Page 258 - The Mechatronics Handbook

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The processes taking place in power systems are sufficiently complicated that idealizations are typically
employed to develop tractable thermodynamic models. The air standard analysis of gas power systems
considered in the present section is a noteworthy example. Depending on the degree of idealization, such
models may provide only qualitative information about the performance of the corresponding real-world
systems. Yet such information frequently is useful in gauging how changes in major operating parameters
might affect actual performance. Elementary thermodynamic models also can provide simple settings to
assess, at least approximately, the advantages and disadvantages of features proposed to improve ther-
modynamic performance.
Work and Heat Transfer in Internally Reversible Processes
Expressions giving work and heat transfer in internally reversible processes are useful in describing the
themodynamic performance of vapor and gas cycles. Important special cases are presented in the dis-
cussion to follow. For a gas as the system, the work of expansion arises from the force exerted by the
system to move the boundary against the resistance offered by the surroundings:

W = ∫ 2 F x =d ∫ 2 pA x
d
1 1

where the force is the product of the moving area and the pressure exerted by the system there. Noting
that Adx is the change in total volume of the system,

W = ∫ 2 p V
d
1
This expression for work applies to both actual and internal expansion processes. However, for an
internally reversible process p is not only the pressure at the moving boundary but also the pressure
throughout the system. Furthermore, for an internally reversible process the volume equals mv, where
the specific volume v has a single value throughout the system at a given instant. Accordingly, the work
of an internally reversible expansion (or compression) process per unit of system mass is

 W  = 2
m  int ∫
d
 ----- pv (12.23)
rev 1
When such a process of a closed system is represented by a continuous curve on a plot of pressure vs.
specific volume, the area under the curve is the magnitude of the work per unit of system mass: area a-
b-c′-d′ of Fig. 12.6.
For one-inlet, one-exit control volumes in the absence of internal irreversibilities, the following expres-
sion gives the work developed per unit of mass flowing:

2
˙
 = – ∫ e vp + v i – v e 2 gz i – ) (12.24a)
W
--------------- +
(
-----
d
 int i 2 z e
m ˙
rev
where the integral is performed from inlet to exit (see Moran and Shapiro (2000) for discussion). If there
is no significant change in kinetic or potential energy from inlet to exit, Eq. (12.24a) reads
˙
W
 = – ∫ e vp ( ∆ke = ∆pe = 0) (12.24b)
d
-----
 int i
m ˙
rev
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