Page 76 - Advanced thermodynamics for engineers

CHAPTER
4
AVAILABILITY AND EXERGY

Many of the analyses performed by engineers are based on the First Law of Thermodynamics,
which is a law of energy conservation. Most mechanical engineers use the Second Law of Ther-
modynamics simply through its derived property – entropy (S). However, it is possible to introduce
other ‘Second Law’ properties to define the maximum amounts of work achievable from certain
systems. Previously, in Chapter 2, the properties Helmholtz energy (F) and Gibbs energy (G)were
derived as means of assessing the equilibrium of various systems. This section considers how the
maximum amount of work available from a system, when interacting with surroundings, can be
estimated. This shows, as expected, that all the energy in a system cannot be converted to work:
the Second Law stated that it is impossible to construct a heat engine that does not reject energy to
the surroundings.

4.1 DISPLACEMENT WORK
The work done by a system can be considered to be made up of two parts: that done against a resisting
force and that done against the environment. This can be seen in Fig. 4.1. The pressure inside the
system, p, is resisted by a force, F, and the pressure of the environment. Hence, for System A, which is
in equilibrium with the surroundings,

pA ¼ F þ p 0 A (4.1)
where A is the area of cross-section of the piston.
If the piston moves a distance, dx, then the work done by the various components shown in
Fig. 4.1 is
pAdx ¼ Fdx þ p 0 Adx (4.2)

System A

F
p
p
0
FIGURE 4.1
Forces acting on a piston.

Advanced Thermodynamics for Engineers. http://dx.doi.org/10.1016/B978-0-444-63373-6.00004-6 61
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