (403.15-623.15) K
The heat capacity data for NaNO3-NaNO2-KNO3 compound in the liquid state in the
temperature range of 403.15 to 623.15 K is fit to a second order polynomial equation. Eqn. (40)
gives the linear equation along with the least square fit parameter (R 2) in the temperature range
for the liquid state of the compound.
·
R2 = 0.941
59
[40]
Heat capacity data of the NaNO3-NaNO2-KNO3 compound in the solid state follows a
second order polynomial curve whereas the heat capacity is linear in the liquid state.
6.2.3.2.3
Thermodynamic properties of solid state 1(298.15-392.15) K:
J/K.mol
[41]
J/mol
[42]
[43]
J/mol
6.2.3.2.4
Thermodynamic properties of liquid state 2(403.15-623.15) K:
J/K·mol
60
[44]
J/mol
[45]
[46]
J/mol
Among the equations above, equation (41)-(43) refer to the thermodynamic properties for
solid state; equations (44)-(46) refer to thermodynamic properties of the liquid. The entropy,
enthalpy and Gibbs energy values in the studied temperature range for solid and liquid state are
given in Table B.1 and B.2 in appendix B, respectively, with the corresponding heat capacity as
function of temperature.
6.2.3.3 LiNO3-NaNO3 -KNO3-MgK (Salt #3)
The heat capacity data can be divided into two sections for LiNO3-NaNO3 -KNO3-MgK
compound; (i) solid state 1 (298.15-364.15) K (ii) liquid state (421.15-623.15) K. Accordingly,
the heat capacity data are fit to two separate polynomial equations corresponding to the three
phases of the compound.
6.2.3.3.1
Heat capacity of solid state 1: (298.15-364.15) K
61
The heat capacity data for LiNO3-NaNO3 -KNO3-MgK compound in the solid state in the
temperature range of 298.15 to 364.15 K is fit to a second order polynomial equation. Eqn. (47)
gives the polynomial equation along with the least square fit parameter (R 2) in the temperature
range for the solid state 1 of the compound.
·
(
[47]
)K
R2 = 0.995
6.2.3.3.2
Heat capacity of liquid state: (421.15-623.15) K
The heat capacity data for LiNO3-NaNO3 -KNO3-MgK compound in the liquid state in the
temperature range of 421.15 to 623.15 K is fit to a second order polynomial equation. Eqn. (48)
gives the linear equation along with the least square fit parameter (R 2) in the temperature range
for the liquid state of the compound.
·
R2 = 0.963
62
[48]
Heat capacity data of the LiNO3-NaNO3 -KNO3-MgK compound in the solid state follows
a second order polynomial curve whereas the heat capacity is linear in the liquid state.
6.2.3.3.3
Thermodynamic properties of solid state 1(298.15-364.15) K:
J/K.mol
[49]
J/mol
[50]
[51]
J/mol
6.2.3.3.4
Thermodynamic properties of liquid state 2(421.15-623.15) K:
63
J/K·mol
[52]
J/mol
[53]
[54]
J/mol
Among the equations above, equation (49)-(51) refer to the thermodynamic properties for
solid state; equations (52)-(54) refer to thermodynamic properties of the liquid. The entropy,
enthalpy and Gibbs energy values in the studied temperature range for solid and liquid state are
given in Table C.1and C.2 in appendix C, respectively, with the corresponding heat capacity as
function of temperature.
6.2.3.4 LiNO3-NaNO3-KNO3-NaNO2 (Salt #4)
The heat capacity data can be divided into two sections for LiNO3-NaNO3-KNO3-NaNO2
compound; (i) solid state 1 (298.15-363.15) K (ii) liquid state (381.15-623.15) K. Accordingly,
the heat capacity data are fit to two separate polynomial equations corresponding to the three
phases of the compound.
6.2.3.4.1
Heat capacity of solid state 1: (298.15-363.15) K
64
The heat capacity data for LiNO3-NaNO3-KNO3-NaNO2 compound in the solid state in the
temperature range of 298.15 to 363.15 K is fit to a second order polynomial equation. Eqn. (55)
gives the polynomial equation along with the least square fit parameter (R2) in the temperature
range for the solid state 1 of the compound.
·
(
[55]
)K
R2 = 0.995
6.2.3.4.2 Heat capacity of liquid state: (381.15-623.15) K
The heat capacity data for LiNO3-NaNO3-KNO3-NaNO2 compound in the liquid state in the
temperature range of 381.15 to 623.15 K is fit to a second order polynomial equation. Eqn. (56)
gives the linear equation along with the least square fit parameter (R 2) in the temperature range
for the liquid state of the compound.
·
[56]
R2 = 0.972
Heat capacity data of the LiNO3-NaNO3 -KNO3-MgK compound in the solid state follows
a second order polynomial curve whereas the heat capacity is linear in the liquid state.
65
6.2.3.4.3
Thermodynamic properties of solid state 1(298.15-363.15) K:
J/K.mol
[57]
J/mol
[58]
[59]
J/mol
6.2.3.4.4
Thermodynamic properties of liquid state 2(381.15-623.15) K:
J/K·mol
J/mol
66
[60]
[61]
J/mol
[62]
Among the equations above, equation (57)-(59) refer to the thermodynamic properties for
solid state; equations (60)-(62) refer to thermodynamic properties of the liquid. The entropy,
enthalpy and Gibbs energy values in the studied temperature range for solid and liquid state are
given in Table D.1 and D.2 in appendix D, respectively, with the corresponding heat capacity as
function of temperature.
6.2.3.5 LiNO3-NaNO3-NaNO2-KNO3-KNO2 (Salt #5)
The heat capacity data can be divided into two sections for LiNO3-NaNO3-NaNO2-KNO3KNO2 compound; (i) solid state 1 (298.15-359.15) K (ii) liquid state (375.15-623.15) K.
Accordingly, the heat capacity data are fit to two separate polynomial equations corresponding to
the three phases of the compound.
6.2.3.5.1 Heat capacity of solid state 1: (298.15-359.15) K
The heat capacity data for LiNO3-NaNO3-NaNO2-KNO3-KNO2 compound in the solid state
in the temperature range of 298.15 to 359.15 K is fit to a second order polynomial equation. Eqn.
(63) gives the polynomial equation along with the least square fit parameter (R 2) in the
temperature range for the solid state 1 of the compound.
67
·
(
[63]
)K
R2 = 0.996
6.2.3.5.2
Heat capacity of liquid state: (375.15-623.15) K
The heat capacity data for LiNO3-NaNO3-NaNO2-KNO3-KNO2 compound in the liquid
state in the temperature range of 375.15 to 623.15 K is fit to a second order polynomial equation.
Eqn. (64) gives the linear equation along with the least square fit parameter (R 2) in the
temperature range for the liquid state of the compound.
·
[64]
R2 = 0.969
Heat capacity data of the LiNO3-NaNO3-NaNO2-KNO3-KNO2 compound in the solid state
follows a second order polynomial curve whereas the heat capacity is linear in the liquid state.
6.2.3.5.3
Thermodynamic properties of Solid state 1(298.15-359.15) K:
J/K.mol
68
[65]
J/mol
[66]
[67]
J/mol
6.2.3.5.4
Thermodynamic properties of liquid state 2(375.15-623.15) K:
J/K·mol
[68]
J/mol
[69]
J/mol
69
[70]
Among the equations above, equation (65)-(67) refer to the thermodynamic properties for
solid state; equations (68)-(70) refer to thermodynamic properties of the liquid. The entropy,
enthalpy and Gibbs energy values in the studied temperature range for solid and liquid state are
given in Table E.1 and E.2 in appendix E, respectively, with the corresponding heat capacity as
function of temperature.
6.2.3.6 LiNO3-NaNO3-KNO3-KNO2 (Salt #6)
The heat capacity data can be divided into two sections for LiNO3-NaNO3-KNO3-KNO2
compound; (i) solid state 1 (298.15-359.15) K (ii) liquid state (375.15-623.15) K. Accordingly,
the heat capacity data are fit to two separate polynomial equations corresponding to the three
phases of the compound.
6.2.3.6.1
Heat capacity of solid state 1: (298.15-365.15) K
The heat capacity data for LiNO3-NaNO3-KNO3-KNO2 compound in the solid state in the
temperature range of 298.15 to 365.15 K is fit to a second order polynomial equation. Eqn. (71)
gives the polynomial equation along with the least square fit parameter (R2) in the temperature
range for the solid state 1 of the compound.
·
(
)K
R2 = 0.998
70
[71]
6.2.3.6.2
Heat capacity of liquid state: (375.15-623.15) K
The heat capacity data for LiNO3-NaNO3-KNO3-KNO2 compound in the liquid state in the
temperature range of 375.15 to 623.15 K is given in Table 20. The data is fit to a second order
polynomial equation. Eqn. (72) gives the linear equation along with the least square fit parameter
(R2) in the temperature range for the liquid state of the compound.
·
[72]
R2 = 0.953
Heat capacity data of the LiNO3-NaNO3-KNO3-KNO2 compound in the solid state follows a
second order polynomial curve whereas the heat capacity is linear in the liquid state.
6.2.3.6.3
Thermodynamic properties of solid state 1(298.15-359.15) K:
71
J/K.mol
[73]
J/mol
[74]
[75]
J/mol
6.2.3.6.4
Thermodynamic properties of liquid state 2(375.15-623.15) K:
J/K·mol
[76]
J/mol
[77]
J/mol
[78]
Among the equations above, equation (73)-(75) refer to the thermodynamic properties for
solid state; equations (76)-(78) refer to thermodynamic properties of the liquid. The entropy,
enthalpy and Gibbs energy values in the studied temperature range for solid and liquid state are
72
given in Table F.1 and F.2 in appendix F, respectively, with the corresponding heat capacity as
function of temperature.
6.2.3.7 LiNO3-KNO3-NaNO2-KNO2 (Salt #7)
The heat capacity data can be divided into three sections; (i) solid state 1 (298.15-354.15)
K (ii) solid state 2 (362.15-373.15) K (iii) liquid state (379.15-623.15) K. Accordingly, the heat
capacity data are fit to three separate polynomial equations corresponding to the three phases of
the compound.
6.2.3.7.1
Heat capacity of solid state 1: (298.15-354.15) K
The heat capacity data for LiNO3-KNO3-NaNO2-KNO2 compound in the solid state 1 in
the temperature range of 298.15 to 354.15 K is fit to a second order polynomial equation. Eqn.
(79) gives the polynomial equation along with the least square fit parameter (R 2) in the
temperature range for the solid state 1 of the compound.
·
[79]
(298.15-354.15) K
R2 = 0.993
6.2.3.7.2
Heat capacity of solid state 2: (362.15-373.15) K
The heat capacity data for LiNO3-KNO3-NaNO2-KNO2 compound in the solid state 2 in
the temperature range of 362.15 to 373.15 K is fit to a second order polynomial equation. Eqn.
73
(80) gives the polynomial equation along with the least square fit parameter (R 2) in the
temperature range for the solid state 2 of the compound.
·
[80]
R2 = 0.977
6.2.3.7.3
Heat capacity of liquid state: (379.15-623.15) K
The heat capacity data for LiNO3-KNO3-NaNO2-KNO2 compound in the liquid state in the
temperature range of 379.15 to 623.15 K is fit to a linear equation. Eqn. (81) gives the
polynomial equation along with the least square fit parameter (R 2) in the temperature range for
the liquid state of the compound.
·
[81]
R2 = 0.961
Heat capacity data of the LiNO3-KNO3-NaNO2-KNO2 compound in the two solid states
follows a second order polynomial curve whereas the heat capacity is linear in the liquid state.
6.2.3.7.4
Thermodynamic properties of solid state 1(298.15-354.15) K:
74
J/K.mol
J/mol
[82]
[83]
[84]
J/mol
6.2.3.7.5
Thermodynamic properties of solid state 2(362.15-373.15) K:
J/K·mol
[85]
J/mol [86]
75
[87]
J/mol
6.2.3.7.6
Thermodynamic properties of liquid state (379.15-623.15) K:
J/K.mol
[88]
J/mol
[89]
J/mol
[90]
Among the equations above, equation (82)-(84) refer to the thermodynamic properties for
solid 1; equation (85)-(87) refer to the thermodynamic properties for solid 2; equations (88)-(90)
refer to thermodynamic properties of the liquid. The entropy, enthalpy and Gibbs energy values
76
in the studied temperature range for solid 1, solid 2 and liquid state are given in Table G.1-G.3 in
appendix G, respectively, with the corresponding heat capacity as function of temperature.
6.2.3.8 LiNO3-KNO3-NaNO2-Mg(NO3)2 (salt #8)
The heat capacity data can be divided into three sections; (i) solid state 1 (298.15-354.15)
K (ii) solid state 2 (362.15-373.15) K (iii) liquid state (379.15-623.15) K. Accordingly, the heat
capacity data are fit to three separate polynomial equations corresponding to the three phases of
the compound.
6.2.3.8.1
Heat capacity of solid state 1: (298.15-337.15) K
The heat capacity data for LiNO3-KNO3-NaNO2-Mg(NO3)2 compound in the solid
state 1 in the temperature range of 298.15 to 337.15 K is fit to a second order polynomial
equation. Eqn. (91) gives the polynomial equation along with the least square fit parameter (R 2)
in the temperature range for the solid state 1 of the compound.
[91]
(298.15-337.15) K
R2 = 0.994
6.2.3.8.2
Heat capacity of solid state 2: (361.15-364.15) K
The heat capacity data for LiNO3-KNO3-NaNO2-Mg(NO3)2 compound in the solid state 2
in the temperature range of 361.15 to 364.15 K is given in Table 4. The data is fit to a second
77
order polynomial equation. Eqn. (92) gives the polynomial equation along with the least square
fit parameter (R2) in the temperature range for the solid state 2 of the compound.
[92]
R2 = 0.992
6.2.3.8.3
Heat capacity of liquid state: (411.15-623.15) K
The heat capacity data for LiNO3-KNO3-NaNO2-Mg(NO3)2 compound in the liquid state in
the temperature range of 411.15 to 623.15 K is given in Table 5. The data is fit to a linear
equation. Eqn. (93) gives the polynomial equation along with the least square fit parameter (R 2)
in the temperature range for the liquid state of the compound.
[93]
R2 = 0.934
Heat capacity data of the LiNO3-KNO3-NaNO2-Mg(NO3)2 compound in the two solid
states follows a second order polynomial curve whereas the heat capacity is linear in the liquid
state.
6.2.3.8.4
Solid state 1(298.15-354.15) K:
78
J/K.mol
[94]
J/mol [95]
[96]
J/mol
6.2.3.8.5
Solid state 2(361.15-364.15) K:
J/K.mol
79
[97]
J/mol [98]
[99]
J/mol
6.2.3.8.6
Liquid state (411.15-623.15) K:
J/K.mol
[100]
J/mol
[101]
J/mol
[102]
Among the equations above, equation (94)-(96) refer to the thermodynamic properties for
solid 1; equation (97)-(99) refer to the thermodynamic properties for solid 2; equations (100)(102) refer to thermodynamic properties of the liquid. The entropy, enthalpy and Gibbs energy
80
values in the studied temperature range for solid 1, solid 2 and liquid state are given in Table H.1
and H.2 in appendix H, respectively, with the corresponding heat capacity as function of
temperature.
6.2.3.9 LiNO3-NaNO3-KNO3-Mg(NO3)2-MgK(Salt #9)
The heat capacity data can be divided into two sections for LiNO3-NaNO3-KNO3Mg(NO3)2-MgK compound; (i) solid state 1 (298.15-353.15) K (ii) liquid state (391.15-623.15) K.
Accordingly, the heat capacity data are fit to two separate polynomial equations corresponding to
the three phases of the compound.
6.2.3.9.1
Heat capacity of solid state 1: (298.15-353.15) K
The heat capacity data for LiNO3-NaNO3-KNO3-Mg(NO3)2-MgK compound in the solid
state in the temperature range of 298.15 to 353.15 K is fit to a second order polynomial equation.
Eqn. (103) gives the polynomial equation along with the least square fit parameter (R2) in the
temperature range for the solid state 1 of the compound.
[103]
(
)K
R2 = 0.996
6.2.3.9.2
Heat capacity of liquid state: (391.15-623.15) K
81
The heat capacity data for LiNO3-NaNO3-KNO3-Mg(NO3)2-MgK compound in the liquid
state in the temperature range of 391.15 to 623.15 K is fit to a second order polynomial equation.
Eqn. (104) gives the linear equation along with the least square fit parameter (R 2) in the
temperature range for the liquid state of the compound.
[104]
R2 = 0.951
Heat capacity data of the LiNO3-NaNO3-KNO3-Mg(NO3)2-MgK compound in the solid
state follows a second order polynomial curve whereas the heat capacity is linear in the liquid
state.
6.2.3.9.3
Solid state 1(298.15-353.15) K:
82
J/K.mol
[105]
J/mol
[106]
[107]
J/mol
6.2.3.9.4
Liquid state 2(391.15-623.15) K:
J/K·mol
[108]
J/mol
[109]
[110]
J/mol
Among the equations above, equation (105)-(107) refer to the thermodynamic properties
for solid state; equations (108)-(110) refer to thermodynamic properties of the liquid. The
entropy, enthalpy and Gibbs energy values in the studied temperature range for solid and liquid
state are given in Table I.1 and I.2 in appendix I, respectively, with the corresponding heat
capacity as function of temperature.
83
6.2.4
Discussion of Gibbs energy change for molten salts
The Gibbs energy change data as function of temperature for 9 systems are given in fig
6.20 and the values at 623.15K are shown in Table 6.7. Every system demonstrates continuous
curve throughout the whole studied temperature range. Most of systems have similar Gibbs
energy change values for each temperature spot due to the comparable compositions and
properties of constituent salts. However, salt #3 and salt #9. Both of these salts have certain
amount of MgKN compound which presents large absolute amount of change of Gibbs energy in
the same studied temperature range [66]. Since the change of Gibbs energy for multi-component
mixture is relevant to that of each constituent salt, the large absolute value of ΔG of MgKN
mainly contributes to the largely negative value of salt #3 and salt #9 shown in fig. 6.20. Besides,
it is observed that most systems contain nitrite salts present lower absolute value of Gibbs energy
change. For example, salt #1 doesn‟t include any nitrite salt and has a relatively high absolute
value of Gibbs energy change as 17.04kJ/mol while other systems having nitrite salts show lower
value varies from 13.72kJ/mol to 15.92kJ/mol.
84
Fig 6.20 Change of Gibbs energy as function of temperature for molten salt systems
Table 6.7 Change of Gibbs energy values at 623.15K for molten salt systems
S.No.
System
ΔG/(kJ/mol)
1
LiNO3-NaNO3-KNO3
17.04
2
NaNO3- NaNO2- KNO3
13.72
3
LiNO3- NaNO3- KNO3- MgKN
28.07
4
LiNO3- NaNO3- KNO3- NaNO2
14.43
5
LiNO3- NaNO3- NaNO2-KNO3- KNO2
14.41
6
LiNO3-NaNO3-KNO3-KNO2
15.70
7
LiNO3-KNO3-NaNO2-KNO2
15.92
8
LiNO3-KNO3-NaNO2-Mg(NO3)2
15.83
9
LiNO3-NaNO3-KNO3-Mg(NO3)2 -MgKN
22.17
85
6.3 Density determination
6.3.1 Density calibration
Several pure molten salts are used to calibrate the density measurement set-up before the
actual density measurement. All the density values decrease as function of temperature in the
liquid state and follow the same linear equations as described in eq. 4. The experimental values
at 350oC for KNO3, NaNO3 and LiNO3 are selected to compare with the literature data at the
same temperature. The results are shown in Table 6.8. Based on the comparison of the literature
data and the experimental data, the variation of density for molten nitrate salt is within in 4%.
Table 6.8 Calibration of density measurements with different pure nitrate salts
Sample
LiNO3
NaNO3
KNO3
6.3.2 Results and discussions
Literature density
g/cm3
1.727
2.066
1.860
Experimental density
g/cm3
1.701
2.144
1.855
The density result of the salt as function of temperature is plotted for all the salts in Figure
6.21 and Figure 6.22. It is observed that the temperature dependence of density above the
melting point is different from that in solid state. As known, in solid state, the density of salt has
an exponential relation with temperature, while in these liquid cases the density values have
linearly dependence with temperature. The stable variation as function of temperature allows the
extrapolation of density at even higher temperature. The regression analysis is performed to get
the coefficient used for describing eq. 4 and the results for the coefficients are shown in
86
Table.6.9 [78-80]. It is observed that the change of composition is implied on the coefficient A
which indicates the initial point at 150oC. The temperature dependence coefficient B doesn‟t
change much with composition, which may be mainly affected by the group of anion and cation.
Table 6.9 Coefficient A and B for density determination of salt #1-salt # 9
Salt No.
1
2
3
4
5
6
7
8
9
System
LiNO3-NaNO3-KNO3
NaNO3- NaNO2- KNO3
LiNO3- NaNO3- KNO3-MgKN
LiNO3- NaNO3- KNO3- NaNO2
LiNO3- NaNO3- NaNO2-KNO3- KNO2
LiNO3-NaNO3-KNO3-KNO2
LiNO3-KNO3-NaNO2-KNO2
LiNO3-KNO3-NaNO2-Mg(NO3)2
LiNO3-NaNO3-KNO3-Mg(NO3)2-MgK
A
(g/cm3)
B×103
(g/cm3·°C)
2.032
2.081
2.055
2.033
2.018
2.060
2.048
2.044
2.060
0.493
0.570
0.526
0.520
0.485
0.554
0.554
0.524
0.566
Figure 6.21 The densities of the salt #1-salt #5 as function of temperature
87
In figure 6.21, all the density values are clustered around 1.98g/cm 3 at 150oC to
1.86g/cm3 at high temperature end and the deviation of density between all the mixtures is within
in 0.047g/ cm3. Among all the salt mixtures, the NaNO3-NaNO2-KNO3 ternary system
demonstrates the highest density value throughout the studied temperature range and LiNO3NaNO3-KNO3 ternary system, LiNO3- NaNO3-KNO3-NaNO2 quaternary system and LiNO3NaNO3-KNO3-NaNO2-KNO2 quinary system show densities at the bottom side of Fig 6.21. For
salt #2, which doesn‟t contain any lithium nitrate, the density at every selected temperature spot
is obviously higher than that of salt #1, #4 and #5 which have large amount of lithium nitrate.
Moreover, the salt #3 which contains the relatively small amount of lithium nitrate stays in
between of salt #1 and salt #2. This comparison illustrates that the addition of lithium nitrate has
an offsetting effect on density for molten salt and it is consistent with previous literature reports
[81]. The four systems presented in figure 6.22 also show even closer density values in the
studied temperature range. Similarly, salt #6 which contains the least lithium nitrate has the
largest density. Salt #7 and salt #8 have almost same composition for the three dominating
components, as a result of that, the density curves for both mixtures are determined by the same
regression coefficient A and B. Moreover, the larger amount of lithium nitrate involved in these
two salt mixtures contributes to the lower density given in figure.6.22, which further verifies the
significantly offsetting effect of lithium nitrate on density.
88
Figure 6.22 The densities of the salt #6-salt #9 as function of temperature
The salt mixtures with maximum and minimum amount of lithium nitrate were plotted and
compared with equimolar NaNO3-KNO3 binary system and pure KNO3 salt in Fig.6.23 [82, 83].
It is observed that the NaNO3-KNO3 binary system has very similar density value to that of salt
#2 because of the analogous type and composition of component in both salts. The density of
pure KNO3 is slightly lower than the binary salt mixture which indicates the density of NaNO3 is
close to but higher than KNO3 in the studied temperature range. Salt #1 shows the lowest density
in Fig.6.23 due to the offsetting effect on density caused by lithium nitrate which has been
discussed above.
89
Figure 6.23 Density of the salt #1, salt #2 as function of temperature compared to the
equimolar NaNO3-KNO3 binary system and pure KNO3.
6.4
Thermal energy storage density of molten salts
The energy density which is considered as one of the most significant parameters of TES
application can be evaluated by calculation based on the measured density, heat capacity and
working temperature range. The equation of the thermal energy storage density (E) at working
temperature of 500oC is expressed in equation. 111:
E = Cp·· (500-Tm)
[111]
Where Cp and  are extrapolated heat capacity and density at 500oC, respectively, Tm is
melting point for salt mixture. The extrapolation of density and heat capacity is based on the
linear temperature dependence for both parameters in molten state and the values are shown in
Table 6.10.
90
Table 6.10 Extrapolated value of density and heat capacity at 500 oC of salt #1-salt #9
Salt
No.
System
Density
(g/mL)
Heat Capacity
(J/g.K)
1
LiNO3-NaNO3-KNO3
1.785
1.70
2
NaNO3- NaNO2- KNO3
1.796
1.68
3
LiNO3-NaNO3-KNO3-MgK
1.773
1.55
4
LiNO3- NaNO3- KNO3- NaNO2
1.792
1.66
5
LiNO3- NaNO3- NaNO2-KNO3- KNO2
1.796
1.70
6
LiNO3-NaNO3-KNO3-KNO2
1.783
1.63
7
LiNO3-KNO3-NaNO2-KNO2
1.771
1.67
8
LiNO3-KNO3-NaNO2-Mg(NO3)2
1.782
1.68
9
LiNO3-NaNO3-KNO3-Mg(NO3)2-MgK
1.777
1.70
The calculated energy density for each salt is given in Table 6.11 compared with that of
solar salt (NaNO3-KNO3). All the new synthesized salt mixtures have significantly higher energy
density than solar salt and salt #3 shows the highest energy density among the new salts.
Although salt #1 has higher heat capacity and good melting point, the energy density is still the
lowest among new salt mixtures given by the effect of low density. The conclusion can be drawn
from these observations that the energy density is a property affected by multiple parameters and
every part plays an important role in determining the efficiency of energy storage of salt
mixtures.
91
Table 6.11 Energy density of salt #1-salt #9 compare to solar salt
Salt No.
Energy Density
500°C (MJ/m3)
756
System
0
1
NaNO3- KNO3
LiNO3-NaNO3-KNO3
2
1135
3
NaNO3- NaNO2- KNO3
LiNO3-NaNO3-KNO3-MgKN
4
LiNO3- NaNO3- KNO3- NaNO2
1189
5
LiNO3- NaNO3- NaNO2-KNO3- KNO2
1232
6
LiNO3-NaNO3-KNO3-KNO2
1174
7
LiNO3-KNO3-NaNO2-KNO2
1183
8
LiNO3-KNO3-NaNO2-Mg(NO3)2
1192
9
LiNO3-NaNO3-KNO3-Mg(NO3)2-MgKN
1242
1162
1099
The gravimetric storage density of new molten salts are listed in Table 6.12 and compared
with those different storage systems in fig 6.24. It is found that in the parabolic trough working
temperature range, the gravimetric storage densities of new molten salts are located on the higher
side. Even though some reported sensible energy storage liquids have larger gravimetric density
values than the new salts, the maximum working temperatures reveal the instable working
condition at 500oC. Taking conversion efficiency, thermal stability and gravimetric storage
density into considerations, the new molten salts are the most suitable choices of the sensible
heat storage for parabolic trough application.
92
Fig 6.24 Gravimetric storage density comparison of different energy storage systems as
function of temperature
Table 6.12 Gravimetric storage densities for solar salt and new molten salts
Salt
No.
0
1
2
3
4
5
6
7
8
9
Gravimetric Storage Density
System
500°C (kJ/kg)
NaNO3- KNO3
LiNO3-NaNO3-KNO3
NaNO3- NaNO2- KNO3
LiNO3-NaNO3-KNO3-MgKN
LiNO3- NaNO3- KNO3- NaNO2
LiNO3- NaNO3- NaNO2-KNO3- KNO2
LiNO3-NaNO3-KNO3-KNO2
LiNO3-KNO3-NaNO2-KNO2
LiNO3-KNO3-NaNO2-Mg(NO3)2
LiNO3-NaNO3-KNO3-Mg(NO3)2-MgKN
93
404
560
533
575
612
595
594
604
610
649
CHAPTER 7
CONCLUSION
The melting points of new molten salts were experimentally determined using DSC.
Different from metals, the melting point was chosen as the peak temperature rather than onset
temperature of the endothermic peak due to the low thermal conductivity and broad phase
transition range of the molten nitride salt mixture. All of the nine new molten salts have melting
points from 89oC to 124oC which are much lower than current sodium-potassium binary solar
salt. Some systems such as salt No.1, No.7 and No.8 have solid phase transformation observed
from the DSC plots. It is found that the phase transformations of salt No. 7 and No. 8 are mainly
contributed to the KNO3-NaNO2 binary system, while the small solid transformation peak of salt
No.1 is resulted from the combined effect of the KNO3-LiNO3 eutectic binary system involved in
the ternary salt and another binary system which is composed of the rest components. The
heating rate of DSC was revealed as a significant parameter for the any endothermic peak
determination. When using lower heating rate, the thermal resistance between the studied sample
and the furnace will be minimal and the resolution of peak detection will be enhanced.
The heat capacities of all the multi-component salts (#1 to #9) were determined using DSC
and found varying from 1.43 to 1.61 J/g.K at 350oC. The heat capacity in the liquid state
demonstrates linear increase trend as function of temperature. On the basis of that, the heat
capacity was extrapolated to parabolic trough operating temperature of 500oC. Besides, heat
capacity data as function of temperature are fit to polynomial equation and thermodynamic
94
properties like enthalpy, entropy and Gibbs energies of the compound as function of temperature
are subsequently deduced.
Experimental measurements of density of multi-component systems were conducted as
function of temperature in their liquid state. In liquid state, the density values decrease linearly
as temperature increases. The results of those mixtures were compared to the solar salt and
individual constituent salts. The comparison demonstrates that the addition of lithium nitrate
lowers the density, which is consistent with the observation that lithium nitrate has the lowest
density among all the individual salts in the studied temperature range. On the basis of densities,
heat capacities and the melting points, energy storage density for all the new salts were
calculated and compared to the binary solar salt. Among all the new molten salt systems,
LiNO3-NaNO3-KNO3-Mg(NO3)2-MgKN quinary system (salt #9) presents the largest thermal
energy storage density as well as the gravimetric density values. Moreover, the larger thermal
energy storage as well as gravimetric storage densities compared to the solar salt indicate the
better energy storage capacities of new salts for solar power generation systems.
95
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103
APPENDIX
Appendix A
Table A.1 Thermodynamic properties of LiNO3-KNO3-NaNO3 compound in solid state
(298.15-403.15K)
T/(K)
298.15
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
ΔS
(J/mol.K)
0.00
0.27
0.59
0.91
1.23
1.54
1.86
2.17
2.48
2.79
3.10
3.40
3.71
4.01
4.32
4.62
4.92
5.21
5.51
5.81
6.10
6.40
6.69
ΔH
(kJ/mol)
0.00
0.08
0.18
0.28
0.37
0.47
0.56
0.66
0.76
0.85
0.95
1.04
1.14
1.23
1.33
1.42
1.52
1.61
1.71
1.80
1.90
1.99
2.09
ΔG
(kJ/mol)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.01
-0.01
-0.01
-0.01
-0.02
-0.02
-0.02
-0.03
-0.03
-0.04
-0.04
-0.05
-0.05
T/(K)
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
104
ΔS
(J/mol.K)
12.90
13.17
13.45
13.72
13.99
14.27
14.54
14.81
15.08
15.35
15.62
15.89
16.16
16.43
16.70
16.97
17.24
17.51
17.77
18.04
18.31
18.58
18.85
ΔH
(kJ/mol)
4.17
4.26
4.36
4.45
4.55
4.64
4.74
4.83
4.93
5.03
5.12
5.22
5.32
5.41
5.51
5.61
5.70
5.80
5.90
6.00
6.10
6.19
6.29
ΔG
(kJ/mol)
-0.25
-0.26
-0.27
-0.28
-0.29
-0.31
-0.32
-0.33
-0.35
-0.36
-0.38
-0.39
-0.41
-0.42
-0.44
-0.45
-0.47
-0.48
-0.50
-0.52
-0.53
-0.55
-0.57
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
6.98
7.27
7.56
7.85
8.14
8.42
8.71
8.99
9.28
9.56
9.84
10.12
10.41
10.69
10.96
11.24
11.52
11.80
12.07
12.35
12.63
2.18
2.28
2.37
2.46
2.56
2.65
2.75
2.84
2.94
3.03
3.13
3.22
3.31
3.41
3.50
3.60
3.69
3.79
3.88
3.98
4.07
-0.06
-0.07
-0.07
-0.08
-0.09
-0.09
-0.10
-0.11
-0.12
-0.12
-0.13
-0.14
-0.15
-0.16
-0.17
-0.18
-0.19
-0.20
-0.21
-0.22
-0.23
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
384.15
19.11
19.38
19.65
19.92
20.18
20.45
20.72
20.98
21.25
21.52
21.79
22.05
22.32
22.59
22.86
23.12
23.39
23.66
23.93
24.20
24.24
6.39
6.49
6.59
6.69
6.79
6.89
6.99
7.09
7.19
7.29
7.39
7.50
7.60
7.70
7.80
7.91
8.01
8.11
8.22
8.32
8.34
-0.59
-0.60
-0.62
-0.64
-0.66
-0.68
-0.70
-0.72
-0.74
-0.76
-0.78
-0.80
-0.82
-0.84
-0.86
-0.88
-0.90
-0.93
-0.95
-0.97
-0.97
Table A.2 Thermodynamic properties of LiNO3-KNO3-NaNO3 compound in liquid state
(403.15-623.15K)
T/(K)
403.15
404
405
406
407
408
409
410
411
412
ΔS
(J/mol.K)
42.87
43.10
43.37
43.63
43.90
44.17
44.43
44.70
44.96
45.23
ΔH
(kJ/mol)
15.65
15.75
15.85
15.96
16.07
16.18
16.29
16.40
16.51
16.62
ΔG
(kJ/mol)
-1.63
-1.67
-1.71
-1.75
-1.80
-1.84
-1.89
-1.93
-1.97
-2.02
T/(K)
514
515
516
517
518
519
520
521
522
523
105
ΔS
(J/mol.K)
70.70
70.94
71.17
71.41
71.65
71.88
72.12
72.35
72.59
72.82
ΔH
(kJ/mol)
28.38
28.50
28.63
28.75
28.87
28.99
29.11
29.24
29.36
29.48
ΔG
(kJ/mol)
-7.96
-8.03
-8.10
-8.17
-8.24
-8.31
-8.39
-8.46
-8.53
-8.60
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
45.49
45.76
46.02
46.29
46.55
46.81
47.08
47.34
47.60
47.86
48.13
48.39
48.65
48.91
49.17
49.43
49.69
49.95
50.21
50.46
50.72
50.98
51.24
51.49
51.75
52.01
52.26
52.52
52.78
53.03
53.29
53.54
53.80
54.05
54.30
54.56
54.81
55.06
55.32
55.57
16.72
16.83
16.94
17.05
17.16
17.27
17.38
17.49
17.60
17.71
17.82
17.93
18.04
18.16
18.27
18.38
18.49
18.60
18.71
18.82
18.94
19.05
19.16
19.27
19.38
19.50
19.61
19.72
19.83
19.95
20.06
20.17
20.28
20.40
20.51
20.62
20.74
20.85
20.97
21.08
-2.06
-2.11
-2.16
-2.20
-2.25
-2.30
-2.34
-2.39
-2.44
-2.49
-2.53
-2.58
-2.63
-2.68
-2.73
-2.78
-2.83
-2.88
-2.93
-2.98
-3.03
-3.08
-3.13
-3.18
-3.23
-3.28
-3.34
-3.39
-3.44
-3.49
-3.55
-3.60
-3.65
-3.71
-3.76
-3.82
-3.87
-3.93
-3.98
-4.04
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
106
73.06
73.29
73.52
73.76
73.99
74.22
74.46
74.69
74.92
75.16
75.39
75.62
75.85
76.08
76.32
76.55
76.78
77.01
77.24
77.47
77.70
77.93
78.16
78.39
78.62
78.85
79.08
79.31
79.53
79.76
79.99
80.22
80.45
80.67
80.90
81.13
81.36
81.58
81.81
82.04
29.60
29.73
29.85
29.97
30.10
30.22
30.34
30.47
30.59
30.71
30.84
30.96
31.09
31.21
31.34
31.46
31.58
31.71
31.83
31.96
32.08
32.21
32.33
32.46
32.59
32.71
32.84
32.96
33.09
33.22
33.34
33.47
33.59
33.72
33.85
33.98
34.10
34.23
34.36
34.48
-8.68
-8.75
-8.82
-8.90
-8.97
-9.04
-9.12
-9.19
-9.27
-9.34
-9.42
-9.49
-9.57
-9.65
-9.72
-9.80
-9.88
-9.95
-10.03
-10.11
-10.18
-10.26
-10.34
-10.42
-10.50
-10.58
-10.66
-10.73
-10.81
-10.89
-10.97
-11.05
-11.13
-11.21
-11.30
-11.38
-11.46
-11.54
-11.62
-11.70
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
55.82
56.07
56.33
56.58
56.83
57.08
57.33
57.58
57.83
58.08
58.33
58.58
58.83
59.07
59.32
59.57
59.82
60.07
60.31
60.56
60.81
61.05
61.30
61.55
61.79
62.04
62.28
62.53
62.77
63.01
63.26
63.50
63.75
63.99
64.23
64.48
64.72
64.96
65.20
65.44
21.19
21.31
21.42
21.54
21.65
21.77
21.88
22.00
22.11
22.23
22.34
22.46
22.57
22.69
22.80
22.92
23.04
23.15
23.27
23.39
23.50
23.62
23.73
23.85
23.97
24.09
24.20
24.32
24.44
24.56
24.67
24.79
24.91
25.03
25.15
25.26
25.38
25.50
25.62
25.74
-4.09
-4.15
-4.21
-4.26
-4.32
-4.38
-4.43
-4.49
-4.55
-4.61
-4.66
-4.72
-4.78
-4.84
-4.90
-4.96
-5.02
-5.08
-5.14
-5.20
-5.26
-5.32
-5.38
-5.44
-5.51
-5.57
-5.63
-5.69
-5.75
-5.82
-5.88
-5.94
-6.01
-6.07
-6.14
-6.20
-6.26
-6.33
-6.39
-6.46
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
107
82.26
82.49
82.71
82.94
83.17
83.39
83.62
83.84
84.07
84.29
84.52
84.74
84.96
85.19
85.41
85.64
85.86
86.08
86.31
86.53
86.75
86.97
87.20
87.42
87.64
87.86
88.08
88.31
88.53
88.75
88.97
89.19
89.41
89.63
89.85
90.07
90.29
90.51
90.73
90.95
34.61
34.74
34.87
34.99
35.12
35.25
35.38
35.51
35.64
35.76
35.89
36.02
36.15
36.28
36.41
36.54
36.67
36.80
36.93
37.06
37.19
37.32
37.45
37.58
37.71
37.84
37.97
38.10
38.23
38.36
38.49
38.63
38.76
38.89
39.02
39.15
39.28
39.42
39.55
39.68
-11.78
-11.87
-11.95
-12.03
-12.12
-12.20
-12.28
-12.37
-12.45
-12.53
-12.62
-12.70
-12.79
-12.87
-12.96
-13.04
-13.13
-13.22
-13.30
-13.39
-13.48
-13.56
-13.65
-13.74
-13.82
-13.91
-14.00
-14.09
-14.18
-14.26
-14.35
-14.44
-14.53
-14.62
-14.71
-14.80
-14.89
-14.98
-15.07
-15.16
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
65.69
65.93
66.17
66.41
66.65
66.89
67.13
67.37
67.61
67.85
68.09
68.33
68.56
68.80
69.04
69.28
69.52
69.75
69.99
70.23
70.47
25.86
25.98
26.10
26.21
26.33
26.45
26.57
26.69
26.81
26.93
27.05
27.17
27.29
27.41
27.54
27.66
27.78
27.90
28.02
28.14
28.26
-6.53
-6.59
-6.66
-6.72
-6.79
-6.86
-6.92
-6.99
-7.06
-7.13
-7.19
-7.26
-7.33
-7.40
-7.47
-7.54
-7.61
-7.68
-7.75
-7.82
-7.89
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
623.15
108
91.17
91.39
91.61
91.83
92.05
92.26
92.48
92.70
92.92
93.14
93.35
93.57
93.79
94.01
94.22
94.44
94.66
94.87
95.09
95.31
95.34
39.81
39.94
40.08
40.21
40.34
40.48
40.61
40.74
40.88
41.01
41.14
41.28
41.41
41.54
41.68
41.81
41.95
42.08
42.22
42.35
42.37
-15.25
-15.35
-15.44
-15.53
-15.62
-15.71
-15.81
-15.90
-15.99
-16.08
-16.18
-16.27
-16.36
-16.46
-16.55
-16.65
-16.74
-16.84
-16.93
-17.03
-17.04
Appendix B
Table B.1 Thermodynamic properties of NaNO3-NaNO2-NaNO3 compound in liquid state
(298.15-392.15K)
T/(K)
298.15
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
ΔS
(J/mol.K)
0.00
0.22
0.49
0.75
1.01
1.27
1.53
1.79
2.05
2.30
2.56
2.82
3.08
3.33
3.59
3.84
4.10
4.35
4.61
4.86
5.11
5.37
5.62
5.87
6.12
6.37
6.63
6.88
7.13
7.38
7.63
7.88
ΔH
(kJ/mol)
0.00
0.06
0.14
0.22
0.29
0.37
0.44
0.52
0.59
0.67
0.75
0.82
0.90
0.98
1.05
1.13
1.21
1.28
1.36
1.44
1.51
1.59
1.67
1.75
1.82
1.90
1.98
2.06
2.14
2.22
2.29
2.37
ΔG
(kJ/mol)
0.00
0.00
-0.01
-0.01
-0.01
-0.02
-0.02
-0.03
-0.03
-0.04
-0.04
-0.05
-0.05
-0.06
-0.07
-0.07
-0.08
-0.09
-0.10
-0.10
-0.11
-0.12
-0.13
-0.14
-0.15
-0.16
-0.17
-0.18
-0.19
-0.20
-0.21
-0.22
109
T/(K)
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
ΔS
(J/mol.K)
12.33
12.58
12.83
13.07
13.32
13.56
13.81
14.05
14.30
14.55
14.79
15.04
15.28
15.53
15.77
16.02
16.26
16.51
16.75
17.00
17.24
17.49
17.73
17.98
18.22
18.47
18.71
18.96
19.20
19.45
19.69
19.94
ΔH
(kJ/mol)
3.82
3.90
3.98
4.06
4.15
4.23
4.31
4.40
4.48
4.56
4.65
4.73
4.82
4.90
4.98
5.07
5.15
5.24
5.33
5.41
5.50
5.58
5.67
5.76
5.84
5.93
6.02
6.11
6.20
6.28
6.37
6.46
ΔG
(kJ/mol)
-0.46
-0.48
-0.49
-0.51
-0.53
-0.54
-0.56
-0.58
-0.60
-0.61
-0.63
-0.65
-0.67
-0.69
-0.71
-0.73
-0.75
-0.77
-0.79
-0.81
-0.83
-0.85
-0.87
-0.89
-0.92
-0.94
-0.96
-0.98
-1.00
-1.03
-1.05
-1.07
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
8.13
8.38
8.63
8.87
9.12
9.37
9.62
9.87
10.11
10.36
10.61
10.86
11.10
11.35
11.60
11.84
2.45
2.53
2.61
2.69
2.77
2.85
2.93
3.01
3.09
3.17
3.25
3.33
3.41
3.49
3.57
3.65
-0.23
-0.24
-0.25
-0.27
-0.28
-0.29
-0.30
-0.32
-0.33
-0.34
-0.36
-0.37
-0.39
-0.40
-0.42
-0.43
379
380
381
382
383
384
385
386
387
388
389
390
391
392
392.15
20.18
20.43
20.68
20.92
21.17
21.41
21.66
21.91
22.15
22.40
22.65
22.89
23.14
23.39
23.42
6.55
6.64
6.73
6.82
6.91
7.00
7.09
7.18
7.27
7.37
7.46
7.55
7.64
7.74
7.75
-1.10
-1.12
-1.15
-1.17
-1.20
-1.22
-1.25
-1.27
-1.30
-1.32
-1.35
-1.38
-1.40
-1.43
-1.44
Table B.2 Thermodynamic properties of NaNO3-NaNO2-NaNO3 compound in liquid state
(413.15-623.15K)
T/(K)
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
ΔS
(J/mol.K)
32.80
33.02
33.25
33.48
33.70
33.93
34.16
34.38
34.61
34.83
35.06
35.29
35.51
35.74
35.96
36.19
ΔH
(kJ/mol)
11.49
11.58
11.67
11.77
11.86
11.96
12.05
12.15
12.24
12.34
12.43
12.53
12.63
12.72
12.82
12.91
ΔG
(kJ/mol)
-2.09
-2.12
-2.16
-2.19
-2.23
-2.26
-2.29
-2.33
-2.36
-2.40
-2.43
-2.47
-2.50
-2.54
-2.57
-2.61
T/(K)
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
110
ΔS
(J/mol.K)
56.08
56.30
56.51
56.72
56.94
57.15
57.36
57.57
57.79
58.00
58.21
58.42
58.64
58.85
59.06
59.27
ΔH
(kJ/mol)
22.35
22.46
22.57
22.68
22.79
22.90
23.02
23.13
23.24
23.35
23.47
23.58
23.69
23.80
23.92
24.03
ΔG
(kJ/mol)
-6.82
-6.87
-6.93
-6.98
-7.04
-7.10
-7.16
-7.21
-7.27
-7.33
-7.39
-7.45
-7.50
-7.56
-7.62
-7.68
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
36.41
36.63
36.86
37.08
37.31
37.53
37.75
37.98
38.20
38.42
38.65
38.87
39.09
39.32
39.54
39.76
39.98
40.21
40.43
40.65
40.87
41.09
41.31
41.54
41.76
41.98
42.20
42.42
42.64
42.86
43.08
43.30
43.52
43.74
43.96
44.18
44.40
44.62
44.84
45.06
13.01
13.11
13.20
13.30
13.40
13.50
13.59
13.69
13.79
13.89
13.98
14.08
14.18
14.28
14.38
14.48
14.58
14.68
14.77
14.87
14.97
15.07
15.17
15.27
15.37
15.47
15.57
15.68
15.78
15.88
15.98
16.08
16.18
16.28
16.39
16.49
16.59
16.69
16.80
16.90
-2.65
-2.68
-2.72
-2.76
-2.79
-2.83
-2.87
-2.91
-2.94
-2.98
-3.02
-3.06
-3.10
-3.14
-3.18
-3.22
-3.26
-3.30
-3.34
-3.38
-3.42
-3.46
-3.50
-3.54
-3.58
-3.63
-3.67
-3.71
-3.75
-3.80
-3.84
-3.88
-3.93
-3.97
-4.01
-4.06
-4.10
-4.15
-4.19
-4.24
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
111
59.48
59.70
59.91
60.12
60.33
60.54
60.75
60.96
61.18
61.39
61.60
61.81
62.02
62.23
62.44
62.65
62.86
63.07
63.28
63.49
63.70
63.91
64.12
64.33
64.54
64.75
64.96
65.17
65.38
65.59
65.80
66.00
66.21
66.42
66.63
66.84
67.05
67.26
67.47
67.67
24.14
24.26
24.37
24.49
24.60
24.71
24.83
24.94
25.06
25.17
25.29
25.40
25.52
25.63
25.75
25.86
25.98
26.10
26.21
26.33
26.45
26.56
26.68
26.80
26.91
27.03
27.15
27.27
27.38
27.50
27.62
27.74
27.86
27.98
28.10
28.21
28.33
28.45
28.57
28.69
-7.74
-7.80
-7.86
-7.92
-7.98
-8.04
-8.10
-8.16
-8.22
-8.28
-8.35
-8.41
-8.47
-8.53
-8.59
-8.66
-8.72
-8.78
-8.84
-8.91
-8.97
-9.04
-9.10
-9.16
-9.23
-9.29
-9.36
-9.42
-9.49
-9.55
-9.62
-9.69
-9.75
-9.82
-9.88
-9.95
-10.02
-10.09
-10.15
-10.22
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
45.28
45.50
45.72
45.93
46.15
46.37
46.59
46.81
47.03
47.24
47.46
47.68
47.90
48.12
48.33
48.55
48.77
48.98
49.20
49.42
49.63
49.85
50.07
50.28
50.50
50.72
50.93
51.15
51.36
51.58
51.80
52.01
52.23
52.44
52.66
52.87
53.09
53.30
53.52
53.73
17.00
17.10
17.21
17.31
17.41
17.52
17.62
17.73
17.83
17.93
18.04
18.14
18.25
18.35
18.46
18.56
18.67
18.77
18.88
18.99
19.09
19.20
19.30
19.41
19.52
19.62
19.73
19.84
19.95
20.05
20.16
20.27
20.38
20.49
20.59
20.70
20.81
20.92
21.03
21.14
-4.28
-4.33
-4.37
-4.42
-4.46
-4.51
-4.56
-4.60
-4.65
-4.70
-4.74
-4.79
-4.84
-4.89
-4.94
-4.98
-5.03
-5.08
-5.13
-5.18
-5.23
-5.28
-5.33
-5.38
-5.43
-5.48
-5.53
-5.58
-5.63
-5.68
-5.74
-5.79
-5.84
-5.89
-5.95
-6.00
-6.05
-6.10
-6.16
-6.21
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
112
67.88
68.09
68.30
68.51
68.71
68.92
69.13
69.34
69.54
69.75
69.96
70.17
70.37
70.58
70.79
71.00
71.20
71.41
71.62
71.82
72.03
72.24
72.44
72.65
72.85
73.06
73.27
73.47
73.68
73.89
74.09
74.30
74.50
74.71
74.91
75.12
75.32
75.53
75.73
75.94
28.81
28.93
29.05
29.17
29.29
29.41
29.53
29.66
29.78
29.90
30.02
30.14
30.26
30.38
30.51
30.63
30.75
30.87
31.00
31.12
31.24
31.37
31.49
31.61
31.74
31.86
31.98
32.11
32.23
32.36
32.48
32.61
32.73
32.86
32.98
33.11
33.23
33.36
33.48
33.61
-10.29
-10.36
-10.42
-10.49
-10.56
-10.63
-10.70
-10.77
-10.84
-10.91
-10.98
-11.05
-11.12
-11.19
-11.26
-11.33
-11.40
-11.47
-11.54
-11.62
-11.69
-11.76
-11.83
-11.90
-11.98
-12.05
-12.12
-12.20
-12.27
-12.34
-12.42
-12.49
-12.57
-12.64
-12.72
-12.79
-12.87
-12.94
-13.02
-13.09
510
511
512
513
514
515
516
517
518
53.94
54.16
54.37
54.59
54.80
55.02
55.23
55.44
55.66
21.25
21.36
21.47
21.58
21.69
21.80
21.91
22.02
22.13
-6.27
-6.32
-6.37
-6.43
-6.48
-6.54
-6.59
-6.65
-6.70
616
617
618
619
620
621
622
623
623.15
113
76.15
76.35
76.56
76.76
76.96
77.17
77.37
77.58
77.61
33.74
33.86
33.99
34.12
34.24
34.37
34.50
34.62
34.64
-13.17
-13.25
-13.32
-13.40
-13.48
-13.55
-13.63
-13.71
-13.72
Appendix C
Table C.1. Thermodynamic properties of LiNO3-NaNO3-KNO3-MgK compound in solid
state (298.15-364.15K)
T/(K)
298.15
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
ΔS
(J/mol.K)
0.00
0.48
1.04
1.60
2.16
2.72
3.29
3.85
4.41
4.96
5.52
6.08
6.64
7.20
7.76
8.31
8.87
9.42
9.98
10.54
11.09
11.64
12.20
12.75
13.31
13.86
14.41
14.96
15.52
16.07
16.62
17.17
ΔH
(kJ/mol)
0.00
0.14
0.31
0.48
0.65
0.82
0.99
1.16
1.33
1.50
1.67
1.85
2.02
2.19
2.36
2.54
2.71
2.89
3.06
3.24
3.41
3.59
3.77
3.95
4.12
4.30
4.48
4.66
4.84
5.02
5.20
5.38
ΔG
(kJ/mol)
0.00
0.00
0.00
0.00
0.00
-0.01
-0.01
-0.01
-0.02
-0.02
-0.03
-0.03
-0.04
-0.05
-0.06
-0.06
-0.07
-0.08
-0.09
-0.10
-0.11
-0.12
-0.14
-0.15
-0.16
-0.18
-0.19
-0.20
-0.22
-0.24
-0.25
-0.27
T/(K)
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
114
ΔS
(J/mol.K)
19.37
19.92
20.47
21.02
21.56
22.11
22.66
23.21
23.75
24.30
24.85
25.39
25.94
26.48
27.03
27.57
28.12
28.66
29.21
29.75
30.29
30.84
31.38
31.92
32.46
33.00
33.55
34.09
34.63
35.17
35.71
36.25
ΔH
(kJ/mol)
6.11
6.29
6.47
6.66
6.84
7.03
7.21
7.40
7.58
7.77
7.96
8.15
8.33
8.52
8.71
8.90
9.09
9.28
9.47
9.66
9.85
10.04
10.24
10.43
10.62
10.82
11.01
11.20
11.40
11.59
11.79
11.99
ΔG
(kJ/mol)
-0.34
-0.36
-0.38
-0.40
-0.42
-0.45
-0.47
-0.49
-0.52
-0.54
-0.56
-0.59
-0.62
-0.64
-0.67
-0.70
-0.72
-0.75
-0.78
-0.81
-0.84
-0.87
-0.90
-0.94
-0.97
-1.00
-1.03
-1.07
-1.10
-1.14
-1.17
-1.21
330
331
332
17.72
18.27
18.82
5.56
5.74
5.93
-0.29
-0.30
-0.32
364.15
36.33
12.02
-1.21
Table C.2 Thermodynamic properties of LiNO3-NaNO3-KNO3-MgK compound in liquid
state (421.15-623.15K)
T/(K)
421.15
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
ΔS
ΔH
ΔG
(J/mol.K) (kJ/mol) (kJ/mol)
74.28
26.73
-4.55
74.68
26.90
-4.61
75.15
27.10
-4.68
75.62
27.30
-4.76
76.08
27.50
-4.84
76.55
27.70
-4.91
77.02
27.90
-4.99
77.48
28.10
-5.07
77.95
28.30
-5.14
78.41
28.49
-5.22
78.87
28.69
-5.30
79.33
28.89
-5.38
79.79
29.09
-5.46
80.25
29.29
-5.54
80.71
29.49
-5.62
81.17
29.69
-5.70
81.63
29.89
-5.78
82.08
30.09
-5.86
82.54
30.29
-5.95
82.99
30.49
-6.03
83.45
30.69
-6.11
83.90
30.89
-6.20
84.35
31.09
-6.28
84.80
31.29
-6.36
85.25
31.49
-6.45
85.70
31.69
-6.54
115
T/(K)
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
ΔS
ΔH
ΔG
(J/mol.K) (kJ/mol) (kJ/mol)
117.88
47.25
-14.40
118.27
47.45
-14.52
118.66
47.66
-14.64
119.04
47.86
-14.76
119.43
48.07
-14.88
119.82
48.27
-15.00
120.21
48.47
-15.12
120.59
48.68
-15.24
120.98
48.88
-15.36
121.37
49.09
-15.48
121.75
49.29
-15.60
122.13
49.50
-15.72
122.52
49.70
-15.84
122.90
49.91
-15.97
123.28
50.11
-16.09
123.66
50.32
-16.21
124.04
50.52
-16.34
124.42
50.73
-16.46
124.80
50.93
-16.59
125.18
51.14
-16.71
125.56
51.34
-16.84
125.94
51.55
-16.96
126.32
51.75
-17.09
126.69
51.96
-17.21
127.07
52.17
-17.34
127.45
52.37
-17.47
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
86.15
86.59
87.04
87.48
87.93
88.37
88.81
89.26
89.70
90.14
90.58
91.02
91.45
91.89
92.33
92.76
93.19
93.63
94.06
94.49
94.92
95.35
95.78
96.21
96.64
97.07
97.49
97.92
98.34
98.77
99.19
99.61
100.04
100.46
100.88
101.30
101.71
102.13
102.55
102.97
31.89
32.09
32.29
32.49
32.69
32.89
33.09
33.29
33.49
33.69
33.89
34.09
34.29
34.49
34.69
34.89
35.09
35.29
35.49
35.70
35.90
36.10
36.30
36.50
36.70
36.90
37.10
37.31
37.51
37.71
37.91
38.11
38.31
38.52
38.72
38.92
39.12
39.32
39.53
39.73
-6.62
-6.71
-6.79
-6.88
-6.97
-7.06
-7.15
-7.24
-7.32
-7.41
-7.50
-7.60
-7.69
-7.78
-7.87
-7.96
-8.06
-8.15
-8.24
-8.34
-8.43
-8.53
-8.62
-8.72
-8.82
-8.91
-9.01
-9.11
-9.21
-9.30
-9.40
-9.50
-9.60
-9.70
-9.80
-9.90
-10.01
-10.11
-10.21
-10.31
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
116
127.82
128.20
128.57
128.94
129.32
129.69
130.06
130.43
130.80
131.17
131.54
131.91
132.28
132.64
133.01
133.38
133.74
134.11
134.47
134.84
135.20
135.57
135.93
136.29
136.65
137.01
137.37
137.73
138.09
138.45
138.81
139.17
139.53
139.88
140.24
140.60
140.95
141.31
141.66
142.01
52.58
52.78
52.99
53.19
53.40
53.61
53.81
54.02
54.22
54.43
54.64
54.84
55.05
55.26
55.46
55.67
55.88
56.08
56.29
56.50
56.70
56.91
57.12
57.32
57.53
57.74
57.95
58.15
58.36
58.57
58.77
58.98
59.19
59.40
59.60
59.81
60.02
60.23
60.44
60.64
-17.60
-17.72
-17.85
-17.98
-18.11
-18.24
-18.37
-18.50
-18.63
-18.76
-18.89
-19.02
-19.16
-19.29
-19.42
-19.56
-19.69
-19.82
-19.96
-20.09
-20.23
-20.36
-20.50
-20.63
-20.77
-20.91
-21.04
-21.18
-21.32
-21.46
-21.60
-21.74
-21.88
-22.02
-22.16
-22.30
-22.44
-22.58
-22.72
-22.86
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
103.38
103.80
104.21
104.62
105.04
105.45
105.86
106.27
106.68
107.09
107.50
107.91
108.31
108.72
109.12
109.53
109.93
110.34
110.74
111.14
111.54
111.94
112.34
112.74
113.14
113.54
113.94
114.33
114.73
115.13
115.52
115.91
116.31
116.70
117.09
117.48
39.93
40.13
40.34
40.54
40.74
40.94
41.14
41.35
41.55
41.75
41.96
42.16
42.36
42.56
42.77
42.97
43.17
43.38
43.58
43.78
43.99
44.19
44.39
44.60
44.80
45.00
45.21
45.41
45.62
45.82
46.02
46.23
46.43
46.64
46.84
47.04
-10.42
-10.52
-10.62
-10.73
-10.83
-10.94
-11.04
-11.15
-11.26
-11.36
-11.47
-11.58
-11.69
-11.79
-11.90
-12.01
-12.12
-12.23
-12.34
-12.45
-12.57
-12.68
-12.79
-12.90
-13.02
-13.13
-13.24
-13.36
-13.47
-13.59
-13.70
-13.82
-13.93
-14.05
-14.17
-14.28
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
623.15
117
142.37
142.72
143.07
143.42
143.78
144.13
144.48
144.83
145.18
145.52
145.87
146.22
146.57
146.92
147.26
147.61
147.95
148.30
148.64
148.99
149.33
149.67
150.02
150.36
150.70
151.04
151.38
151.72
152.06
152.40
152.74
153.08
153.42
153.75
154.09
154.14
60.85
61.06
61.27
61.48
61.68
61.89
62.10
62.31
62.52
62.73
62.93
63.14
63.35
63.56
63.77
63.98
64.19
64.39
64.60
64.81
65.02
65.23
65.44
65.65
65.86
66.07
66.28
66.49
66.70
66.91
67.12
67.33
67.54
67.74
67.95
67.99
-23.00
-23.15
-23.29
-23.43
-23.58
-23.72
-23.86
-24.01
-24.15
-24.30
-24.44
-24.59
-24.74
-24.88
-25.03
-25.18
-25.33
-25.47
-25.62
-25.77
-25.92
-26.07
-26.22
-26.37
-26.52
-26.67
-26.82
-26.97
-27.13
-27.28
-27.43
-27.58
-27.74
-27.89
-28.04
-28.07
Appendix D
Table D.1 Thermodynamic properties of LiNO3-NaNO3-KNO3-NaNO2 compound in solid state
(298.15-363.15K)
T/(K)
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
ΔS
(J/mol.K)
0.21
0.47
0.72
0.97
1.22
1.47
1.72
1.97
2.23
2.48
2.73
2.98
3.23
3.48
3.73
3.98
4.23
4.47
4.72
4.97
5.22
5.47
5.72
5.96
6.21
6.46
6.70
6.95
7.20
7.44
7.69
7.93
ΔH
(kJ/mol)
0.06
0.14
0.22
0.29
0.37
0.45
0.53
0.60
0.68
0.76
0.84
0.92
0.99
1.07
1.15
1.23
1.31
1.39
1.47
1.55
1.63
1.71
1.79
1.87
1.95
2.03
2.11
2.20
2.28
2.36
2.44
2.52
ΔG
(kJ/mol)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.01
-0.01
-0.01
-0.01
-0.02
-0.02
-0.02
-0.03
-0.03
-0.03
-0.04
-0.04
-0.05
-0.05
-0.06
-0.06
-0.07
-0.08
-0.08
-0.09
-0.10
T/(K)
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
363.15
118
ΔS
(J/mol.K)
8.67
8.91
9.16
9.40
9.64
9.89
10.13
10.37
10.61
10.85
11.09
11.34
11.58
11.82
12.06
12.30
12.54
12.77
13.01
13.25
13.49
13.73
13.96
14.20
14.44
14.67
14.91
15.14
15.38
15.61
15.84
15.88
ΔH
(kJ/mol)
2.77
2.85
2.93
3.02
3.10
3.18
3.27
3.35
3.43
3.52
3.60
3.69
3.77
3.85
3.94
4.02
4.11
4.19
4.28
4.36
4.45
4.53
4.62
4.70
4.79
4.87
4.96
5.04
5.13
5.22
5.30
5.32
ΔG
(kJ/mol)
-0.12
-0.12
-0.13
-0.14
-0.15
-0.16
-0.17
-0.18
-0.19
-0.19
-0.20
-0.21
-0.22
-0.24
-0.25
-0.26
-0.27
-0.28
-0.29
-0.30
-0.32
-0.33
-0.34
-0.35
-0.37
-0.38
-0.39
-0.41
-0.42
-0.43
-0.45
-0.45
331
8.18
2.60
-0.10
Table D.2 Thermodynamic properties of LiNO3-NaNO3-KNO3-NaNO2 compound in liquid
state (381.15-623.15K)
T/(K)
381.15
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
ΔS
ΔH
ΔG
(J/mol.K) (kJ/mol) (kJ/mol)
22.81
7.65
-1.04
23.07
7.75
-1.06
23.38
7.87
-1.09
23.69
7.98
-1.11
23.99
8.10
-1.13
24.30
8.22
-1.16
24.60
8.34
-1.18
24.91
8.46
-1.21
25.21
8.57
-1.23
25.51
8.69
-1.26
25.82
8.81
-1.28
26.12
8.93
-1.31
26.42
9.05
-1.34
26.72
9.17
-1.36
27.02
9.28
-1.39
27.32
9.40
-1.42
27.62
9.52
-1.44
27.92
9.64
-1.47
28.21
9.76
-1.50
28.51
9.88
-1.53
28.81
9.99
-1.56
29.10
10.11
-1.59
29.40
10.23
-1.62
29.69
10.35
-1.64
29.99
10.47
-1.67
30.28
10.59
-1.70
30.57
10.71
-1.74
30.87
10.83
-1.77
119
T/(K)
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
ΔS
ΔH
ΔG
(J/mol.K) (kJ/mol) (kJ/mol)
56.39
22.42
-5.94
56.64
22.55
-6.00
56.89
22.67
-6.06
57.13
22.80
-6.11
57.38
22.92
-6.17
57.63
23.05
-6.23
57.87
23.17
-6.29
58.12
23.30
-6.34
58.36
23.42
-6.40
58.61
23.55
-6.46
58.85
23.67
-6.52
59.10
23.80
-6.58
59.34
23.92
-6.64
59.59
24.05
-6.70
59.83
24.17
-6.76
60.07
24.30
-6.82
60.32
24.43
-6.88
60.56
24.55
-6.94
60.80
24.68
-7.00
61.04
24.80
-7.06
61.28
24.93
-7.12
61.52
25.06
-7.18
61.76
25.18
-7.24
62.00
25.31
-7.31
62.24
25.44
-7.37
62.48
25.56
-7.43
62.72
25.69
-7.49
62.96
25.81
-7.56
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
31.16
31.45
31.74
32.03
32.32
32.61
32.90
33.19
33.47
33.76
34.05
34.33
34.62
34.90
35.19
35.47
35.75
36.04
36.32
36.60
36.88
37.16
37.44
37.72
38.00
38.28
38.56
38.83
39.11
39.39
39.66
39.94
40.21
40.49
40.76
41.03
41.31
41.58
41.85
42.12
10.95
11.07
11.19
11.30
11.42
11.54
11.66
11.78
11.90
12.02
12.14
12.26
12.38
12.50
12.62
12.74
12.86
12.98
13.10
13.22
13.34
13.46
13.58
13.71
13.83
13.95
14.07
14.19
14.31
14.43
14.55
14.67
14.79
14.91
15.04
15.16
15.28
15.40
15.52
15.64
-1.80
-1.83
-1.86
-1.89
-1.92
-1.96
-1.99
-2.02
-2.06
-2.09
-2.12
-2.16
-2.19
-2.23
-2.26
-2.30
-2.33
-2.37
-2.40
-2.44
-2.48
-2.51
-2.55
-2.59
-2.63
-2.67
-2.70
-2.74
-2.78
-2.82
-2.86
-2.90
-2.94
-2.98
-3.02
-3.06
-3.10
-3.14
-3.19
-3.23
120
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
63.20
63.44
63.68
63.91
64.15
64.39
64.62
64.86
65.10
65.33
65.57
65.80
66.04
66.27
66.50
66.74
66.97
67.20
67.44
67.67
67.90
68.13
68.36
68.60
68.83
69.06
69.29
69.52
69.75
69.98
70.20
70.43
70.66
70.89
71.12
71.34
71.57
71.80
72.03
72.25
25.94
26.07
26.19
26.32
26.45
26.57
26.70
26.83
26.96
27.08
27.21
27.34
27.46
27.59
27.72
27.85
27.97
28.10
28.23
28.36
28.48
28.61
28.74
28.87
29.00
29.12
29.25
29.38
29.51
29.64
29.76
29.89
30.02
30.15
30.28
30.41
30.54
30.66
30.79
30.92
-7.62
-7.68
-7.75
-7.81
-7.87
-7.94
-8.00
-8.07
-8.13
-8.20
-8.26
-8.33
-8.39
-8.46
-8.53
-8.59
-8.66
-8.73
-8.79
-8.86
-8.93
-9.00
-9.07
-9.13
-9.20
-9.27
-9.34
-9.41
-9.48
-9.55
-9.62
-9.69
-9.76
-9.83
-9.90
-9.97
-10.05
-10.12
-10.19
-10.26
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
42.40
42.67
42.94
43.21
43.47
43.74
44.01
44.28
44.55
44.81
45.08
45.35
45.61
45.88
46.14
46.41
46.67
46.93
47.20
47.46
47.72
47.98
48.25
48.51
48.77
49.03
49.29
49.55
49.80
50.06
50.32
50.58
50.83
51.09
51.35
51.60
51.86
52.11
52.37
52.62
15.76
15.89
16.01
16.13
16.25
16.37
16.50
16.62
16.74
16.86
16.98
17.11
17.23
17.35
17.47
17.60
17.72
17.84
17.96
18.09
18.21
18.33
18.46
18.58
18.70
18.82
18.95
19.07
19.19
19.32
19.44
19.56
19.69
19.81
19.94
20.06
20.18
20.31
20.43
20.55
-3.27
-3.31
-3.36
-3.40
-3.44
-3.49
-3.53
-3.57
-3.62
-3.66
-3.71
-3.75
-3.80
-3.84
-3.89
-3.94
-3.98
-4.03
-4.08
-4.12
-4.17
-4.22
-4.27
-4.32
-4.37
-4.41
-4.46
-4.51
-4.56
-4.61
-4.66
-4.71
-4.76
-4.81
-4.87
-4.92
-4.97
-5.02
-5.07
-5.13
121
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
72.48
72.70
72.93
73.15
73.38
73.60
73.83
74.05
74.28
74.50
74.72
74.94
75.17
75.39
75.61
75.83
76.05
76.28
76.50
76.72
76.94
77.16
77.38
77.60
77.82
78.04
78.25
78.47
78.69
78.91
79.13
79.34
79.56
79.78
80.00
80.21
80.43
80.64
80.86
81.07
31.05
31.18
31.31
31.44
31.57
31.70
31.83
31.96
32.08
32.21
32.34
32.47
32.60
32.73
32.86
32.99
33.12
33.25
33.38
33.51
33.64
33.77
33.90
34.03
34.16
34.29
34.42
34.55
34.69
34.82
34.95
35.08
35.21
35.34
35.47
35.60
35.73
35.86
35.99
36.13
-10.33
-10.41
-10.48
-10.55
-10.63
-10.70
-10.77
-10.85
-10.92
-11.00
-11.07
-11.14
-11.22
-11.29
-11.37
-11.45
-11.52
-11.60
-11.67
-11.75
-11.83
-11.91
-11.98
-12.06
-12.14
-12.22
-12.29
-12.37
-12.45
-12.53
-12.61
-12.69
-12.77
-12.85
-12.93
-13.01
-13.09
-13.17
-13.25
-13.33
489
490
491
492
493
494
495
496
497
498
499
500
501
502
52.88
53.13
53.38
53.64
53.89
54.14
54.39
54.64
54.89
55.14
55.39
55.64
55.89
56.14
20.68
20.80
20.93
21.05
21.17
21.30
21.42
21.55
21.67
21.80
21.92
22.05
22.17
22.30
-5.18
-5.23
-5.28
-5.34
-5.39
-5.45
-5.50
-5.55
-5.61
-5.66
-5.72
-5.78
-5.83
-5.89
122
611
612
613
614
615
616
617
618
619
620
621
622
623
623.15
81.29
81.50
81.72
81.93
82.15
82.36
82.58
82.79
83.00
83.21
83.43
83.64
83.85
83.88
36.26
36.39
36.52
36.65
36.78
36.92
37.05
37.18
37.31
37.44
37.57
37.71
37.84
37.86
-13.41
-13.49
-13.57
-13.66
-13.74
-13.82
-13.90
-13.98
-14.07
-14.15
-14.23
-14.32
-14.41
-14.43
Appendix E
Table E.1 Thermodynamic properties of LiNO3-NaNO3-NaNO2-KNO3-KNO2 compound
in solid state (298.15-359.15K)
T/(K)
298.15
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
ΔS
ΔH
ΔG
(J/mol.K) (kJ/mol) (kJ/mol)
0.00
0.00
0.00
0.25
0.07
0.00
0.54
0.16
0.00
0.83
0.25
0.00
1.12
0.34
0.00
1.41
0.42
0.00
1.70
0.51
0.00
1.99
0.60
-0.01
2.28
0.69
-0.01
2.57
0.78
-0.01
2.86
0.87
-0.01
3.15
0.96
-0.02
3.43
1.05
-0.02
3.72
1.13
-0.02
4.01
1.22
-0.03
4.30
1.31
-0.03
4.58
1.40
-0.03
4.87
1.49
-0.04
5.16
1.59
-0.04
5.44
1.68
-0.05
5.73
1.77
-0.06
6.02
1.86
-0.06
6.30
1.95
-0.07
6.59
2.04
-0.07
6.87
2.13
-0.08
7.15
2.22
-0.09
7.44
2.32
-0.09
7.72
2.41
-0.10
8.00
2.50
-0.11
8.29
2.59
-0.12
8.57
2.69
-0.13
8.85
2.78
-0.13
T/(K)
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
359.15
123
ΔS
ΔH
ΔG
(J/mol.K) (kJ/mol) (kJ/mol)
9.13
2.87
-0.14
9.41
2.96
-0.15
9.70
3.06
-0.16
9.98
3.15
-0.17
10.26
3.24
-0.18
10.54
3.34
-0.19
10.81
3.43
-0.20
11.09
3.53
-0.21
11.37
3.62
-0.22
11.65
3.71
-0.24
11.93
3.81
-0.25
12.21
3.90
-0.26
12.48
4.00
-0.27
12.76
4.09
-0.28
13.04
4.19
-0.30
13.31
4.28
-0.31
13.59
4.38
-0.32
13.86
4.47
-0.34
14.14
4.57
-0.35
14.41
4.66
-0.36
14.68
4.76
-0.38
14.96
4.86
-0.39
15.23
4.95
-0.41
15.50
5.05
-0.42
15.77
5.14
-0.44
16.05
5.24
-0.46
16.32
5.34
-0.47
16.59
5.43
-0.49
16.86
5.53
-0.50
17.13
5.63
-0.52
17.17
5.64
-0.52
Table E.2 Thermodynamic properties of LiNO3-NaNO3-NaNO2-KNO3-KNO2 compound
in liquid state (376-623.15K)
T/(K)
375.15
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
ΔS
ΔH
ΔG
(J/mol.K) (kJ/mol) (kJ/mol)
23.23
7.77
-0.94
23.47
7.86
-0.96
23.75
7.97
-0.98
24.03
8.08
-1.01
24.31
8.18
-1.03
24.59
8.29
-1.06
24.87
8.39
-1.08
25.15
8.50
-1.11
25.42
8.61
-1.13
25.70
8.71
-1.16
25.98
8.82
-1.18
26.26
8.93
-1.21
26.53
9.03
-1.23
26.81
9.14
-1.26
27.08
9.25
-1.29
27.36
9.35
-1.32
27.63
9.46
-1.34
27.91
9.57
-1.37
28.18
9.68
-1.40
28.45
9.78
-1.43
28.73
9.89
-1.46
29.00
10.00
-1.48
29.27
10.11
-1.51
29.54
10.22
-1.54
29.81
10.32
-1.57
30.08
10.43
-1.60
30.35
10.54
-1.63
30.62
10.65
-1.66
30.89
10.76
-1.69
31.16
10.86
-1.72
31.43
10.97
-1.76
124
T/(K)
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
ΔS
ΔH
ΔG
(J/mol.K) (kJ/mol) (kJ/mol)
55.25
21.73
-5.90
55.48
21.84
-5.95
55.72
21.96
-6.01
55.95
22.08
-6.06
56.19
22.20
-6.12
56.42
22.32
-6.18
56.65
22.43
-6.23
56.89
22.55
-6.29
57.12
22.67
-6.35
57.35
22.79
-6.40
57.59
22.91
-6.46
57.82
23.03
-6.52
58.05
23.15
-6.58
58.28
23.26
-6.64
58.52
23.38
-6.69
58.75
23.50
-6.75
58.98
23.62
-6.81
59.21
23.74
-6.87
59.44
23.86
-6.93
59.67
23.98
-6.99
59.90
24.10
-7.05
60.13
24.22
-7.11
60.36
24.34
-7.17
60.59
24.46
-7.23
60.82
24.58
-7.29
61.05
24.70
-7.35
61.28
24.82
-7.41
61.51
24.94
-7.47
61.73
25.06
-7.54
61.96
25.18
-7.60
62.19
25.30
-7.66
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
31.70
31.97
32.23
32.50
32.77
33.03
33.30
33.56
33.83
34.09
34.36
34.62
34.88
35.15
35.41
35.67
35.93
36.19
36.45
36.71
36.97
37.23
37.49
37.75
38.01
38.27
38.52
38.78
39.04
39.29
39.55
39.81
40.06
40.32
40.57
40.83
41.08
41.33
41.59
41.84
11.08
11.19
11.30
11.41
11.52
11.63
11.74
11.85
11.95
12.06
12.17
12.28
12.39
12.50
12.61
12.72
12.83
12.94
13.05
13.17
13.28
13.39
13.50
13.61
13.72
13.83
13.94
14.05
14.16
14.28
14.39
14.50
14.61
14.72
14.83
14.95
15.06
15.17
15.28
15.40
-1.79
-1.82
-1.85
-1.88
-1.92
-1.95
-1.98
-2.02
-2.05
-2.08
-2.12
-2.15
-2.19
-2.22
-2.26
-2.29
-2.33
-2.36
-2.40
-2.44
-2.47
-2.51
-2.55
-2.59
-2.62
-2.66
-2.70
-2.74
-2.78
-2.82
-2.86
-2.90
-2.94
-2.98
-3.02
-3.06
-3.10
-3.14
-3.18
-3.22
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
125
62.42
62.65
62.87
63.10
63.33
63.55
63.78
64.00
64.23
64.45
64.68
64.90
65.13
65.35
65.58
65.80
66.02
66.25
66.47
66.69
66.92
67.14
67.36
67.58
67.80
68.03
68.25
68.47
68.69
68.91
69.13
69.35
69.57
69.79
70.01
70.23
70.45
70.67
70.89
71.10
25.42
25.54
25.66
25.78
25.91
26.03
26.15
26.27
26.39
26.51
26.63
26.76
26.88
27.00
27.12
27.24
27.37
27.49
27.61
27.73
27.86
27.98
28.10
28.22
28.35
28.47
28.59
28.72
28.84
28.96
29.09
29.21
29.33
29.46
29.58
29.71
29.83
29.95
30.08
30.20
-7.72
-7.78
-7.85
-7.91
-7.97
-8.04
-8.10
-8.16
-8.23
-8.29
-8.36
-8.42
-8.49
-8.55
-8.62
-8.68
-8.75
-8.82
-8.88
-8.95
-9.02
-9.08
-9.15
-9.22
-9.29
-9.35
-9.42
-9.49
-9.56
-9.63
-9.70
-9.77
-9.83
-9.90
-9.97
-10.04
-10.11
-10.19
-10.26
-10.33
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
42.09
42.34
42.60
42.85
43.10
43.35
43.60
43.85
44.10
44.35
44.60
44.85
45.10
45.34
45.59
45.84
46.09
46.33
46.58
46.83
47.07
47.32
47.56
47.81
48.05
48.30
48.54
48.78
49.03
49.27
49.51
49.75
50.00
50.24
50.48
50.72
50.96
51.20
51.44
51.68
15.51
15.62
15.73
15.85
15.96
16.07
16.18
16.30
16.41
16.52
16.64
16.75
16.87
16.98
17.09
17.21
17.32
17.43
17.55
17.66
17.78
17.89
18.01
18.12
18.24
18.35
18.47
18.58
18.70
18.81
18.93
19.04
19.16
19.27
19.39
19.51
19.62
19.74
19.85
19.97
-3.27
-3.31
-3.35
-3.39
-3.44
-3.48
-3.52
-3.57
-3.61
-3.65
-3.70
-3.74
-3.79
-3.83
-3.88
-3.93
-3.97
-4.02
-4.06
-4.11
-4.16
-4.20
-4.25
-4.30
-4.35
-4.40
-4.44
-4.49
-4.54
-4.59
-4.64
-4.69
-4.74
-4.79
-4.84
-4.89
-4.94
-4.99
-5.04
-5.10
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
126
71.32
71.54
71.76
71.98
72.19
72.41
72.63
72.84
73.06
73.28
73.49
73.71
73.93
74.14
74.36
74.57
74.79
75.00
75.22
75.43
75.64
75.86
76.07
76.28
76.50
76.71
76.92
77.14
77.35
77.56
77.77
77.99
78.20
78.41
78.62
78.83
79.04
79.25
79.46
79.67
30.33
30.45
30.58
30.70
30.83
30.95
31.08
31.20
31.33
31.45
31.58
31.70
31.83
31.95
32.08
32.21
32.33
32.46
32.58
32.71
32.84
32.96
33.09
33.22
33.34
33.47
33.60
33.73
33.85
33.98
34.11
34.23
34.36
34.49
34.62
34.75
34.87
35.00
35.13
35.26
-10.40
-10.47
-10.54
-10.61
-10.69
-10.76
-10.83
-10.90
-10.98
-11.05
-11.12
-11.20
-11.27
-11.34
-11.42
-11.49
-11.57
-11.64
-11.72
-11.79
-11.87
-11.94
-12.02
-12.10
-12.17
-12.25
-12.33
-12.40
-12.48
-12.56
-12.64
-12.71
-12.79
-12.87
-12.95
-13.03
-13.11
-13.18
-13.26
-13.34
486
487
488
489
490
491
492
493
494
495
496
497
498
499
51.92
52.16
52.40
52.64
52.88
53.12
53.35
53.59
53.83
54.07
54.30
54.54
54.78
55.01
20.09
20.20
20.32
20.44
20.55
20.67
20.79
20.90
21.02
21.14
21.26
21.37
21.49
21.61
-5.15
-5.20
-5.25
-5.30
-5.36
-5.41
-5.46
-5.52
-5.57
-5.62
-5.68
-5.73
-5.79
-5.84
611
612
613
614
615
616
617
618
619
620
621
622
623
623.15
127
79.88
80.09
80.30
80.51
80.72
80.93
81.14
81.35
81.56
81.77
81.98
82.19
82.39
82.42
35.39
35.51
35.64
35.77
35.90
36.03
36.16
36.29
36.42
36.55
36.67
36.80
36.93
36.95
-13.42
-13.50
-13.58
-13.66
-13.74
-13.83
-13.91
-13.99
-14.07
-14.15
-14.23
-14.31
-14.40
-14.41
Appendix F
Table F.1 Thermodynamic properties of LiNO3-NaNO3 -KNO3-KNO2 compound in solid
state (298.15-359.15K)
T/(K)
298.15
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
ΔS
(J/mol.K)
0.00
0.29
0.63
0.97
1.31
1.65
1.99
2.33
2.67
3.00
3.34
3.68
4.01
4.35
4.68
5.02
5.35
5.69
6.02
6.35
6.68
7.02
7.35
7.68
8.01
8.34
8.67
9.00
9.32
9.65
9.98
10.30
ΔH
(kJ/mol)
0.00
0.09
0.19
0.29
0.39
0.50
0.60
0.70
0.81
0.91
1.01
1.12
1.22
1.33
1.43
1.53
1.64
1.74
1.85
1.96
2.06
2.17
2.27
2.38
2.48
2.59
2.70
2.80
2.91
3.02
3.13
3.23
ΔG
(kJ/mol)
0.00
0.00
0.00
0.00
0.00
0.00
-0.01
-0.01
-0.01
-0.01
-0.02
-0.02
-0.02
-0.03
-0.03
-0.04
-0.04
-0.05
-0.05
-0.06
-0.06
-0.07
-0.08
-0.09
-0.09
-0.10
-0.11
-0.12
-0.13
-0.14
-0.15
-0.16
T/(K)
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
359.15
128
ΔS
(J/mol.K)
10.63
10.96
11.28
11.61
11.93
12.25
12.58
12.90
13.22
13.55
13.87
14.19
14.51
14.83
15.15
15.47
15.78
16.10
16.42
16.74
17.05
17.37
17.69
18.00
18.32
18.63
18.94
19.26
19.57
19.88
19.93
ΔH
(kJ/mol)
3.34
3.45
3.56
3.66
3.77
3.88
3.99
4.10
4.21
4.32
4.43
4.54
4.64
4.75
4.86
4.97
5.08
5.19
5.31
5.42
5.53
5.64
5.75
5.86
5.97
6.08
6.19
6.31
6.42
6.53
6.55
ΔG
(kJ/mol)
-0.17
-0.18
-0.19
-0.20
-0.21
-0.22
-0.24
-0.25
-0.26
-0.28
-0.29
-0.30
-0.32
-0.33
-0.35
-0.36
-0.38
-0.39
-0.41
-0.43
-0.44
-0.46
-0.48
-0.49
-0.51
-0.53
-0.55
-0.57
-0.59
-0.61
-0.61
Table F.2 Thermodynamic properties of LiNO3-NaNO3 -KNO3-KNO2 compound in liquid
state (375.15-623.15K)
T/(K)
375.15
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
ΔS
ΔH
ΔG
(J/mol.K) (kJ/mol) (kJ/mol)
26.91
9.26
-0.83
27.17
9.36
-0.85
27.47
9.48
-0.88
27.78
9.59
-0.91
28.08
9.71
-0.94
28.38
9.82
-0.96
28.69
9.94
-0.99
28.99
10.05
-1.02
29.29
10.17
-1.05
29.59
10.28
-1.08
29.89
10.40
-1.11
30.19
10.51
-1.14
30.49
10.63
-1.17
30.79
10.75
-1.20
31.09
10.86
-1.23
31.38
10.98
-1.26
31.68
11.09
-1.29
31.98
11.21
-1.33
32.27
11.32
-1.36
32.57
11.44
-1.39
32.86
11.56
-1.42
33.16
11.67
-1.46
33.45
11.79
-1.49
33.74
11.91
-1.52
34.03
12.02
-1.56
34.33
12.14
-1.59
34.62
12.26
-1.63
34.91
12.37
-1.66
35.20
12.49
-1.70
35.49
12.61
-1.73
35.78
12.72
-1.77
129
T/(K)
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
ΔS
ΔH
ΔG
(J/mol.K) (kJ/mol) (kJ/mol)
61.11
24.16
-6.40
61.36
24.28
-6.46
61.61
24.40
-6.52
61.85
24.53
-6.58
62.10
24.65
-6.65
62.35
24.78
-6.71
62.59
24.90
-6.77
62.84
25.02
-6.83
63.08
25.15
-6.90
63.33
25.27
-6.96
63.57
25.40
-7.02
63.81
25.52
-7.09
64.06
25.65
-7.15
64.30
25.77
-7.21
64.54
25.90
-7.28
64.79
26.02
-7.34
65.03
26.15
-7.41
65.27
26.27
-7.47
65.51
26.40
-7.54
65.75
26.52
-7.60
65.99
26.65
-7.67
66.24
26.77
-7.74
66.48
26.90
-7.80
66.72
27.02
-7.87
66.96
27.15
-7.94
67.19
27.27
-8.00
67.43
27.40
-8.07
67.67
27.53
-8.14
67.91
27.65
-8.21
68.15
27.78
-8.27
68.39
27.90
-8.34
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
36.06
36.35
36.64
36.93
37.21
37.50
37.78
38.07
38.35
38.64
38.92
39.20
39.48
39.77
40.05
40.33
40.61
40.89
41.17
41.45
41.72
42.00
42.28
42.56
42.83
43.11
43.38
43.66
43.93
44.21
44.48
44.75
45.03
45.30
45.57
45.84
46.11
46.38
46.65
46.92
12.84
12.96
13.07
13.19
13.31
13.43
13.54
13.66
13.78
13.90
14.01
14.13
14.25
14.37
14.49
14.60
14.72
14.84
14.96
15.08
15.19
15.31
15.43
15.55
15.67
15.79
15.91
16.03
16.14
16.26
16.38
16.50
16.62
16.74
16.86
16.98
17.10
17.22
17.34
17.46
-1.80
-1.84
-1.87
-1.91
-1.95
-1.99
-2.02
-2.06
-2.10
-2.14
-2.18
-2.22
-2.26
-2.30
-2.34
-2.38
-2.42
-2.46
-2.50
-2.54
-2.58
-2.62
-2.66
-2.71
-2.75
-2.79
-2.84
-2.88
-2.92
-2.97
-3.01
-3.06
-3.10
-3.15
-3.19
-3.24
-3.28
-3.33
-3.38
-3.42
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
130
68.62
68.86
69.10
69.33
69.57
69.81
70.04
70.28
70.51
70.75
70.98
71.22
71.45
71.68
71.92
72.15
72.38
72.61
72.85
73.08
73.31
73.54
73.77
74.00
74.23
74.46
74.69
74.92
75.15
75.38
75.61
75.84
76.07
76.29
76.52
76.75
76.97
77.20
77.43
77.65
28.03
28.15
28.28
28.41
28.53
28.66
28.79
28.91
29.04
29.17
29.29
29.42
29.55
29.67
29.80
29.93
30.05
30.18
30.31
30.44
30.56
30.69
30.82
30.95
31.07
31.20
31.33
31.46
31.59
31.71
31.84
31.97
32.10
32.23
32.35
32.48
32.61
32.74
32.87
33.00
-8.41
-8.48
-8.55
-8.62
-8.69
-8.76
-8.83
-8.90
-8.97
-9.04
-9.11
-9.18
-9.25
-9.32
-9.39
-9.47
-9.54
-9.61
-9.68
-9.76
-9.83
-9.90
-9.98
-10.05
-10.13
-10.20
-10.27
-10.35
-10.42
-10.50
-10.58
-10.65
-10.73
-10.80
-10.88
-10.96
-11.03
-11.11
-11.19
-11.26
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
47.19
47.46
47.73
48.00
48.26
48.53
48.80
49.06
49.33
49.59
49.86
50.12
50.39
50.65
50.91
51.18
51.44
51.70
51.96
52.22
52.48
52.74
53.00
53.26
53.52
53.78
54.04
54.30
54.55
54.81
55.07
55.32
55.58
55.83
56.09
56.34
56.60
56.85
57.10
57.36
17.58
17.70
17.82
17.94
18.06
18.18
18.30
18.42
18.54
18.66
18.78
18.90
19.02
19.14
19.26
19.38
19.51
19.63
19.75
19.87
19.99
20.11
20.23
20.35
20.48
20.60
20.72
20.84
20.96
21.08
21.21
21.33
21.45
21.57
21.70
21.82
21.94
22.06
22.19
22.31
-3.47
-3.52
-3.56
-3.61
-3.66
-3.71
-3.76
-3.81
-3.86
-3.91
-3.96
-4.01
-4.06
-4.11
-4.16
-4.21
-4.26
-4.31
-4.36
-4.41
-4.47
-4.52
-4.57
-4.63
-4.68
-4.73
-4.79
-4.84
-4.90
-4.95
-5.00
-5.06
-5.12
-5.17
-5.23
-5.28
-5.34
-5.40
-5.45
-5.51
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
131
77.88
78.11
78.33
78.56
78.78
79.01
79.23
79.45
79.68
79.90
80.12
80.35
80.57
80.79
81.01
81.24
81.46
81.68
81.90
82.12
82.34
82.56
82.78
83.00
83.22
83.44
83.66
83.88
84.10
84.32
84.54
84.75
84.97
85.19
85.41
85.62
85.84
86.06
86.27
86.49
33.13
33.26
33.38
33.51
33.64
33.77
33.90
34.03
34.16
34.29
34.42
34.55
34.68
34.81
34.94
35.07
35.20
35.33
35.46
35.59
35.72
35.85
35.98
36.11
36.24
36.37
36.50
36.63
36.76
36.90
37.03
37.16
37.29
37.42
37.55
37.68
37.81
37.95
38.08
38.21
-11.34
-11.42
-11.50
-11.58
-11.66
-11.73
-11.81
-11.89
-11.97
-12.05
-12.13
-12.21
-12.29
-12.37
-12.45
-12.54
-12.62
-12.70
-12.78
-12.86
-12.94
-13.03
-13.11
-13.19
-13.28
-13.36
-13.44
-13.53
-13.61
-13.69
-13.78
-13.86
-13.95
-14.03
-14.12
-14.20
-14.29
-14.38
-14.46
-14.55
486
487
488
489
490
491
492
493
494
495
496
497
498
499
57.61
57.86
58.12
58.37
58.62
58.87
59.12
59.37
59.62
59.87
60.12
60.37
60.62
60.86
22.43
22.55
22.68
22.80
22.92
23.05
23.17
23.29
23.42
23.54
23.66
23.79
23.91
24.03
-5.57
-5.63
-5.68
-5.74
-5.80
-5.86
-5.92
-5.98
-6.04
-6.10
-6.16
-6.22
-6.28
-6.34
611
612
613
614
615
616
617
618
619
620
621
622
623
623.15
132
86.70
86.92
87.13
87.35
87.56
87.78
87.99
88.21
88.42
88.64
88.85
89.06
89.28
89.31
38.34
38.47
38.60
38.74
38.87
39.00
39.13
39.26
39.40
39.53
39.66
39.79
39.93
39.95
-14.64
-14.72
-14.81
-14.90
-14.98
-15.07
-15.16
-15.25
-15.34
-15.42
-15.51
-15.60
-15.69
-15.70
Appendix G
Table G.1 Thermodynamic properties of LiNO3-KNO3-NaNO2-Mg(NO3)2 compound in
solid I state (298.15-337.15K)
T/(K)
298.15
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
ΔS
(J/mol.K)
0.00
0.24
0.52
0.80
1.08
1.36
1.64
1.92
2.19
2.47
2.75
3.03
3.30
3.58
3.86
4.13
4.41
4.68
4.96
5.23
5.51
ΔH
(kJ/mol)
0.00
0.00
0.00
0.07
0.16
0.24
0.32
0.41
0.49
0.58
0.67
0.75
0.84
0.92
1.01
1.09
1.18
1.27
1.35
1.44
1.53
ΔG
(kJ/mol)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.01
-0.01
-0.01
-0.01
-0.02
-0.02
-0.02
-0.03
-0.03
-0.03
-0.04
T/(K)
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
337.15
ΔS
(J/mol.K)
5.78
6.06
6.33
6.60
6.88
7.15
7.42
7.69
7.96
8.23
8.51
8.78
9.05
9.32
9.59
9.85
10.12
10.39
10.66
10.70
ΔH
(kJ/mol)
1.62
1.70
1.79
1.88
1.97
2.05
2.14
2.23
2.32
2.41
2.50
2.59
2.68
2.77
2.85
2.94
3.03
3.12
3.21
3.31
ΔG
(kJ/mol)
-0.04
-0.05
-0.05
-0.06
-0.07
-0.07
-0.08
-0.09
-0.09
-0.10
-0.11
-0.11
-0.12
-0.13
-0.14
-0.15
-0.16
-0.17
-0.18
-0.19
Table G.2 Thermodynamic properties of LiNO3-KNO3-NaNO2-Mg(NO3)2 compound in
solid II state (361.15-364.15K)
T/(K)
361.15
ΔS
ΔH
ΔG
(J/mol.K) (kJ/mol) (kJ/mol)
24.33
8.25
-0.54
133
362
363
364
364.15
24.54
24.78
25.03
25.06
8.32
8.41
8.50
8.51
-0.56
-0.59
-0.61
-0.62
Table G.3 Thermodynamic properties of LiNO3-KNO3-NaNO2-Mg(NO3)2 compound in
liquid state (411.15-623.15K)
T/(K)
411.15
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
ΔS
(J/mol.K)
38.33
38.57
38.85
39.13
39.41
39.69
39.97
40.25
40.53
40.81
41.09
41.37
41.65
41.92
42.20
42.48
42.75
43.03
43.30
43.58
43.85
44.12
44.39
44.67
ΔH
(kJ/mol)
13.66
13.76
13.87
13.99
14.11
14.22
14.34
14.46
14.57
14.69
14.81
14.93
15.04
15.16
15.28
15.39
15.51
15.63
15.75
15.87
15.98
16.10
16.22
16.34
ΔG
(kJ/mol)
-2.10
-2.13
-2.17
-2.21
-2.25
-2.29
-2.33
-2.37
-2.41
-2.45
-2.49
-2.53
-2.57
-2.62
-2.66
-2.70
-2.74
-2.79
-2.83
-2.87
-2.92
-2.96
-3.00
-3.05
T/(K)
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
134
ΔS
(J/mol.K)
66.04
66.28
66.52
66.75
66.99
67.23
67.47
67.70
67.94
68.18
68.41
68.65
68.88
69.12
69.35
69.59
69.82
70.05
70.29
70.52
70.75
70.98
71.22
71.45
ΔH
(kJ/mol)
26.49
26.61
26.74
26.86
26.99
27.11
27.23
27.36
27.48
27.61
27.73
27.86
27.98
28.10
28.23
28.35
28.48
28.60
28.73
28.85
28.98
29.10
29.23
29.35
ΔG
(kJ/mol)
-7.72
-7.78
-7.85
-7.92
-7.98
-8.05
-8.12
-8.19
-8.25
-8.32
-8.39
-8.46
-8.53
-8.60
-8.67
-8.73
-8.80
-8.87
-8.94
-9.02
-9.09
-9.16
-9.23
-9.30
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
44.94
45.21
45.48
45.75
46.02
46.29
46.56
46.83
47.10
47.36
47.63
47.90
48.16
48.43
48.69
48.96
49.22
49.49
49.75
50.02
50.28
50.54
50.80
51.06
51.32
51.59
51.85
52.11
52.36
52.62
52.88
53.14
53.40
53.66
53.91
54.17
54.42
54.68
54.94
55.19
16.46
16.57
16.69
16.81
16.93
17.05
17.16
17.28
17.40
17.52
17.64
17.76
17.88
18.00
18.12
18.23
18.35
18.47
18.59
18.71
18.83
18.95
19.07
19.19
19.31
19.43
19.55
19.67
19.79
19.91
20.03
20.15
20.27
20.39
20.51
20.63
20.75
20.87
20.99
21.11
-3.09
-3.14
-3.18
-3.23
-3.28
-3.32
-3.37
-3.41
-3.46
-3.51
-3.56
-3.60
-3.65
-3.70
-3.75
-3.80
-3.85
-3.90
-3.95
-4.00
-4.05
-4.10
-4.15
-4.20
-4.25
-4.30
-4.35
-4.40
-4.46
-4.51
-4.56
-4.61
-4.67
-4.72
-4.78
-4.83
-4.88
-4.94
-4.99
-5.05
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
135
71.68
71.91
72.14
72.37
72.60
72.83
73.06
73.29
73.52
73.75
73.98
74.20
74.43
74.66
74.89
75.11
75.34
75.57
75.79
76.02
76.25
76.47
76.70
76.92
77.14
77.37
77.59
77.82
78.04
78.26
78.49
78.71
78.93
79.15
79.37
79.60
79.82
80.04
80.26
80.48
29.48
29.60
29.73
29.86
29.98
30.11
30.23
30.36
30.48
30.61
30.74
30.86
30.99
31.11
31.24
31.37
31.49
31.62
31.75
31.87
32.00
32.13
32.25
32.38
32.51
32.63
32.76
32.89
33.02
33.14
33.27
33.40
33.52
33.65
33.78
33.91
34.04
34.16
34.29
34.42
-9.37
-9.44
-9.51
-9.59
-9.66
-9.73
-9.80
-9.88
-9.95
-10.03
-10.10
-10.17
-10.25
-10.32
-10.40
-10.47
-10.55
-10.62
-10.70
-10.77
-10.85
-10.93
-11.00
-11.08
-11.16
-11.23
-11.31
-11.39
-11.47
-11.55
-11.62
-11.70
-11.78
-11.86
-11.94
-12.02
-12.10
-12.18
-12.26
-12.34
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
55.45
55.70
55.95
56.21
56.46
56.71
56.96
57.22
57.47
57.72
57.97
58.22
58.47
58.72
58.97
59.22
59.47
59.71
59.96
60.21
60.46
60.70
60.95
61.19
61.44
61.69
61.93
62.17
62.42
62.66
62.91
63.15
63.39
63.63
63.88
64.12
64.36
64.60
64.84
65.08
21.23
21.35
21.47
21.60
21.72
21.84
21.96
22.08
22.20
22.32
22.44
22.57
22.69
22.81
22.93
23.05
23.17
23.30
23.42
23.54
23.66
23.79
23.91
24.03
24.15
24.27
24.40
24.52
24.64
24.77
24.89
25.01
25.13
25.26
25.38
25.50
25.63
25.75
25.87
26.00
-5.10
-5.16
-5.21
-5.27
-5.33
-5.38
-5.44
-5.50
-5.55
-5.61
-5.67
-5.73
-5.79
-5.85
-5.90
-5.96
-6.02
-6.08
-6.14
-6.20
-6.26
-6.32
-6.38
-6.45
-6.51
-6.57
-6.63
-6.69
-6.75
-6.82
-6.88
-6.94
-7.01
-7.07
-7.13
-7.20
-7.26
-7.33
-7.39
-7.46
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
136
80.70
80.92
81.14
81.36
81.58
81.80
82.01
82.23
82.45
82.67
82.89
83.10
83.32
83.54
83.75
83.97
84.19
84.40
84.62
84.83
85.05
85.26
85.48
85.69
85.91
86.12
86.33
86.55
86.76
86.97
87.19
87.40
87.61
87.82
88.03
88.25
88.46
88.67
88.88
89.09
34.55
34.68
34.80
34.93
35.06
35.19
35.32
35.45
35.57
35.70
35.83
35.96
36.09
36.22
36.35
36.48
36.60
36.73
36.86
36.99
37.12
37.25
37.38
37.51
37.64
37.77
37.90
38.03
38.16
38.29
38.42
38.55
38.68
38.81
38.94
39.07
39.20
39.33
39.46
39.59
-12.42
-12.50
-12.58
-12.66
-12.74
-12.83
-12.91
-12.99
-13.07
-13.15
-13.24
-13.32
-13.40
-13.49
-13.57
-13.65
-13.74
-13.82
-13.91
-13.99
-14.08
-14.16
-14.25
-14.33
-14.42
-14.51
-14.59
-14.68
-14.76
-14.85
-14.94
-15.03
-15.11
-15.20
-15.29
-15.38
-15.47
-15.55
-15.64
-15.73
515
516
517
65.32
65.56
65.80
26.12
26.24
26.37
-7.52
-7.59
-7.65
622
623
623.15
137
89.30
89.51
89.54
39.72
39.85
39.87
-15.82
-15.91
-15.92
Appendix H
Table H.1 Thermodynamic properties of LiNO3-KNO3-NaNO2-KNO2 compound in solid I
state (298.15-354.15K)
T/(K)
298.15
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
ΔS
(J/mol.K)
0.00
0.23
0.50
0.77
1.04
1.31
1.58
1.85
2.12
2.39
2.65
2.92
3.19
3.45
3.72
3.99
4.25
4.52
4.78
5.05
5.31
5.58
5.84
6.11
6.37
6.63
6.89
7.16
7.42
ΔH
(kJ/mol)
0.00
0.07
0.15
0.23
0.31
0.39
0.48
0.56
0.64
0.72
0.81
0.89
0.97
1.05
1.14
1.22
1.30
1.39
1.47
1.56
1.64
1.72
1.81
1.89
1.98
2.06
2.15
2.23
2.32
ΔG
(kJ/mol)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.01
-0.01
-0.01
-0.01
-0.01
-0.02
-0.02
-0.02
-0.03
-0.03
-0.04
-0.04
-0.04
-0.05
-0.05
-0.06
-0.07
-0.07
-0.08
-0.08
-0.09
-0.10
T/(K)
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
354.15
138
ΔS
(J/mol.K)
7.68
7.94
8.20
8.46
8.72
8.98
9.24
9.50
9.76
10.02
10.28
10.53
10.79
11.05
11.30
11.56
11.82
12.07
12.33
12.58
12.84
13.09
13.35
13.60
13.85
14.11
14.36
14.61
14.65
ΔH
(kJ/mol)
2.41
2.49
2.58
2.66
2.75
2.84
2.92
3.01
3.10
3.18
3.27
3.36
3.44
3.53
3.62
3.71
3.79
3.88
3.97
4.06
4.15
4.24
4.33
4.41
4.50
4.59
4.68
4.77
4.78
ΔG
(kJ/mol)
-0.11
-0.11
-0.12
-0.13
-0.14
-0.15
-0.16
-0.16
-0.17
-0.18
-0.19
-0.20
-0.21
-0.22
-0.24
-0.25
-0.26
-0.27
-0.28
-0.29
-0.31
-0.32
-0.33
-0.35
-0.36
-0.37
-0.39
-0.40
-0.40
Table H.2 Thermodynamic properties of LiNO3-KNO3-NaNO2-KNO2 compound in solid 2
state (362.15-373.15K)
T/(K)
362.15
363
364
365
366
367
368
369
370
371
372
373
373.15
ΔS
(J/mol.K)
23.87
24.08
24.32
24.57
24.81
25.06
25.30
25.55
25.79
26.04
26.28
26.53
26.57
ΔH
(kJ/mol)
7.77
8.09
8.17
8.26
8.35
8.43
8.52
8.61
8.70
8.79
8.88
8.98
9.07
ΔG
(kJ/mol)
-0.46
-0.55
-0.57
-0.60
-0.62
-0.65
-0.67
-0.70
-0.72
-0.75
-0.77
-0.80
-0.83
Table H.3 Thermodynamic properties of LiNO3-KNO3-NaNO2-KNO2 compound in liquid
state (379.15-623.15K)
T/(K)
379.15
380
381
382
383
384
385
386
387
ΔS
(J/mol.K)
29.66
29.91
30.20
30.48
30.77
31.05
31.34
31.62
31.91
ΔH
(kJ/mol)
10.25
10.34
10.45
10.56
10.67
10.78
10.89
11.00
11.11
ΔG
(kJ/mol)
-1.00
-1.02
-1.05
-1.08
-1.12
-1.15
-1.18
-1.21
-1.24
T/(K)
502
503
504
505
506
507
508
509
510
139
ΔS
(J/mol.K)
61.74
61.98
62.22
62.46
62.70
62.94
63.17
63.41
63.65
ΔH
(kJ/mol)
24.32
24.44
24.56
24.68
24.80
24.92
25.04
25.16
25.28
ΔG
(kJ/mol)
-6.67
-6.74
-6.80
-6.86
-6.92
-6.99
-7.05
-7.11
-7.18
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
32.19
32.47
32.75
33.04
33.32
33.60
33.88
34.16
34.44
34.72
35.00
35.27
35.55
35.83
36.11
36.38
36.66
36.93
37.21
37.48
37.76
38.03
38.30
38.57
38.85
39.12
39.39
39.66
39.93
40.20
40.47
40.74
41.01
41.28
41.54
41.81
42.08
42.34
42.61
42.88
11.22
11.33
11.44
11.55
11.66
11.77
11.88
11.99
12.10
12.21
12.32
12.43
12.54
12.65
12.76
12.87
12.99
13.10
13.21
13.32
13.43
13.54
13.66
13.77
13.88
13.99
14.10
14.22
14.33
14.44
14.55
14.67
14.78
14.89
15.00
15.12
15.23
15.34
15.46
15.57
-1.27
-1.30
-1.34
-1.37
-1.40
-1.44
-1.47
-1.50
-1.54
-1.57
-1.61
-1.64
-1.68
-1.71
-1.75
-1.79
-1.82
-1.86
-1.90
-1.93
-1.97
-2.01
-2.05
-2.09
-2.13
-2.16
-2.20
-2.24
-2.28
-2.32
-2.36
-2.40
-2.45
-2.49
-2.53
-2.57
-2.61
-2.65
-2.70
-2.74
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
140
63.88
64.12
64.36
64.59
64.83
65.06
65.30
65.53
65.77
66.00
66.24
66.47
66.70
66.94
67.17
67.40
67.63
67.86
68.10
68.33
68.56
68.79
69.02
69.25
69.48
69.71
69.94
70.17
70.40
70.63
70.86
71.08
71.31
71.54
71.77
71.99
72.22
72.45
72.67
72.90
25.41
25.53
25.65
25.77
25.89
26.01
26.13
26.25
26.38
26.50
26.62
26.74
26.86
26.98
27.11
27.23
27.35
27.47
27.60
27.72
27.84
27.96
28.09
28.21
28.33
28.45
28.58
28.70
28.82
28.95
29.07
29.19
29.32
29.44
29.57
29.69
29.81
29.94
30.06
30.19
-7.24
-7.30
-7.37
-7.43
-7.50
-7.56
-7.63
-7.69
-7.76
-7.82
-7.89
-7.96
-8.02
-8.09
-8.16
-8.22
-8.29
-8.36
-8.43
-8.50
-8.56
-8.63
-8.70
-8.77
-8.84
-8.91
-8.98
-9.05
-9.12
-9.19
-9.26
-9.33
-9.40
-9.47
-9.55
-9.62
-9.69
-9.76
-9.84
-9.91
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
43.14
43.41
43.67
43.93
44.20
44.46
44.72
44.99
45.25
45.51
45.77
46.03
46.29
46.55
46.81
47.07
47.33
47.59
47.85
48.10
48.36
48.62
48.88
49.13
49.39
49.64
49.90
50.15
50.41
50.66
50.92
51.17
51.42
51.67
51.93
52.18
52.43
52.68
52.93
53.18
15.68
15.80
15.91
16.02
16.14
16.25
16.36
16.48
16.59
16.71
16.82
16.94
17.05
17.16
17.28
17.39
17.51
17.62
17.74
17.85
17.97
18.08
18.20
18.32
18.43
18.55
18.66
18.78
18.89
19.01
19.13
19.24
19.36
19.47
19.59
19.71
19.82
19.94
20.06
20.17
-2.78
-2.82
-2.87
-2.91
-2.96
-3.00
-3.05
-3.09
-3.14
-3.18
-3.23
-3.27
-3.32
-3.36
-3.41
-3.46
-3.51
-3.55
-3.60
-3.65
-3.70
-3.75
-3.79
-3.84
-3.89
-3.94
-3.99
-4.04
-4.09
-4.14
-4.19
-4.24
-4.30
-4.35
-4.40
-4.45
-4.50
-4.56
-4.61
-4.66
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
141
73.13
73.35
73.58
73.80
74.03
74.25
74.48
74.70
74.92
75.15
75.37
75.60
75.82
76.04
76.26
76.49
76.71
76.93
77.15
77.37
77.59
77.82
78.04
78.26
78.48
78.70
78.92
79.14
79.36
79.57
79.79
80.01
80.23
80.45
80.67
80.88
81.10
81.32
81.54
81.75
30.31
30.44
30.56
30.68
30.81
30.93
31.06
31.18
31.31
31.43
31.56
31.69
31.81
31.94
32.06
32.19
32.31
32.44
32.57
32.69
32.82
32.94
33.07
33.20
33.32
33.45
33.58
33.70
33.83
33.96
34.08
34.21
34.34
34.47
34.59
34.72
34.85
34.98
35.10
35.23
-9.98
-10.05
-10.13
-10.20
-10.28
-10.35
-10.42
-10.50
-10.57
-10.65
-10.72
-10.80
-10.87
-10.95
-11.03
-11.10
-11.18
-11.26
-11.33
-11.41
-11.49
-11.57
-11.64
-11.72
-11.80
-11.88
-11.96
-12.04
-12.12
-12.20
-12.28
-12.36
-12.44
-12.52
-12.60
-12.68
-12.76
-12.84
-12.92
-13.00
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
53.43
53.68
53.93
54.18
54.43
54.68
54.93
55.17
55.42
55.67
55.92
56.16
56.41
56.65
56.90
57.15
57.39
57.63
57.88
58.12
58.37
58.61
58.85
59.10
59.34
59.58
59.82
60.06
60.30
60.55
60.79
61.03
61.27
61.51
20.29
20.41
20.53
20.64
20.76
20.88
21.00
21.11
21.23
21.35
21.47
21.58
21.70
21.82
21.94
22.06
22.18
22.29
22.41
22.53
22.65
22.77
22.89
23.01
23.13
23.24
23.36
23.48
23.60
23.72
23.84
23.96
24.08
24.20
-4.72
-4.77
-4.82
-4.88
-4.93
-4.99
-5.04
-5.10
-5.15
-5.21
-5.26
-5.32
-5.37
-5.43
-5.49
-5.54
-5.60
-5.66
-5.72
-5.78
-5.83
-5.89
-5.95
-6.01
-6.07
-6.13
-6.19
-6.25
-6.31
-6.37
-6.43
-6.49
-6.55
-6.61
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
623.15
142
81.97
82.19
82.40
82.62
82.83
83.05
83.27
83.48
83.70
83.91
84.13
84.34
84.55
84.77
84.98
85.20
85.41
85.62
85.83
86.05
86.26
86.47
86.68
86.90
87.11
87.32
87.53
87.74
87.95
88.16
88.37
88.58
88.79
88.83
35.36
35.49
35.62
35.74
35.87
36.00
36.13
36.26
36.39
36.52
36.64
36.77
36.90
37.03
37.16
37.29
37.42
37.55
37.68
37.81
37.94
38.07
38.20
38.33
38.46
38.59
38.72
38.85
38.98
39.11
39.24
39.37
39.50
39.52
-13.08
-13.17
-13.25
-13.33
-13.41
-13.50
-13.58
-13.66
-13.75
-13.83
-13.91
-14.00
-14.08
-14.17
-14.25
-14.34
-14.42
-14.51
-14.59
-14.68
-14.77
-14.85
-14.94
-15.03
-15.11
-15.20
-15.29
-15.38
-15.46
-15.55
-15.64
-15.73
-15.82
-15.83
Appendix I
Table I.1 Thermodynamic properties of LiNO3-NaNO3 -KNO3-Mg(NO3)2-MgK compound
in solid state (298.15-353.15K)
T/(K)
298.15
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
ΔS
(J/mol.K)
0.00
0.35
0.76
1.17
1.58
1.99
2.40
2.81
3.22
3.63
4.04
4.45
4.86
5.26
5.67
6.08
6.48
6.89
7.29
7.70
8.10
8.50
8.91
9.31
9.71
10.11
10.51
10.91
11.31
ΔH
(kJ/mol)
0.00
0.10
0.23
0.35
0.48
0.60
0.72
0.85
0.97
1.10
1.22
1.35
1.48
1.60
1.73
1.86
1.98
2.11
2.24
2.37
2.50
2.62
2.75
2.88
3.01
3.14
3.27
3.40
3.53
ΔG
(kJ/mol)
0.00
0.00
0.00
0.00
0.00
0.00
-0.01
-0.01
-0.01
-0.02
-0.02
-0.02
-0.03
-0.03
-0.04
-0.05
-0.05
-0.06
-0.07
-0.07
-0.08
-0.09
-0.10
-0.11
-0.12
-0.13
-0.14
-0.15
-0.16
T/(K)
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
353.15
143
ΔS
(J/mol.K)
11.71
12.11
12.50
12.90
13.30
13.69
14.09
14.48
14.88
15.27
15.66
16.05
16.44
16.83
17.22
17.61
18.00
18.39
18.77
19.16
19.55
19.93
20.31
20.70
21.08
21.46
21.84
21.90
ΔH
(kJ/mol)
3.66
3.79
3.92
4.05
4.18
4.31
4.44
4.58
4.71
4.84
4.97
5.10
5.24
5.37
5.50
5.63
5.77
5.90
6.03
6.17
6.30
6.43
6.57
6.70
6.83
6.97
7.10
7.12
ΔG
(kJ/mol)
-0.17
-0.18
-0.19
-0.21
-0.22
-0.23
-0.25
-0.26
-0.28
-0.29
-0.31
-0.32
-0.34
-0.36
-0.37
-0.39
-0.41
-0.43
-0.44
-0.46
-0.48
-0.50
-0.52
-0.54
-0.56
-0.59
-0.61
-0.61
Table I.2 Thermodynamic properties of LiNO3-NaNO3 -KNO3-Mg(NO3)2-MgK compound
in liquid state (391.15-623.15K)
T/(K)
391.15
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
ΔS
(J/mol.K)
44.13
44.50
44.92
45.35
45.77
46.20
46.62
47.04
47.46
47.89
48.31
48.72
49.14
49.56
49.97
50.39
50.80
51.22
51.63
52.04
52.45
52.86
53.27
53.68
54.09
54.50
54.90
55.31
55.71
56.12
56.52
ΔH
(kJ/mol)
10.56
15.35
15.49
15.66
15.83
15.99
16.16
16.33
16.50
16.66
16.83
17.00
17.17
17.34
17.51
17.67
17.84
18.01
18.18
18.35
18.52
18.69
18.85
19.02
19.19
19.36
19.53
19.70
19.87
20.04
20.21
ΔG
(kJ/mol)
-1.91
-1.95
-2.00
-2.04
-2.09
-2.13
-2.18
-2.23
-2.27
-2.32
-2.37
-2.42
-2.47
-2.52
-2.57
-2.62
-2.67
-2.72
-2.77
-2.82
-2.87
-2.93
-2.98
-3.03
-3.09
-3.14
-3.20
-3.25
-3.31
-3.36
-3.42
T/(K)
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
144
ΔS
(J/mol.K)
88.90
89.24
89.59
89.93
90.27
90.62
90.96
91.30
91.64
91.98
92.32
92.66
93.00
93.34
93.68
94.02
94.35
94.69
95.03
95.36
95.70
96.03
96.37
96.70
97.03
97.37
97.70
98.03
98.36
98.69
99.02
ΔH
(kJ/mol)
35.21
35.38
35.56
35.74
35.91
36.09
36.26
36.44
36.61
36.79
36.97
37.14
37.32
37.50
37.67
37.85
38.02
38.20
38.38
38.55
38.73
38.91
39.08
39.26
39.44
39.62
39.79
39.97
40.15
40.32
40.50
ΔG
(kJ/mol)
-9.78
-9.86
-9.95
-10.04
-10.13
-10.22
-10.31
-10.41
-10.50
-10.59
-10.68
-10.77
-10.87
-10.96
-11.05
-11.15
-11.24
-11.34
-11.43
-11.52
-11.62
-11.72
-11.81
-11.91
-12.01
-12.10
-12.20
-12.30
-12.40
-12.49
-12.59
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
56.92
57.32
57.72
58.12
58.52
58.92
59.32
59.71
60.11
60.51
60.90
61.29
61.69
62.08
62.47
62.86
63.25
63.64
64.03
64.42
64.80
65.19
65.57
65.96
66.34
66.73
67.11
67.49
67.87
68.25
68.63
69.01
69.39
69.77
70.15
70.52
70.90
71.28
71.65
72.02
20.38
20.55
20.72
20.89
21.06
21.23
21.40
21.57
21.74
21.91
22.08
22.25
22.42
22.59
22.76
22.93
23.10
23.27
23.44
23.61
23.78
23.95
24.12
24.29
24.46
24.64
24.81
24.98
25.15
25.32
25.49
25.66
25.84
26.01
26.18
26.35
26.52
26.70
26.87
27.04
-3.47
-3.53
-3.59
-3.65
-3.71
-3.76
-3.82
-3.88
-3.94
-4.00
-4.06
-4.12
-4.19
-4.25
-4.31
-4.37
-4.44
-4.50
-4.56
-4.63
-4.69
-4.76
-4.82
-4.89
-4.95
-5.02
-5.09
-5.15
-5.22
-5.29
-5.36
-5.43
-5.50
-5.57
-5.64
-5.71
-5.78
-5.85
-5.92
-5.99
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
145
99.35
99.68
100.01
100.34
100.66
100.99
101.32
101.65
101.97
102.30
102.62
102.95
103.27
103.59
103.92
104.24
104.56
104.88
105.20
105.53
105.85
106.17
106.48
106.80
107.12
107.44
107.76
108.08
108.39
108.71
109.02
109.34
109.65
109.97
110.28
110.60
110.91
111.22
111.54
111.85
40.68
40.86
41.04
41.21
41.39
41.57
41.75
41.92
42.10
42.28
42.46
42.64
42.82
42.99
43.17
43.35
43.53
43.71
43.89
44.07
44.24
44.42
44.60
44.78
44.96
45.14
45.32
45.50
45.68
45.86
46.04
46.22
46.40
46.58
46.76
46.94
47.12
47.30
47.48
47.66
-12.69
-12.79
-12.89
-12.99
-13.09
-13.19
-13.29
-13.40
-13.50
-13.60
-13.70
-13.80
-13.91
-14.01
-14.11
-14.22
-14.32
-14.43
-14.53
-14.64
-14.74
-14.85
-14.96
-15.06
-15.17
-15.28
-15.38
-15.49
-15.60
-15.71
-15.82
-15.93
-16.04
-16.15
-16.26
-16.37
-16.48
-16.59
-16.70
-16.81
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
72.40
72.77
73.14
73.51
73.88
74.25
74.62
74.99
75.36
75.73
76.09
76.46
76.82
77.19
77.55
77.92
78.28
78.64
79.00
79.37
79.73
80.09
80.45
80.80
81.16
81.52
81.88
82.23
82.59
82.94
83.30
83.65
84.01
84.36
84.71
85.06
85.42
85.77
86.12
86.47
27.21
27.38
27.56
27.73
27.90
28.07
28.25
28.42
28.59
28.77
28.94
29.11
29.28
29.46
29.63
29.80
29.98
30.15
30.32
30.50
30.67
30.84
31.02
31.19
31.37
31.54
31.71
31.89
32.06
32.24
32.41
32.59
32.76
32.93
33.11
33.28
33.46
33.63
33.81
33.98
-6.06
-6.14
-6.21
-6.28
-6.36
-6.43
-6.50
-6.58
-6.65
-6.73
-6.80
-6.88
-6.96
-7.03
-7.11
-7.19
-7.27
-7.35
-7.42
-7.50
-7.58
-7.66
-7.74
-7.82
-7.91
-7.99
-8.07
-8.15
-8.23
-8.32
-8.40
-8.48
-8.57
-8.65
-8.73
-8.82
-8.90
-8.99
-9.08
-9.16
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
146
112.16
112.47
112.78
113.09
113.40
113.71
114.02
114.33
114.64
114.95
115.25
115.56
115.87
116.17
116.48
116.78
117.09
117.39
117.70
118.00
118.31
118.61
118.91
119.21
119.52
119.82
120.12
120.42
120.72
121.02
121.32
121.62
121.92
122.22
122.52
122.81
123.11
123.41
123.70
124.00
47.84
48.02
48.20
48.38
48.56
48.74
48.92
49.10
49.28
49.46
49.64
49.82
50.01
50.19
50.37
50.55
50.73
50.91
51.09
51.28
51.46
51.64
51.82
52.00
52.18
52.37
52.55
52.73
52.91
53.09
53.28
53.46
53.64
53.82
54.01
54.19
54.37
54.56
54.74
54.92
-16.92
-17.04
-17.15
-17.26
-17.37
-17.49
-17.60
-17.72
-17.83
-17.94
-18.06
-18.17
-18.29
-18.41
-18.52
-18.64
-18.76
-18.87
-18.99
-19.11
-19.23
-19.35
-19.46
-19.58
-19.70
-19.82
-19.94
-20.06
-20.18
-20.30
-20.42
-20.55
-20.67
-20.79
-20.91
-21.03
-21.16
-21.28
-21.40
-21.53
502
503
504
505
506
507
86.81
87.16
87.51
87.86
88.20
88.55
34.16
34.33
34.51
34.68
34.86
35.03
-9.25
-9.34
-9.42
-9.51
-9.60
-9.69
619
620
621
622
623
623.15
147
124.30
124.59
124.89
125.18
125.48
125.52
55.10
55.29
55.47
55.65
55.84
56.02
-21.65
-21.78
-21.90
-22.03
-22.15
-22.17