Universität Duisburg-Essen
Fakultät für Ingenieurwissenschaften, IVG
Fachgebiet Thermodynamik
Dr. M. A. Siddiqi
4. Semester
April 2013
Thermodynamics Lab
Properties of Matter:
Measurement of properties of matter
2
Experiment: Measurement of Properties of matter
Introduction
All substances have properties that we can use to identify them.
There are two basic types of properties that we can associate with matter. These properties are
called as physical properties and chemical properties. Properties that do not change the chemical nature of matter are called physical properties and the properties that do change the chemical nature of matter are called chemical properties. Color, smell, freezing point, boiling
point, melting point, infra-red spectrum, attraction (paramagnetic) or repulsion (diamagnetic)
to magnets, opacity, viscosity and density are the examples of physical properties. Heat of
combustion (calorific value), reactivity with water, pH etc. are the examples of chemical
properties of matter. The exact knowledge of these properties of fluids is necessary for the
proper design and functioning of technical plants.
The measurement of these properties is of utmost importance. Some properties of fluids
which are important for process industries are:
1. Transport properties
(Viscosity, Thermal conductivity, Diffusion coefficient)
2. Thermal and Calorific Properties (Specific heat capacity, Coefficient of expansion, Enthalpy of vaporization, Calorific value (higher heating
value), Lower heating value, Density, Compressibility)
In this practical the viscosity, the heating values, and the enthalpy of vaporization for a given
fluid will be measured.
1. Experiment
Measurement of the higher and the lower heating values for a fuel gas
1.1
Description
The heating value or energy value of a substance, usually a fuel or food (see food energy), is
the amount of heat released during the combustion of a specified amount of it. The energy
value is a characteristic for each substance. It is measured in units of energy per unit of the
substance, usually mass, such as: kJ/kg, kJ/mol.
The higher heating value (HHV) (or gross energy or upper heating value or gross calorific
value (GCV) or higher calorific value (HCV)) is determined by bringing all the products of
combustion back to the original pre-combustion temperature, and in particular condensing any
vapor produced. Such measurements often use a temperature of 25°C. This is the same as the
thermodynamic enthalpy of combustion since the enthalpy change for the reaction assumes a
common temperature of the compounds before and after combustion, in which case the water
produced by combustion is liquid. The higher heating value takes into account the latent heat
of vaporization of water in the combustion products, and is useful in calculating heating values for fuels where condensation of the reaction products is practical (e.g., in a gas-fired boiler used for space heat). In other words, HHV assumes all the water component is in liquid
state at the end of combustion (in product of combustion).
3
The lower heating value (LHV) (net calorific value (NCV) or lower calorific value (LCV)) is
determined by subtracting the heat of vaporization of the water vapor from the higher heating
value. This treats any H2O formed as a vapor. The energy required to vaporize the water
therefore is not realized as heat.
2. Physical basis
2.1
Definitions:
The higher heating value (Ho ) (or gross energy or upper heating value or gross calorific
value (GCV) or higher calorific value (HCV)) is determined by bringing all the products of
combustion back to the original pre-combustion temperature, and in particular condensing any
vapor produced. Such that:
a)
b)
c)
d)
the measurements are at a temperature of 25°C,
the combustion products from carbon and sulphur, namely carbon dioxide and sulphur
dioxide are present as gas,
nitrogen is not oxidised,
the water present in the fuel (before combustion) and the water formed during the
combustion are in liquid form.
This is the same as the thermodynamic enthalpy of combustion since the enthalpy change for
the reaction assumes a common temperature of the compounds before and after combustion,
in which case the water produced by combustion is liquid. The higher heating value takes into
account the latent heat of vaporization of water in the combustion products, and is useful in
calculating heating values for fuels where condensation of the reaction products is practical
(e.g., in a gas-fired boiler used for space heat). In other words, HHV assumes all the water
component is in liquid state at the end of combustion (in product of combustion).
The lower heating value (Hu ) (net calorific value (NCV) or lower calorific value (LCV)) is
determined by subtracting the heat of vaporization of the water vapor from the higher heating
value. This treats any H2O formed as a vapor. The energy required to vaporize the water
therefore is not realized as heat. In this case the conditions
a) b) and c) given above hold and
d) the water present in the fuel (before combustion) and the water formed during the
combustion are in vapor form at 25 °C.
Ho and Hu differ only when the water is present in the products. The difference between the
two heating values depends on the chemical composition of the fuel. In the case of pure carbon or carbon monoxide, the two heating values are almost identical.
If water is present in the combustion products the lower heating value (Hu ) is lower than the
higher heating value (Ho ) by the amount of the enthalpy of vaporization of water. The enthalpy of vaporization of water at 25 °C is 2442 kJ/kg. Most applications that burn fuel produce water vapor, which is unused and thus wastes its heat content. In such applications, the
lower heating value Hu is the applicable measure.
4
2.2
Measurement of higher (Ho) and lower (Hu) heating values
Junker´s calorimeter consists of two open systems, a cold water system and a combustion gas
system, which are thermally isolated from outside atmosphere. Heat transfer takes place between these two (see Figure 1).
The heat transfer can be written in terms of First law for stationary flow processes.
m W h1W
m G h2G
Q 12G
adiabatic
Q 12W
m W h2W
m G h1G
Figure 1: Schematic sketch of Junker´s calorimeter
1. Law of Thermodynamics applied to stationary flow processes
1


2
2
Q12 + Pt12 = m h2 − h1 + ( v 2 − v1 ) + g ( z 2 − z1 )
2


As no technical work is done Pt12 = 0.
By appropriate design of inlet and outlet surface areas the condition v1 = v2 can be achieved.
The change in the potential energy can be neglected. Hence for combustion gas system
Q 12G = m G ( h2G − h1G )
(1)
and for cold water system
Q 12 W = m W ( h2W − h1W )
(2)
Under the assumption that Junker´s calorimeter is adiabatic outside
Q 12W + Q 12G = 0.
(3)
5
From equations (1), (2), (3) and hW = c W TW + hOW follows for the isobaric process:
Q 12G = −m W ⋅ cw ⋅ (T2W − T1W )
So that the higher heating value Ho for one kmol fuel gas
H0 =
− Q12G
nG
=
m w ⋅ cw (T2W − T1W ) kJ
nG
kmol
where nG is the mole flow (kmol/s) of the fresh fuel gas before combustion.
Under the assumtion that the fuel gas behaves as an ideal gas, the molar volume of the fresh
gas can be calculated.
Rm ⋅ T1
T1 = Temperature of fresh fuel gas
pG
pG is the pressure of dry gas.
υm =
However, the gas during its flow through the gas flow meter will be saturated with water and
is, therefore, a mixture of dry fuel gas water vapor in saturated state. Hence pG is to be calculated.
It holds
pges = pG + ps
and
pges = pBa + Δp
so that
pG = pBa + Δp - ps
ps = ps (T) ≙
Saturation partial pressure of water vapor
pBa ≙ Barometric pressure
Δp = Pressure difference of gas from the surroundings
 through the molar volume υ , gives the mole
Dividing the measured flow rate of fresh gas V
1
m
flow rate n in kmol/s
n =

V
1
υm
Lower heating value Hu
The lower heating value Hu follows from the higher heating value Ho, when the enthalpy of
vaporization of condensed water per kmol of fresh fuel gas is subtracted from Ho:
6
Hu = Ho −
m K ∆hv
n
kJ
kmol
m K = Amount of water condensed per second
∆hv = Enthalpy of vaporization of water
7
8
3. Experimental set up
(s. Bild 2)
Fuel gas will be drawn from the gas cylinder [Druckflasche] (16) by setting the pressure reducing valve [Druckminderer] (15) at the appropriate position and passed through the gas
flow meter [Gaszähler] (1). At this point the gas volume and the temperature [Temperatur des
Frischgases] (18) as well as the pressure difference of gas relative to atmospheric pressure
(17) will be measured. During its flow through the gas flow meter the gas will be wetted by
water and saturated. Then the gas passes through the pressure regulator [Druckregler] (2),
which holds the pressure to a constant defined value. Ultimately it will be burnt in the combustion chamber of Junker´s calorimeter with the help of a burner [Brenner] (3) taking the
saturated air from below from the air humidifier [Luftbefeuchter] (6). The overflow water will
moisten the air humidifier. The combustion gases pass through the calorimeter, supply the
heat to the cold water and flow out from the valve [Abgasstutzen] (12). Cold water flows
from inlet (7) into calorimeter and takes the heat from the gas up to the outlet (8). The change
in the temperature of cold water ( T1W – T1W ) will be recorded with the help of mercury thermometers (10) + (11). The amount of cold water will be held constant with the help of overflow devices [Überlaufvorrichtungen] (4) and (8) and determined by weighing. The condensed water will be collected in a measuring cylinder to determine its amount. Three series
of experiments will be performed burning each time 10 liter fuel gas.
4. Experimental procedure
(siehe Bild 2)
4.1
Open the tap on the water storage tank for the cold water inlet to the calorimeter. The
water storage tank is placed at a height of 2 m from the floor for
compensating (reducing) the pressure and temperature variations in
the water pipe line. The two way tap [Zweiwegehahn] (9) must stay
in the position „Abwasser“ stehen. (see the sketch ).
4.2
Keep the pressure 1.5- 2 bar at the pressure reducing valve [Druckmindererventil] (15)
of the fuel gas cylinder [Erdgasflasche] (16), whereby the discharge valve [Druckmindererventil] remains closed.
4.3
Turn out the burner [Brenner] (3) at the calorimeter (Bajonet connection). The gas
should not flow through the burner to the calorimeter when the burner is not ignited.
Otherwise a mixture of gas and air may build up in the calorimeter and may lead to
explosion when the burner is turned on.
4.4
Carefully open the discharge valve at pressure reducing device [Druckminderer] (15),
till the manometer (17) at the gas flow meter [Gasuhr] (1) shows an overpressure of
about 40 mm water level above the atmosphere. This provides the required flow of
about 2.2 liter/min of fuel gas in case the setting of the gas pressure regulator [Gasdruckreglers] (2) is not disturbed.
9
4.5
Ignite (turn on) the burner [Brenner] (3) which is still outside the calorimeter and adjust the flame so that it is almost colorless.
4.6
Place the ignited burner [Brenner] (3) just below the calorimeter.
4.7
It takes about 15 minutes to reach the stationary state so that the outlet temperature
(11) does not rise any more. The temperature difference between the cold water entrance [Kühlwassereintritt] (10) and exit [Austritt] (11) should be about 10° C. This
can be adjusted by regulating the flow of water at the tap [Wasserdosierhahn] (7).
The temperature of the exhaust gas [Abgastemperatur] (13) is (almost) equal to the
temperature of the flowing gas air mixture (18), because the gas in the gas meter [
Zähler] is cooled by the cold water, the air due to intake of water (moisture) also cools
down to cold water temperature. Thus the exhaust gas is brought to the temperature of
cold water by cross flow heat exchange.
The condensed water at the condenser [Kondensatabfluss] (14) up to the first experiment will be collected in a small pot. However, it is not used for the calculations.
4.8
Record the necessary readings and calculated vaues in the protocol while you are waiting:
4.8.1 Read the room temperature and the barometer reading for the pressure (Thermometer
and mercury barometer are hanging nearby on the wall).
The reading of the barometer has been explained i the pressure measurement experiment in the 3rd semester. The supervisor may help you too.
The correction of barometer reading to 0° C (KT) will be done with the help of the enclosed table. It may be necessary to interpolate. (Only the most important temperature
correction will be done. After correction the values will be set accordingly, i.e. 1 mm
Hg = 1 Torr).
4.8.2
Read the overpressure of gas in the gas flow meter [Gaszähler] p against the atmospheric pressure at the manometer (17) and convert it in Torr.
4.8.3
Calculate the total pressure pges in gas flow meter.
4.8.4 Read the gas temperature at the Thermometer (18). Thermometer is fixed 180 ° turned.
4.8.5 The partial pressure of water vapor ps in gas mixture at the temperature T1G can be taken from the enclosed table.
4.8.6 Calculate the partial pressure pG of dry gas (in Torr) and convert in N/m2.
4.8.7
Calculate the molar volume of dry gas.
10
4.9
Three series of experiments will be performed. Each time 10 liter gas will be burned.
Just after each experiment 10 more liter of gas will be burnt without determining the
amount of cold water; that means total 60 liter gas will be burnt. The water condensed
during the complete burning of 60 liter gas will be collected in a measuring flask and
weighed. The higher heating value and the lower heating value will be determined at
the entrance temperature of cooling water. The temperature dependence of the heating
value is weak.
Note and record the mass of the empty flask in the beginning of the experiment.
1.Measurement run: The two way tap will be set on „Messen“ (see sketch) as the meter of gas flow meter crosses 0-liter-mark. The cold water and the condensed water will be collected in the respective empty flasks.
At the same time the beaker to measure the condensed water will be put under [Kondensatabfluss] (14) and the first reading of the temperature of cooling water at the inlet
and outlet will be noted. The inlet and outlet temperature will be read at the intervals
for full liter gas. After the flow of 10 liter fuel gas the two way tap [Zweiwegehahn]
will be set at „Abwasser“ and the collected amount of cold water and the flask
weighed
At the end the measuring flask for the condensed water will be changed.
1.Empty Run: In the period when the next 10 liter of gas are still burnt without any
measurement steps the mean values of the inlet and outlet temperature , the amount of
cooling water, the amount of condensed water and from these the higher heating value
Ho can be calculated (the condensed water still being collected in another beaker).
2.Measurement Run: As the 10 liter empty run of the gas is finished the second measurement run is started. This is done as the first one.
2. Empty Run is made as the first empty run. Then the third measurement and empty
runs are made.
After the third Empty Run the condensed water measuring flask is taken away, the
valve on the pressure reducing device is slowly closed. The flow of water to the storage tank is closed. The total amount of condensed water collected during the three
measurement and three empty runs is noted.
4.10
Calculate the mean values of Ho and Hu.
4.11
Calculate the percentage deviation from the values given by the supplier.
Error: the errors in the measured values may come from:
The readings at the beginning of the experiment and at the end are not recorded
at proper time; Error in temperature reading; error in weighing.
11
Universität Duisburg-Essen
Fachbereich Maschinenbau
Grundlagenpraktikum
Thermodynamik
Date:____________________
Time:
____________________
Matr.-No.:_____________________
Name:
______________________
Experiment : Measurement of the higher and the lower heating values for a
fuel gas
Determination of the partial pressure of dry fuel gas ptr
Roomtemperature
Tu =
°C
Barometerstand reading
pBa =
mmHg
Correction to 0 °C
KT =
mmHg
pBa,Korr = pBa - KT
pBa,Korr =
Torr
Overpressure in gas flow meter
Δp =
mmWS
1mm WS = 0,074 Torr
Δp =
Torr
pges. = pBa,Korr + Δp
pges. =
Torr
Temperature in gas flow meter
T1G =
°C
T1G (K) = 273.15 + T1G (°C)
T1G =
Corrected Barometerstand
Total pressure in gas flow meter
K
Saturation pressure of water vapor
at T1G
ps =
Torr
12
Partial pressure of dry fuel gas
pG = pges - ps
1 Torr = 133.3
N
m2
Molar volume of dry fuel gas
υm =
Rm ⋅ T1G
pG
Notices e.g.
Weight of empty flask
liter
pG =
Torr
pG =
N
m2
 J 
8315
⋅ T1 [ K ]
kmol K  G

υ m=
N
pG  2 
m 
3
m
υm =
kmol
1. Measurement 2. Measurement 3. Measurement
T1W °C T2W °C T1W °C T2W °C T1W °C T2W °C
0
1
2
3
4
5
6
7
8
9
10
Mean value
Thermometer error
Corrected mean value
mean temperature difference
Mass1) Cooling water + flask
Masse Behälter
Cooling water amount
Amount of gas burnt (0.01 m3)
ΔTW =
°C ΔTW =
kg
mw =
0.01
=
n=
kg mw =
°C ΔTW =
kg
°C
kg
kg mw =
kg
kg
υm
kmol
13
Higher heating valuet
Ho =
Ho =
Ho =
Ho =
mw
⋅ c w ⋅ ∆Tw
n
c W = 4,2
kJ
kg
kJ
kmol
Mean value of higher heating value
Ho =
kJ
kmol
kJ
kmol
kJ
kmol
Total condensed water
(after 60 liter gas)
mKges. =
kg
Condensed water per Measure. (10 liter gas)
mK =
kg
Lower heating value
Hu = Ho −
∆hv = 2442
mk ⋅ ∆hV
n
kJ
kg
Supplier´s value HoH
Hu =
kJ
kmol
HoH =
kJ
kmol
Percentage deviation Ho
H o − H oH
⋅ 100
H oH
Supplier´s value HuH
%
HuH =
kJ
kmol
Percentage deviation Hu
H u − H uH
⋅ 100
H uH
Weight of empty flask
%
14
Saturation pressure of water vapor ps at various temperatures
T[°C]
ps [Torr]
T[°C]
ps[Torr]
0
4.60
15
12.70
1
4.94
16
13.54
2
5.30
17
14.42
3
5.69
18
15.36
4
6.10
19
16.35
5
6.53
20
17.39
6
7.00
21
18.50
7
7.50
22
19.66
8
8.02
23
20.89
9
8.57
24
22.18
10
9.17
25
23.55
11
9.79
26
24.99
12
10.46
27
26.51
13
11.16
28
28.10
14
11.91
29
29.78
15
Correction of recorded barometer readings at temperature Tu [°C] to 0°C
pBa (mmHg)
Tu[°C]
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
620
0.14
0.24
0.35
0.45
0.56
0.67
0.77
0.88
0.98
1.09
1.19
1.30
1.41
1.51
1.62
1.72
1.83
1.93
2.04
2.14
2.25
2.35
2.46
2.56
2.67
2.77
2.88
2.98
3.09
3.19
3.29
640
0.14
0.25
0.36
0.47
0.58
0.69
0.80
0.91
1.01
1.12
1.23
1.34
1.45
1.56
1.67
1.78
1.89
2.00
2.10
2.21
2.32
2.43
2.54
2.65
2.76
2.86
2.97
3.08
3.19
3.30
3.40
660
0.15
0.26
0.37
0.48
0.60
0.71
0.82
0.93
1.05
1.16
1.27
1.38
1.50
1.61
1.72
1.83
1.95
2.06
2.17
2.28
2.39
2.51
2.62
2.73
2.84
2.95
3.07
3.18
3.19
3.30
3.51
Barometer Reading pBa [mm Hg]
680
700
720 740
0.15
0.15
0.16
0.16
0.27
0.27
0.28
0.29
0.38
0.39
0.40
0.42
0.50
0.51
0.53
0.54
0.61
0.63
0.65
0.67
0.73
0.75
0.77
0.79
0.85
0.87
0.90
0.92
0.96
0.99
1.02
1.05
1.08
1.11
1.14
1.17
1.19
1.23
1.26
1.30
1.31
1.35
1.39
1.43
1.43
1.47
1.51
1.55
1.54
1.59
1.63
1.68
1.66
1.71
1.75
1.80
1.77
1.83
1.88
1.93
1.89
1.94
2.00
2.06
2.00
2.06
2.12
2.18
2.12
2.18
2.24
2.31
2.24
2.30
2.37
2.43
2.35
2.42
2.49
2.56
2.47
2.54
2.61
2.68
2.58
2.66
2.73
2.81
2.70
2.78
2.86
2.93
2.81
2.90
2.98
3.06
2.93
3.01
3.10
3.19
3.04
3.13
3.22
3.31
3.16
3.25
3.34
3.44
3.27
3.37
3.47
3.56
3.39
3.49
3.59
3.69
3.50
3.61
3.71
3.81
3.61
3.72
3.82
3.93
The correction values for KT will be subtracted from pBa.
760
0.17
0.30
0.43
0.56
0.69
0.82
0.95
1.08
1.20
1.33
1.46
1.59
1.72
1.85
1.98
2.11
2.24
2.37
2.50
2.63
2.76
2.89
3.01
3.14
3.27
3.40
3.53
3.66
3.79
3.92
4.04
780
0.17
0.30
0.44
0.57
0.70
0.84
0.97
1.10
1.24
1.37
1.50
1.64
1.77
1.90
2.03
2.17
2.30
2.43
2.56
2.70
2.83
2.96
3.09
3.23
3.36
3.49
3.62
3.75
3.89
4.02
4.14
800
0.18
0.31
0.45
0.59
0.72
0.86
1.00
1.13
1.27
1.40
1.54
1.68
1.81
1.95
2.09
2.22
2.36
2.49
2.63
2.77
2.90
3.04
3.17
3.31
3.44
3.58
3.72
3.85
3.99
4.12
4.25
16
Experiment 2: Measurement of the enthalpy of vaporization
1. Description
The aim of this experiment is to determine the enthalpy of vaporization of distilled water
with the help of the apparatus shown in Figure Bild 3. For this an energy balance across
the calorimeter is to be done.
2. Physical basis
Every substance can exist in three different aggregate states (solid, liquid or gas). In which
aggregate state it is depends on its thermodynamic state (p, T, V). In this experiment the
heat energy involved during the change of state of water from gas (vapor) to liquid state
(liquid water) will be determined. In the case of reversible and isobaric-isothermal change
of state this is a defined quantity, the enthalpy of vaporization
We will study an isobaric, reversible change of state from state 1 to state 3 for a stationary flow process as shown in the T-s diagram given below (see Figure 4 [Bild 4]). This
will describe the phase changes clearly. The state changes can be seen in three steps (see
Bild 4).
17
a) Change of state from 1 – 2″
Isobaric heat addition from the condition of superheated vapor [Überhitzter Dampf] up
to the boundary line: The amount of heat transferred is displayed through the area 1 –
2″ s2″ – s1 or
qü = h2″ – h1.
b) Change of state from 2″ – 2′
Isobaric heat withdrawl till the saturated vapor [Sattdampf] changes to saturated liquid
[Siedendes Wasser]: This reversible change of state is not only isobaric but also isothermal. The amount of heat transferred is displayed by the area 2″ – 2′, -s2′ –s2″ or
qverd = T(s2′ – s2″) = h2′ – h2″ in the case of isobaric process.
It follows from here the definition for the enthalpy of vaporization (also called enthalpy of evaporation)
Δhv = h2″ - h2′.
It is the amount of heat which should be added isobarically and reversibly to produce
saturated vapor from saturated liquid (boiling liquid).
c) Change of state from 2′ – 3
The heat transferred is displayed by the area 2′ – 3 – s3 – s2′ or
qfl = h3 –h2′.
This is also the heat which must be withdrawn from the saturated water to reach state
3.
From Bild 4 and from the knowledge about the change of states it can be said that the enthalpy of vaporization depends only on temperature and pressure. It decreases with increasing
pressure and will vanish at critical point. Introducing the definition equation h = u + pυ leads
to following relation
Δhv= u″+ pυ″ – u′ – pυ′ = (u″ – u′) + p (υ″ – υ′)
with
u″ – u′ = internal energy of vaporization
p (υ″ – υ′) = external energy of vaporization
From this relation it becomes evident that at p and T = constant the heat added during evaporation is largely used to increase the internal energy. The remaining part represents the work
18
required to compensate for the work due to change in volume (increase in volume) during the
evaporation of water.
Calculation of the enthalpy of vaporization
Boundary conditions: The system can be regarded as adiabatic; an assumption which is valid
if the cooling water temperature does not differ more than 5 °C from the temperature oft he
surroundings. The change of state in cooling water mantel and in the glass spiral [Glaswendel] can be described by the equations for the stationary flow process.
The change of state in the experimental apparatus is shown the change of state 2″ – 3 in Figure [Bild] 4.
Energy balance:
m K ⋅ h s + m W ⋅ hWE = m K ⋅ h K + m W hWA
with
m K =
mK
;
∆t
hs − h K =
m W =
mW
∆t
Δt = Measurement time
m W
m
⋅ ( hWA − hWE ) = ( W ) ⋅ cW ⋅ (T2W − T1W )
m K
m K
For hs – hK one can write
 m
″
(hs − h′) + (h′ − hK ) = ∆hV + cW ⋅ (Ts − TK ) =  W
 m K

 ⋅ cW ⋅ (T2W −1W )

It follows then:
 m

∆hv = cW  W ⋅ (T2w − T1w ) − (Ts − TK )
 m K

In this relation cW is the specific heat capacity of cooling water which can be taken to be the
same for isobaric and isochoric change of state.
3. Experimental set up Procedure
Apparatus
The set up may be divided into three groups which are marked in Figure [Bild] 3 with dashed
lines.
a)
b)
Boiler, which consists of a heater [Heizplatte] and a glass beaker [Glaskolben] filled
with ditilled water
Isolated connecting tube [Rohrleitung] to calorimeter [Kalorimeter]
19
c)
Glass calorimeter [Kalorimeter], in which the saturated water vapor enters inside the
spiral [Glaswendel] and during ist flow condensed completely. The outer of the spiral
is cooled by flowing cold water stream.
Measurements:
Measurement of temperature at different points with the help of mercury thermometer
1. Measurement of the temperature of saturated vapor TS
2. Measurement of the temperature of cooling water at entrance T1
W
3. Measurement of the temperature of cooling water at entrance T2
W
4. Measurement of the temperature of condensed water TK
5. Measurement of the temperature of surroundings TU (will also be required).
Measurement of the amount of water flowing through the calorimeter
6. Mass of condensed water mK (it will be collected in a measuring cylinder and weighed)
7. Mass of cold water mW. The amount of cooling water flowing through the calorimeter mW
will be collected in a vessel and weighed.
4. Experimental Procedure
Three runs for the measurement will be performed. About 5 liter of cooling water will be collected in each run.
1. Open the tap of the cold water storage tank. The outlet tube of the water should be put
inside the wash basin drain. Check the water level in gall beaker (3/4 full).
2.
Put on the hot plate on 3 [Heizplatte (Heizstufe 3)].
3.
Note the temperature of the surroundings (room) TU (Thermometer on the wall near the
mercury barometer).
4.
Wait till saturated vapor temperature TS = 100 °C is attained.
5.
As the temperature TS = 100 ° C is reached regulate the amount of cooling water flow
through the tap (it may sometimes be necessary to regulate the heating [Heizstufe]), so
that the surroundings temperature is almost the middle of the inlet and outlet temperatures of cooling water. With this the heat transfer with the surroundings will be minimized and adiabatic condition can be assumed.
6.
1. Run: The collection of the cooling water in the vessel and that of the condensed water
in the measuring cylinder will be started at the same time (simultaneously). The inlet and
outlet temperatures (estimated up to one tenth degree), the temperature of the condensed
water will be read and noted in the protocol. The temperature readings should be repeated
after the collection of ca. 25 milliliter of condensed water. After about 50 milliliter condensed water is collected the run will be stopped noting at the same time the reading of
the balance for the amount of condensed water and that of cooling water. The amount of
cold water (mass of cold water + vessel minus the mass of empty vessel) will be determined by the other balance placed there.
7.
As you wait for the 2nd Run calculate the enthalpy of vaporization from the 1st Run. If
necessary regulate the inlet and outlet temperature by varying the flow rate of cooling
water.
20
8.
2. and 3. Runs are performed as 1st Run.
9.
After finishing the 3rd Run the heater should be switched off and the cooling water flow
stopped.
10. The percentage deviation of the three measurements from the given value of the enthalpy
of vaporization will be calculated.
Sources of error: The errors in the measurements error may arise from:
a)
b)
c)
d)
Readings of balances (for condensed water and the cold water) not taken at the same
time.
The temperature difference between the mean temperature of cooling water and the
surroundings is large.
Cooling of the condensed water.
Errors in reading the temperature or balance or both.
21
Universität Duisburg-Essen
Fachbereich Maschinenbau/IVG
Thermodynamics Lab
Date:____________________
Time: ____________________
Matr.-Nr.:_____________________
Name: ______________________
Experiment 2: Determination of the enthalpy of vaporization
Temperature of the surroundings
TU =
°C
Temperature of saturated vapor
TS =
°C
1.Run
1. Reading:Balance condensed water
Temperature of cold water entrance T1w and
2. Run
3. Run
kg
T1w T2w TK
kg
T1w T2w TK
kg
T1w T2w TK
exit T2w; condensed water TK(°C)
1. Reading
2. Reading
3. Reading
Mean value of T1w,T2w and TK
Mean Temperature difference T2w-T1w
°C
°C
°C
2. Reading :Balance condensed water
kg
kg
kg
kg mK=
kg mK=
kg
kg
kg
kg
kg
kg
kg
°C
°C
°C
°C
°C
°C
kJ
∆hv =
kg
kJ
kg
2.-1. Reading Balance condensed water
mK=
Mass Cold water + Vessel
Mass Vessel
kg
Mass of cold water
mW
⋅ (T2W − T1W )
mk
TS - TK
Enthalpy of vaporization
m

∆hv = cW  W (T2W − T1W ) − (TS − TK ) ∆hv =
 mK

cw=4.2 [kJ/kgK]
Literature value ∆
Percentage deviation ∆hv − ∆hvH ⋅ 100
∆hvH
∆hv = 2442
%
∆hv =
kJ
kg
kJ
kg
%
%
22
Experiment 3: Viscosity measurement with a Höppler viscometer
1.Brief Description
The viscosity of a given oil is determined at a definite temperature with a Höppler falling ball
viscometer. The viscosity is determined from the measurement of the time for the fall of a
ball, the density of the fluid and the constants of the apparatus (Höppler viscometer). Since
the viscosity is highly temperature dependent, its measurement is done at definite temperature
and constant speed. This is done with the help of a thermostat. The viscosity is a measure of
the resistance to the relative movement of adjacent layers of liquid. The falling ball Höppler
viscometer is used to determine the viscosity of the resistance that a ball undergoes when it is
dropped in a fluid under the influence of gravity.
2. Physical Principles
To characterize the forces occurring during a flow process, we define the coefficient of dynamic viscosity, which is mainly a temperature-dependent material quantity. The physical
meaning of this material quantity is determined by the following consideration.
Between two parallel plates A and B (see Figure 5) with the area A, the layer of a viscous
liquid of the thickness L. Neglecting gravity, force F can be determined, which is necessary
for the plate A to move with constant velocity v relative to plate B. As adhesion conditions
resulting in the generation of a laminar flow of the fluid between the plates is assumed, so that
the immediately adjacent liquid layers to the plates have the speed v (A) and 0 (B).
A
v
F
L
Figure 5: Determination of the viscosity
B
(v=0)
The necessary force F for the mutual displacement of two layers of liquid is greater, the greater the velocity gradient existing between them and the greater their contact surface (contact
surface here = plate area). Then
dv
F ~ A⋅
dL
(1)
By introducing a proportionality factor it follows from (1):
dv
(2)
F =η ⋅ A⋅
dL
or after being divided by the contact area A
dv
(3)
τ =η ⋅
dL
where
F/A = τ the shear stress, prevailing between
dv /dL is the velocity
η is dynamic viscosity coefficient.
two adjacent layers of liquid
Substances for which the relationship between η and dv / dL is given by (3) are called "Newtonian fluids". In many cases, however, the viscosity apart from depending on the temperature
also depends on the prevailing shear stress, so that equation (3) needs to be written as:
23
dv
dL
with shear
τ = η (τ , T ) ⋅
Fluids
(3a)
stress-dependent
viscosity are
called
"non-Newtonian"
fluids.
In addition to these cases, there exist also so-called plastic media that follow equation (3) or
(3a) only after certain τ0 is exceeded. However, these are elastically deformed in the beginning following Hooke’s law. If the yield curve is a straight line passing from τ0, then one
speaks of "Binghamschen media", for example toothpaste, honey.
They follow the equation
dv
1
(4)
=
⋅ (τ − τ 0 )
dL η (T )
Frequently also encounters the plastic materials showing non - Newtonian behavior after exceeding the minimum shear stress (yield point) . Then equation (4) should be written as:
dv
1
(4a)
=
⋅ (τ − τ 0 )
dL η (τ , T )
Units of Viscosity
From equation (2), dimension and unit of dynamic viscosity can be determined
N
kg m s
kg
(5)
= 2 2 =
m
1
m
s
m
⋅
s
2
m ⋅ ⋅
s m
In practice the unit Poise (P) or Centipoise (cP) is frequently used.
g
kg
1P =
= 0,1
cm ⋅ s
m⋅s
Kinematic Viscosity:
For many technical problems, a new measure of viscosity, kinematic viscosity ν is used. It is
given as dynamic viscosity divided by the density of the flowing medium.
ν=
η
ρ
The unit of Kinematic viscosity is therefore
kg m 3 m 2
⋅
=
= 10 4 Stokes
m ⋅ s kg
s
Falling body viscometer:
A falling ball in a liquid is subject to the gravity, buoyancy and the frictional force. While
gravity and buoyancy are constant, the frictional forces grow at an increasing rate. The ball
which falls is first accelerated up with the increasing speed till the frictional forces increase to
such an extent that the resultant of the three forces is equal to zero (Fig. 6). Using the law of
inertia it follows
Weight
=
buoyancy
+
frictional
force.
According to Stokes, the frictional force on a ball at low Reynolds numbers is
24
FR
FA
FE
Figure 6: balance of forces on the ball
6
v
v ⋅ 2rKu
2
where Re =
⋅ 4π rKu ,
ρF
FR =
Re
2
v
For FR
FR = 6π ⋅ rKu ⋅η ⋅ v
4
3
FA = ρ F ⋅ V ⋅ g = ρ F π rKu ⋅ g
3
This will be
4
4
π ⋅ rKu 3 ⋅ ρ K ⋅ g = π ⋅ rKu 3 ⋅ ρ F ⋅ g + 6π rKu ⋅η ⋅ v
3
3
FE
FA
FR
It follows for the viscosity
2
2rKu ⋅ g ⋅ t
η=
⋅ ( ρ Ku − ρ F )
9⋅l
2
(8)
l


da t = v 
(9)
Where l is the distance of fall, and t is the drop time. Since the drop distance is constant, all
the variables of the first factor on the right side of the last equation can be summarized to a
constant, which is characteristic of a specific ball and a particular viscosimeter.
Then it follows:
η = K e ⋅ t ⋅ ( ρ Ku − ρ F )
(10)
Höppler Viscometer:
In Höppler viscometer, the ball is not freely falling through the downpipe which is slightly
inclined during the downward movement, but it is guided. Through this the errors due to irregular rolling motion of the ball can be avoided. The ball then rolls down on cycloidal path.
Of course, in this case the equation (10) is no longer valid in the strict sense the viscometer is
to be calibrated! This calibration is carried out by the manufacturer that indicates an empirically determined ball constant Ke for each ball. With a known ball constant Ke and the measured fall time t, the densities of the sphere and the liquid, the dynamic or kinematic viscosity
can be determined immediately with the help of equation (10).
η = K e ⋅ t ⋅ ( ρ Ku − ρ F )
ρ
(11)
ν = K e ⋅ t ⋅ ( Ku − 1)
ρF
Ball constant, ball density and density of the liquid used are already specified. , The viscosity
should be in centipoise or centistokes.
25
3. Experimental setup and measurement
procedure:
The experimental setup consists of the Hoppler viscometer and the thermostat.
The Hoppler viscometer (Fig. 7) consists of a slanted downpipe (Fallrohr), which is surrounded with a heatable glass coating. The possibility of an accurate temperature adjustment is necessary, since the viscosity strongly depends on the temperature, for example for normal engine oil the viscosity increases by a factor of 10 at an increase in temperature from 20 ° C to
70 ° C, so that a temperature change of 1 ° C will bring a change in viscosity of about 2% .
The liquid is continuously circulated by a pump in the thermostat. The inflow into the jacket
of the viscometer body is carried through the inlet port 1 and runs back through the drain port
2 in the thermostat. Heat losses through the viscometer jacket and hose lines, may give rise to
a small temperature difference between the fluid temperature in the thermostat and the liquid
temperature in the viscometer. The temperature can be set equal to that of the medium under
investigation after setting the temperature equilibrium.
Normal position of the viscometer: The locking pin 17 must fit into the stopper hole 18 of the
support beam. This is also the starting position for the measurement.
The thermostat (Fig. 8) consists essentially of the tank with the bath fluid, the heater, the cool-
26
ing circuit for cooling the bath liquid, the contact thermometer with relay for temperature control and the circulatory pumps to promote circulation of the liquid in the viscometer. Thermostat and viscometers are connected via tubing for supply and removal of the bath liquid.
4. Experiment Procedure:
4.1 Check the level in the normal position of the viscometer.
4.2 Setting of 20 ° C ± 0.1 ° C (ask the instructor) in the viscometer using the thermostat by
regulating the flow of water and the heating power.
4.3 The Viscometer is rotated through 180 ° and locked in place. The ball falls to its initial
position.(serves the porpose of mixing of the liquid)
4.4 The body of viscometer is unlocked and rotated through 180 ° to bring it to normal position. The time for the ball between the two marks A and B is measured using a stopwatch.
The falling time is determined such that in each case the placement of the ball stops on the
mark. This is repeated 5 times and from these the average is calculated.
4.5 Evaluation:
The basis is Eq. (11)
η = K e ⋅ ( ρ ku − ρ F ) ⋅ t m
ν=
tm = average measured time for the fall of ball
η
ρF
Ball constant Ke, ball density ρku and density of the liquid ρF are given and should be recorded
in the protocol. The calculation of the viscosity should be in centipoise (g/m.s) or centistokes
(10-6 m2/s). The percentage deviation of the manufacturer is to be determined
(see protocol).
Error:
27
The manufacturer's instructions state that the appliance is working to within 1% accuracy.
The sources of error in the experiment are the time, temperature measurements and fluctuations in temperature.
Other measurement methods:
The various viscometers differ according to the type of flow generation, which develops in
them. The different types are: Capillary viscometer (Hagen-Poisseuillsches Law), rotational
viscometer (Couette flow: flow between two concentric rotating relative to each other cylindrical surfaces) and the Falling ball viscometer. The majority of the devices used in practice
are capillary viscometer. Rotational viscometers are also used for non - Newtonian fluids.
All models in appropriately modified form are used as the operating devices for continuous
and automatic monitoring.
Universität Duisburg-Essen
Fachbereich MaschinenbauGrundlagenpraktikum Thermodynamics Lab
Date:____________________
Time: ____________________
Matr.-No.:_____________________
Name: ______________________
Experiment 3: Viscosity measurement with a Höppler Viscometer
Bath temperature
Ball density1)
Density of the fluid1)
Ball constants1)
Falling time (5 readings)
Average
Dynamic Viscosity
η = K e ⋅ t m ( ρ Ku − ρ F )
Kinematic Viscosity
η
ν =
ρF
Manufacturers data1)
Percentage deviation
η − ηH
⋅ 100
η
1)
1
1
kg
= 10 3 cP
ms
m2
= 10 6 cSt
s
ν −ν H
⋅ 100
ν
to be taken from the Instructor
T=
ρKu =
ρF =
Ke =
t1 =
°C
kg/m3
kg/m3
m2/s3
s
t2 =
s
t3 =
s
t4 =
s
t5 =
s
tm =
η=
η=
ν=
ν=
s
kg/ms
cP
ηH =
νH =
cP
cSt
m2/s
cSt
%
%
28
Abkürzungen und Formelzeichen (Short terms and Formula)
A
m2
c
KJ/(kgK)
F
N
g
m/s2
h
kJ/kg
Ho
kJ/kmol oder kJ/kg
Hu
kJ/kmol oder kJ/kg
Ke
m2/s2
L
m
KT
°C
lit.
m3
l
m
kg/s
m
n
kmol
kmol/s
n
p
bar
Δp
bar
Pt
kJ/s
q
kJ/kg
kJ/s
Q
rKu
m
r
kJ/kg
Re
Rm = 8,3153 kJ/(kmol K)
s
kJ/(kgK)
t
s
T
K;°C
u
kJ/kg
v
m/s
V
m3

m3/s
V
m3/kmol
υm
z
m
η
kg/(ms)
ν
m2/s
ρ
kg/m3
τ
N/m2
τ0
N/m2
Fläche (area)
spezifische Wärmekapazität (specific heat capacity)
Kraft (force)
Erdbeschleunigung (acceleration due to gravity)
Spezifische Enthalpie (specific enthalpy)
Brennwert (calorific value)
Heizwert (heating value)
Kugelkonstante (ball constant)
Dicke einer Flüssigkeitsschicht (thickness of a layer of liquid)
Temperaturkorrektur des Barometerstandes (temp. correction)
Liter (liter)
Fallstrecke der Kugel (fall distance of the ball)
Massenstrom (mass flow rate)
Anzahl der Kilomole (kilo moles)
Molenstrom (mole flow rate)
Druck (pressure)
Druckdifferenz (pressure difference)
technische Leistung (technical power)
spezifische ausgetauschte Wärme (specific heat exchanged)
Wärmestrom (heat flow rate)
Kugelradius (radius of the ball)
Verdampfungswärme (enthalpy of vaporization)
Reynoldsche Zahl (Reynold number)
allgemeine Gaskonstante (universal gas constant)
spezifische Entropie (specific entropy)
Zeit (time)
Temperatur (temperature)
spezifische innere Energie (specific internal energy)
Geschwindigkeit (velocity)
Volumen (volume)
Volumenstrom (volumetric flow rate)
Molvolumen (molar volume)
Höhenkoordinate (height coordinate)
dynamische Zähigkeit (dynamic voscosity)
kinematische Zähigkeit (kinematic viscosity)
Dichte (density)
Schubspannung (shear stress)
Fließgrenze (flow limit)
29
I n d i z e s (Index)
c
Zenti (0,01) [centi (0.01)]
untere:[subscript]
A
Auftrieb (impulse)
Ba
Barometer
E
Erdbeschleunigung (acceleration)
F
Flüssigkeit (liquid)
G
Gas (gas)
ges
gesamt (total)
H
Herstellerangabe (manufacturers data)
K
Kondensat (condensate)
Korr.
Korrigiert (corrected)
Ku
Kugel (sphere, ball)
Kr
kritisch (critical)
m
Mittelwert (außer bei vm = Molvolumen) [average value, (vm = molar volume)]
W
Kühlwasser (cold water)
R
Reibung (friction)
s
gesättigt (saturated)
tr
trocken (dry)
u
Umgebungszustand (surroundings)
ü
überhitzt (super heated)
1
Eintritt (entrance)
2
Austritt (exit)
obere: (superscript)
′
Siedezustand (liquid state)
″
Sättigungszustand (vapour state)
30
L i t e r a t u r (literature)
Versuch 1
Baehr, H. D.
Thermodynamik,
Springer Verlag, Berlin
Knoche, K.F.
Technische Thermodynamik,
Braunschweig, Vieweg Verlag 1972
DIN 51900
Bestimmung des Brennwertes und des Heizwertes
DIN 51850
Gasförmige Brennstoffe
Heizwerte der Komponenten
DIN 5499
Brennwert und Heizwert
Versuch 2
Schaefer-BergmannKliefoth
Grundaufgaben des physikalischen Praktikums,
Teubner Verlag Stuttgart, 1957
Ulrich
Physikalisches Praktikum
Giradet Verlag; Essen, 1963
Kohlrausch, F.
Praktische Physik, Band I,
Teubner Verlag, Stuttgart, 1960
Versuch 3
Prandtl, L.
Führer durch die Strömungslehre, Vieweg Verlag,
Braunschweig, 1965
Schlichting, H.
Grenzschicht-Theorie,
Braun-Verlag, Karlsruhe 1964
DIN 1342
Viskosität bei Newtonschen Flüssigkeiten
DIN 53015
Messung der Viskosität mit dem Kugelfallviskosimeter
DIN 51550
Bestimmung der Viskosität
Hengstenberg
Sturm
Winkler
Messen und Regeln in der Chemischen Technik
Springer-Verlag, Berlin, 1964