Heat is a form of disorganized energy, and thus only a portion of it can
be converted to work, which is a form of organized energy (the second
law). We can always produce work from heat at a temperature above the
environment temperature by transferring it to a heat engine that rejects the
waste heat to the environment. Therefore, heat transfer is always accom-
panied by exergy transfer. Heat transfer Qat a location at thermodynamic
temperature T is always accompanied by exergy transfer Xheat in the
amount of
Exergy transfer by heat: (8–24)
This relation gives the exergy transfer accompanying heat transfer Q
whether Tis greater than or less than T 0. When TT 0 , heat transfer to a
system increases the exergy of that system and heat transfer from a sys-
tem decreases it. But the opposite is true when TT 0. In this case, the
heat transfer Qis the heat rejected to the cold medium (the waste heat),
and it should not be confused with the heat supplied by the environment
at T 0. The exergy transferred with heat is zero when TT 0 at the point
of transfer.
Perhaps you are wondering what happens when TT 0. That is, what if
we have a medium that is at a lower temperature than the environment? In
this case it is conceivable that we can run a heat engine between the environ-
ment and the “cold” medium, and thus a cold medium offers us an opportu-
nity to produce work. However, this time the environment serves as the heat
source and the cold medium as the heat sink. In this case, the relation above
gives the negative of the exergy transfer associated with the heat Qtrans-
ferred to the cold medium. For example, for T100 K and a heat transfer
of Q1 kJ to the medium, Eq. 8–24 gives Xheat(1 300/100)(1 kJ)
2 kJ, which means that the exergy of the cold medium decreases by
2 kJ. It also means that this exergy can be recovered, and the cold
medium–environment combination has the potential to produce 2 units of
work for each unit of heat rejected to the cold medium at 100 K. That is,
a Carnot heat engine operating between T 0 300 K and T100 K pro-
duces 2 units of work while rejecting 1 unit of heat for each 3 units of
heat it receives from the environment.
When TT 0 , the exergy and heat transfer are in the same direction.
That is, both the exergy and energy content of the medium to which heat is
transferred increase. When TT 0 (cold medium), however, the exergy and
heat transfer are in opposite directions. That is, the energy of the cold
medium increases as a result of heat transfer, but its exergy decreases. The
exergy of the cold medium eventually becomes zero when its temperature
reaches T 0. Equation 8–24 can also be viewed as the exergy associated with
thermal energy Qat temperature T.
When the temperature Tat the location where heat transfer is taking place
is not constant, the exergy transfer accompanying heat transfer is deter-
mined by integration to be
Xheata 1 (8–25)
T 0
Tb dQXheata 1 T 0
TbQ¬¬ 1 kJ 2
Chapter 8 | 441HEAT SOURCEHEAT SOURCE
Temperature: Temperature: T
Energy transferred: Energy transferred: EExergy = Exergy = (^) ( 1 – TT^0 (E
T 0
FIGURE 8–26
The Carnot efficiency hc 1 T 0 /T
represents the fraction of the energy
transferred from a heat source at
temperature Tthat can be converted
to work in an environment at
temperature T 0.