EXERGY CONCEPT AND ITS APPLICATION
TO THE BUILT ENVIRONMENT
Masanori Shukuya †
Graduate School of Environmental and Information Studies, Musashi Institute of Technology,
Yokohama, Japan
ABSTRACT
This paper first introduces the concept of “exergy”, which quantifies what is consumed by any working
systems from man-made systems such as heat engines to biological systems including human body.
“Exergy” balance equation for a system can be derived by combining both mass/energy and entropy
balance equations based upon the two thermodynamic laws together with the concept of
“environmental temperature” for the system to be described. The unique feature of the exergy balance
equation, distinct from the energy balance equation, is that a term quantifying “consumption” appears
explicitly. Exergetic view leads us to deepening our understanding of the built environment and thereby
to the development of various low-exergy systems for future buildings. The rest of the paper outlines
some of the findings obtained from the recent exergy research focusing on the built environment.
What follows are that 1) exergy contained by a volume of indoor air consists of “warm” or “cool” exergy
and “wet” or “dry” exergy; 2) a heat pump is basically an equipment to separate exergy supplied by
electricity into warm, cool and dry exergies; 3) there is the lowest human-body exergy consumption rate
in winter season; 4) availability of cool radiant exergy seems very important for a naturally-ventilated
room in summer season; 5) “cool” radiant exergy available from the sky is not marginal even in the hot
and humid regions so that its exploitation for cooling is to be pursued.
KEYWORDS
Energy, Entropy, Exergy, Heating, and Cooling
INTRODUCTION
People often claim that energy is consumed; this is not only in everyday conversation but also even in
scientific discussion associated with so-called energy and environmental issues. This claim, however,
conflicts with the first law of thermodynamics stating that the total amount of energy is conserved even
though forms of energy may change from one to another. All macroscopic natural phenomena
happening around us involve the dispersion of energy and matter, which in due course change their
forms from one to another, but the total amount of energy and matter involved is never consumed but
necessarily conserved.
When we use such expressions as “energy consumption”, “energy saving”, and even “energy
conservation”, we implicitly refer to “energy” as intense energy available from fossil fuels or from
condensed uranium. But, it is confusing to use one of the most well-established scientific terms,
energy, to mean “to be conserved” and “to be consumed” simultaneously. This is why we need to use
one of the thermodynamic concepts, exergy, intensively and extensively to articulate what is consumed
and how a system in question works in accordance with exergy supply, consumption, the resultant
entropy generation and disposal. The built environment is no exception.
Here in this paper, we briefly review the fundamental laws of thermodynamics aiming at the derivation
of the exergy concept and then discuss some of the findings obtained from the recent exergy research
†
Corresponding Author: Tel: +81 45 910 2552, Fax: +81 45 910 2553
E-mail address: [email protected]
focusing on the built environment.
EXERGY-ENTROPY PROCESS
Let us first discuss using a simple imaginary heat engine working under a steady-state condition as
schematically shown in the left-hand side of Figure 1. We first set up its energy balance equation
according to the “energy conservation law”. The inflow of energy equals the sum of the outflows of
energy. The heat engine works in the dispersing flow of energy, namely “heat”, from the hot source to
the cold source and thereby it extracts non-dispersing flow of energy, namely “work”.
Whenever the heat engine produces the useful work, some positive value of entropy is necessarily
generated. With this in mind, we can set up the entropy balance equation to be consistent with the
energy balance equation. The limit condition of the heat engine that does not generate even a scant
amount of entropy is that it is operated with the infinitely-slow motion. The heat engine under such
condition is not useful at all. Therefore, any useful heat engines generate some amount of entropy.
The unique feature in the entropy balance equation is that there exists a term of “entropy generation”.
The sum of the inflowing entropy to the system and the generated entropy within it equals the entropy
flowing out from it. This implies that the generated entropy is discarded out of the system.
The concept of entropy can be regarded to be a measure to quantify in what degree an amount of
energy or matter is dispersed or how much the dispersion occurs. “Heat” is one way of energy transfer
by dispersion due to conduction, convection or radiation, sometimes together with mass diffusion,
namely evaporation. On the other hand, “work” is the other way of energy transfer not by dispersion;
work is, in other words, performed by a directional (parallel) movement of molecules composing of a
substance that has a certain shape as solid. Energy transfer by heat necessarily accompanies with
entropy transfer and entropy generation, while on the other hand, energy transfer by work itself alone
accompanies with no entropy transfer.
Generally speaking, energy contained by a body, which has an ability to disperse, is called an energy
source. Such an energy source exists within the environmental space, which is filled with dispersed
energy. Therefore the cold source shown in Figure 1 can be regarded as the environmental space for
the heat source and for the heat engine. Since the concept of entropy is, as mentioned above, a
measure to quantify the degree of dispersion and its unit is J/K (=Onnes) (W/K (=Onnes/s) for the rate),
the dispersed energy level of the heat source surrounded by the environmental space can be
expressed as the product of entropy contained by the source and its environmental temperature in
Heat Source
TH
QH
Energy and Mass
Conservation
Entropy Generation
Heat
Engine
W
Environmental
Temperature
QL
Cold Source
TL
Exergy Consumption
Theorem
Figure 1 An imaginary heat engine working with the heat source whose temperature is
constant at TH and with the cold source (heat sink) whose temperature is constant at TL .
The engine extracts an amount of work, W , which is not yet dispersed, through the two
dispersing flows of thermal energy, QH and QL , from the heat source to the cold source.
Table 1
Exergy-entropy process
1.
Feed on exergy
2.
Consume exergy
3.
Generate entropy
4.
Dispose of entropy
Disposing of the generated entropy from the system makes new room
for feeding on exergy and consuming it again. Thus the process cycles.
Kelvin scale. The product of entropy and environmental temperature is called “anergy”, which implies
dispersed energy; the unit of both energy and anergy is J (W for the rate).
A portion of energy to be expressed as the difference between total energy and its dispersed portion,
anergy, is the amount of energy, which has an ability to disperse. This is exactly the concept of “exergy”.
Exergy balance equation is therefore obtained from the two balance equations in terms of energy and
entropy together with the concept of “environmental temperature”. The unique feature of the exergy
balance equation is that there exists a term of “exergy consumption”; this implies that a portion of
exergy supplied from the source flowing into the system is necessarily consumed (destroyed) and
thereby an amount of work, which is exergy itself, is extracted.
The heat engine must be operated cyclically to produce the work continuously and thereby becomes
useful. To make this cycle realize, it is essential for the engine to keep get rid of the generated entropy
so that its state, expressed by temperature and pressure, remains unchanged. The entropy contained
by a certain body is a function of the body temperature and pressure; its general characteristic is that
the value of entropy increases as the body temperature rises or the body pressure decreases (the
volume increases). In order to remain the state of the engine unchanged, it is necessary for the engine
to keep disposing of the generated entropy. We call the process described above “exergy-entropy
process”. Table 1 shows the four fundamental steps of this exergy-entropy process. Any working
systems perform these four steps in series and cyclically. The built-environmental systems such as
lighting, heating, cooling, or ventilating systems and also the human-body system are no exceptions
(Shukuya, 1994; 2004).
EXERGETIC VIEW OF THE BUILT ENVIRONMENT
Warm and Cool Exergies
The amount of exergy contained by a substance varies with its temperature and also with its
environmental temperature. A graph shown in the left of Figure 2 is an example of thermal exergy
3
contained by 81 m (= 6m x 5m x 2.7m), a room size, of air as a function of its temperature, assuming
the environmental temperature of 288 K (=15 °C). It should be noted that a volume of indoor air has a
certain amount of exergy both when its temperature is higher than the environment and when lower
than the environment (Shukuya and Hammache, 2002).
The exergy contained by a volume of air at a temperature higher than its environment is an ability of
thermal energy contained by the air to disperse into the environment. On the other hand, the exergy
contained at a temperature lower than its environment is an ability of the air, in which there is a lack of
thermal energy compared to the environment, to let the thermal energy in the environment flow into it.
We call the former “warm” exergy and the latter “cool” exergy (Shukuya, 1996).
Either “warm” exergy or “cool” exergy described above is a quantity of state contained by a substance
relative to its environment. When a room space is heated, we have room temperature higher than the
outdoor environment. In such a case room air has “warm” exergy as a quantity of state. On the other
hand, when the room space is cooled, we have room temperature lower than the outdoor environment.
In this case, the room air has “cool” exergy as a quantity of state.
1000
90
1000
400
100
200
600
1500
800
3000
50
2500
60
2000
400
dry
200
70
warm
40
4000
0.2
Relative Humidity [%]
[kJ]
Xr
To
cool
0.4
warm
3
(15 ºC)
[kJ/m ]
0.6
40
xr
0.8
60
20
600 800
wet
80
80
cool
30
0
270
280
290
Tr
300
[K]
0.0
310
0
10
20
30
40
Temperature [°C]
Figure 2 Thermal exergy contained by air, X r , as a function of temperature, Tr (see on your
3
left). The unit of thermal exergy, X r , is kJ. Air volume is assumed to be 81m (= 6m x 5m x
2.7m). Environmental temperature, To , is 288 K (=15 °C). Shown on your right is exergy
contained by a cubic meter of moist air, which is the sum of warm/cool exergy and wet/dry
exergy, assuming that the outdoor environmental condition of air temperature at 30 °C and
relative humidity at 65 %. Two bold dashed lines splits the chart into four areas, each of which
has “warm” or “cool” and “wet” or “dry” exergies. Thin solid lines represent the same amount of
3
exergy contained by a cubic meter of moist air, namely in the unit of J/m .
The role of heating systems is to supply and consume exergy for keeping “warm” exergy contained by
room space in a certain desired level. Cooling systems, on the other hand, are the systems that supply
and consume exergy for keeping “cool” exergy contained by room space at a certain desired level. The
exergy supply is to transfer exergy either by flows of conduction, convection, or radiation.
Most of the contemporary space heating and cooling systems are based on the use of convection. For
those systems, their purposes are exactly to supply warm or cool exergy to the indoor air and keep its
exergy as the quantity of state at a desired level.
Wet and Dry Exergies
In addition to conditioning indoor “warm” or “cool” exergy level, it is sometimes necessary to condition
the indoor humidity level. We can also calculate “wet” or “dry” exergy, which is parallel to “warm” or
“cool” exergy. “Wet” exergy is an ability of a volume of air with water vapor to disperse into the
environmental space filled with less humid air; and “dry” exergy to disperse into the environmental
space filled with more humid air. The chart shown in the right of Figure 2 shows an example of “wet” or
“dry” exergy together with “warm” or “cool” exergy contained by a volume of air with varieties of
temperature and humidity, assuming that the environmental temperature and relative humidity are
30 °C and 65 %. A unique and useful feature of wet/dry exergy is that it has the same unit as warm/cool
exergy. Therefore it is possible that wet/dry exergy is added to or extracted from warm/cool exergy,
though, in the case of energy calculation, an amount of water vapor measured by the unit of mass (kg)
must be converted into the quantity of thermal energy measured by the unit of Joule using the value of
latent heat. According to the graph in the right of Figure 2, cool and dry exergy of a volume of air at
3
3
25 °C; 50 % is 400 J/m and those at 28 °C and 60 % is 100 J/m . The latter is one-fourth the former;
this implies that conventional dehumidifying together with convective cooling is rather exergy-wise
intensive and low-exergy radiant cooling systems together with natural ventilation may be of
importance to pursue (Shukuya et al., 2006; Iwamatsu et al., 2007).
Heat Pump
A heat-pump system works under a summer condition as schematically drawn in the left of Figure 3. Its
Cool exergy with
conditioned air
Warm exergy with
Exhaust air
BaseCase
Case1
Consumed
Case 2
With External Shading
Warm Exergy
Cool Exergy
Case 3
With Daylighting
Exergy input
through electricity grid
0
500
1000
1500
2000
Exergy [W]
Figure 3 An electricity-driven heat pump works (see the drawing on your left) as the exergy
supplied is consumed to compress and expand the circulating medium and thereby extract
warm, cool and dry exergies. The bar graphs on your right show typical exergy balance in
summer and the possible reduction exergy consumption by external shading and by daylighting.
exergy balance equation can be written as follows (Shukuya et al., 1994; 2004).
[Electric power] – [Exergy consumed] = [Warm exergy] + [Cool/dry exergy] + [Cool/wet exergy].
(1)
An ordinary so-called air-source heat pump is a device that feeds on an amount of exergy from the
electricity grid, consumes its portion and thereby split the rest of exergy into warm, cool/dry and
cool/wet exergies. In winter, provided that the condensing unit of the heat pump is located inside a
room space, warm exergy can be supplied into the room space and consumed for heating.
Either cool or warm exergies can be found in our outdoor environment such as ground, sky, rain water,
snow, river, sea water and others. A heat pump coupled with, for example, the ground in summer
seasons can provide cool exergy into room space with the lower electricity supply and the lower exergy
consumption. Exergy balance equation for such a case should be expressed as follows.
[Electric power] + [Cool exergy from the ground (#)] - [Exergy consumed] = [Warm exergy] +
+ [Cool exergy from the ground (¥)] + [Cool exergy from the electricity ($)].
(2)
In equation (2), dry and wet exergy is neglected. A challenge must be to decrease electric-power supply
as much as possible while at the same time to increase the cool exergy (denoted by a symbol #) up to
the level of cool exergy demand (denoted by a symbol ¥ and $).
The bar graph in the right of Figure 3 shows a numerical example of exergy balance calculation for
three cases of cooling. In this calculation, dry/wet exergy is excluded. The installation of external
shading over the window and also the use of daylight for lighting indoors contribute dramatically to
reducing the exergy consumption rate at the heat pump.
Human-body Exergy Consumption Rate and Thermal Comfort in Winter
Biological systems including human body also works as a kind of heat engine. So-called metabolism is
another expression of exergy-entropy process. Whether one can feel thermally comfortable or
uncomfortable in a room space is related to the human-body exergy balance. Figure 4 shows an
example of such relationship in winter condition obtained from human thermo-regulatory system
analysis from the exergetic viewpoint (Isawa et al., 2002; 2003).
The horizontal axis represents air temperature and the vertical axis mean radiant temperature
surrounding a human body. Mean radiant temperature is the average of internal surface temperatures
of building windows, walls, floor, and ceiling. Fine lines with numbers are equi-exergy-consumption-rate
lines within the human body. The bold line drawn from upper-left down to lower-right corresponds to the
state of human body whose metabolic energy emission rate equals the energy outflow due to radiation,
convection, evaporation, and conduction.
Mean Radiant Temperature [°C]
30
0
2.6
2.5
2.8
2.7
25
Metabolic energy
rate equal to
outgoing energy
*
flow rate
PMV =0
2.5
20
2.9
3
3.2
15
3.1
3.3
3.5 3.4
3.7 3.6
4.9
10
10
4.6
4.8
4.5
4.7
15
4.4
4.3
20
4.2
3.9
4.1
3.8
4
25
30
Ambient Air Temperature [°C]
Figure 4 Relationships between human-body exergy consumption rate, whose unit is
W/m2(body surface), and his/her environmental temperature under a winter condition (0ºC;
40%rh). There is a set of room air temperature (18 to 20 ºC) and mean radiant temperature
(23 to 25 ºC) which provides him/her with the lowest exergy consumption rate.
According to the previous knowledge of human thermal physiology, such a condition in which overall
energy outflow from the human-body surface equals the metabolic energy emission rate provides the
human body with thermal comfort. In other words, any sets of room air temperature and mean radiant
temperature on the bold line in Figure 4 must give a comfortable indoor thermal condition. Nevertheless,
according to experienced architects and engineers concerned about designing comfortable built
environment, a set of relatively high mean radiant temperature and relatively low air temperature brings
about a better indoor thermal quality in winter season. This sounds consistent with such an indoor
condition that brings about the lowest exergy consumption rate within the human body as shown in
Figure 4. It suggests that the human body as a biological system has evolved over long years since the
birth of life on the earth so that we humans can feel the most comfortable with the lower exergy
consumption rate, at least in winter conditions.
Cool and Warm Radiant Exergies and Thermal Comfort in Summer
We can make a similar chart to Figure 4 as we change the outdoor environmental condition for summer
season. The values obtained are different, but such a relationship that a combination of higher mean
radiant temperature and lower air temperature gives the lowest exergy consumption rate becomes
almost the same. This seems consistent with what has been so far aimed at in case of conventional
convective cooling.
A good combination of nocturnal natural ventilation together both with external solar shading and with
an appropriate amount of internal thermal mass provides us with an indoor condition of a little lower
mean radiant temperature and higher air temperature during daytime, which is comfortable enough
especially in residential buildings. Figure 5 shows an experimental example of the relationship
between the percentage of comfort votes and warm/cool radiant exergies available in a naturally
ventilated room where the subjects perceived no air current because of little outdoor wind, though the
windows for cross ventilation were open. This result was obtained from an in-situ experiment made in
two small wooden buildings with natural ventilation in summer (Shukuya et al., 2006).
The closed circles “●” denote the cases that cool radiant exergy is available and the open circles “○”
denote warm radiant exergy. As the warm radiant exergy rate grows, the percentage of subjects voting
2
for comfort decreases. The warm radiant exergy flow rate reaching 20 mW/m results in the condition
that no subjects vote for comfort. On the other hand, the same rate of “cool” radiant exergy results in a
2
Radiant exergy [mW/m ]
The percentage of
comfort votes
[%]
160
100
80
60
Cool
40
Warm
20
0
0
10
20
30
2
Radiant exergy [mW/m ]
40
120
80
To = 3 06 K
40
0
Cool
28
30
W arm
32
34
36
Surface te mperature [ºC]
Figure 5 The percentage of comfort votes under the condition of no perceived air current as a
function of radiant exergy emitted from interior wall surfaces (see the graph on your left). Warm
and cool radiant exergies are both in the range of 0 to 100 mW/m2 (see the graph on your right).
totally opposite condition in which most of the subjects vote for comfort. An amount of cool radiant
2
exergy rate at 20mW/m is available provided that the mean radiant temperature is lowered slightly
compared to the outdoor air temperature (See the graph on your right in Figure 5).
This result confirms that the use of external solar shading is the first priority in order to make a
comfortable built environmental condition in summer with natural ventilation. The use of external solar
shading devices together with nocturnal ventilation and the use of moderate thermal mass of floors and
walls realize the production of cool radiant exergy during the daytime in summer. There are a lot of
existing buildings having no external but internal solar shading. The built environment in those
buildings in summer is equivalent to being heated by internal solar shading devices as radiant heating
panels. This in turn requires lower air temperature and humidity to be realized by high-exergy supply.
Radiant Exergy from the Sun and the Sky
It is interesting to take a look at thermodynamic and heat transfer phenomena occurring in our
surroundings with the concept of exergy, since it lets us notice that there are a variety of warm-exergy
or cool-exergy sources in respective regions. Either warm or cool radiant exergy is given by thermal
radiation, whose wavelength ranges from 3 to 100 µm.
Floor surfaces that absorb solar radiation transmitted through window glass panes provides us with a
good amount of “warm” radiant exergy during winter season. This is a smart use of warm exergy
available in the room space originating from the short-wavelength (solar) radiation; solar exergy, whose
rate is very large, is consumed at various surfaces on the ground including buildings. Solar exergy
consumption takes place inevitably outdoors and indoors so that it is wise to make use of warm exergy
originating from the solar exergy for passive solar radiative heating. There have been a lot of such trails
over the last couple of decades in various regions whose winter is cold enough to necessitate space
heating, but its importance should be recalled from the exergetic view.
Radiative cooling is also possible by cold sources. One of such cold sources can be the sky. The sky
emits “cool” radiant exergy. Figure 6 shows the relationship between cool radiant exergy available from
the sky as a function of the ambient air temperature and humidity. The cool radiant exergy from the sky
is large when the ambient temperature or relative humidity is low. In hot and humid summer climate,
2
cool radiant exergy is about 1 W/m on the horizontal surface outside. It may look very small, if
2
compared to the energy rate of solar radiation, 400~700 W/m , but it is significantly large if compared to
2
the cool radiant exergy rate of 20 to 40 mW/m shown in Figure 5; it is worth keeping in mind that 1
W/m2, namely 1000 mW/m2, is fifty times larger than 20 mW/m2.
The “cool” radiant exergy available from the sky is very attractive for low-exergy cooling in hot and dry
regions, but the same is also true even in hot and humid regions, provided that an appropriate control
of long-wavelength radiation is made as discussed above (Shukuya et al., 2003, 2004, 2006).
2
Cool Radiant Exergy [W/m ]
8
Relative Humidity
20%
6
4
40%
2
60%
80%
0
0
10
20
30
Ambient Air Temperature [°C]
Figure 6 Cool radiant exergy available from the sky, which varies with the ambient air
temperature and relative humidity. The amount of cool radiant exergy becomes large as the
ambient relative humidity is low or the ambient air temperature is low.
CONCLUDING REMARKS
As described above, exergy consumption is always accompanied with entropy generation, thus the
generated entropy must be discarded constantly from the room space to the outdoor environment to
keep “warm” or “cool” exergy at a desired level. A challenge is to seek a design solution of a system
that works with as small amount of exergy supply as possible, while at the same time producing the
required exergy from our immediate outdoor environment and making its smart use to get a certain
level of well-being in the built-environmental space.
REFERENCES
1. M. Shukuya (1994) “Energy, entropy, exergy and space heating systems”, Proceedings of the 3rd
International Conference "Healthy Buildings ’94", Vol.1, 369-374.
2. M. Shukuya ed. (2004) “Theory on Exergy and Environment”, Hokuto Shuppan Publishers Ltd.(in
Japanese).
3. M. Shukuya and A. Hammache (2002) “Introduction to the concept of exergy –for a better
understanding of low-temperature-heating and high-temperature-cooling systems–”, VTT
RESEARCH NOTES-2158, 1-41.
4. M. Shukuya (1996) “Warm exergy and cool exergy”, Proceedings of Annual Meeting, Building
Science Section, Architectural Institute of Japan, 453-454 (in Japanese).
5. M. Shukuya, K. Tokunaga, M. Nishiuchi, T. Iwamatsu, and H. Yamada (2006) “Thermal radiant
exergy in naturally-ventilated room space and its role on thermal comfort”, Proceedings of Healthy
Buildings 2006, Vol.IV, 257-262.
6. T. Iwamatsu, Y. Hoshino, E. Kataoka, and M. Shukuya (2007) “Exergetic Evaluation of
nd
High-Temperature Radiative Cooling Combined with Natural Ventilation”, 2 PALENC Conference
th
and 28 AIVC Conference (Crete Island, Greece), 27-29 September.
7. K. Isawa, T. Komizo, and M. Shukuya (2002), “Low exergy systems will provide us with the lowest
human-body exergy consumption and thermal comfort”, LOWEX NEWS, IEA-ECBCS-Annex 37:
Low Exergy Systems for Heating and Cooling of Buildings, 5-6.
8. K. Isawa, T. Komizo, and M. Shukuya (2003) “The relationships between human-body exergy
consumption, surrounding air temperature and mean radiant temperature”, Transactions of the
Built-Environmental Science, Architectural Institute of Japan, No.570, 29-35(in Japanese with
English abstract).
9. D. Schmidt and M. Shukuya (2003) “New ways towards increased efficiency in the utilization of
energy flows in buildings”, Research in Building Physics, 671-681.