Page 101 - Advanced thermodynamics for engineers

86 CHAPTER 4 AVAILABILITY AND EXERGY

when both the temperature and pressure of the system are equal to those of the dead state. The
term exergy was proposed by Rant (1956), and similar functions had previously been defined by
Gibbs (1928) and Keenan (1963).
Exergy will be given the symbol B (sometimes it is given the symbol X) and specific exergy will be
denoted by b (or x). The exergy of a system at state 1 is defined by

B 1 ¼ A 1 A 0 (4.51)
where
A 1 is the available energy at state 1 and
A 0 is the available energy at the dead state.

If a system undergoes a process between states 1 and 2 the maximum useful work, or available
energy, that may be obtained from it is given by

W ¼ A 1 A 2 ¼ðA 1 A 0 Þ ðA 2 A 0 Þ¼ B 1 B 2 (4.52)
Hence the maximum work, or heat transfer, that can be obtained as a system changes between two
states is defined as the difference in exergy of those two states.
Exergy is very similar to available energy and is a quasi-, or pseudo-property. This is because it is
not defined solely by the state of the system but also by the datum, or dead, state that is used.
A number of examples of the use of exergy will be given.

4.9.1 HEAT TRANSFER
It is possible for energy to be transferred from one body to another without any loss of available energy.
This occurs when the heat or energy transfer is ideal or reversible. No real heat transfer process will
exhibit such perfection and exergy can be used to show the best way of optimising the effectiveness of
such an energy transfer. All actual heat transfer processes are irreversible and the irreversibility results
in a loss of exergy.
It should be noted in this section that even though the heat transfer processes for each of the systems
are internally reversible, they might also be externally irreversible.
4.9.1.1 Ideal, reversible heat transfer
Ideal reversible heat transfer can be approached in a counterflow heat exchanger. In this type of device,
the temperature difference between the two streams is kept to a minimum, because the hot ‘source’
fluid on entering the heat exchanger is in closest contact to the ‘sink’ fluid which is leaving the device,
and vice versa. The processes involved are depicted by two almost coincident lines from 1 to 2 in
Fig. 4.10.
In this ideal process, it will be assumed that, at all times, the fluid receiving the heat is at tem-
perature, T, while the temperature of the source of heat is at all times at temperature, T þ dT,i.e. T 1c
is dT less than T 2h etc. From the First Law of Thermodynamics it is obvious that, if the boundaries of
the control volume are insulated from the surroundings, the energy transferred from the hot stream
must be equal to the energy received by the cold stream. This means that the areas under the curves in
Fig. 4.10 must be equal; in this case they are identical. The exergy change of the hot stream is then
given by