Page 240 - The Mechatronics Handbook

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destroyed by irreversibilities within the system or control volume. Exergy balances can be written in
various forms, depending on whether a closed system or control volume is under consideration and
whether steady-state or transient operation is of interest. Owing to its importance for a wide range of
applications, an exergy rate balance for control volumes at steady state is presented alternatively as
Eqs. (12.12a) and (12.12b).

˙
˙
˙
0 = ∑ E q, j – W + ∑ E i – ∑ E e – E D (12.12a)
˙
˙
j i e
------------------------------- ---
rates of rate of
exergy exergy
transfer destruction
˙
0 = ∑   1 – T 0 ˙ W + ∑ m ˙ i e i ∑ m ˙ e e e – E D (12.12b)
˙
----- Q j –
–

j T j i e
˙
˙
W has the same significance as in Eq. (12.7a): the work rate excluding the flow work. Q j is the time rate of
heat transfer at the location on the boundary of the control volume where the instantaneous temperature
is T j . The associated rate of exergy transfer is
E q, j =   1 – T 0 ˙ (12.13)
˙

----- Q j
T j
As for other control volume rate balances, the subscripts i and e denote inlets and exits, respectively. The
exergy transfer rates at control volume inlets and exits are denoted, respectively, as E i = m ˙ ie i and
˙
E e = m ˙ e e . Finally, E D accounts for the time rate of exergy destruction due to irreversibilities within
˙
˙
e
the control volume. The exergy destruction rate is related to the entropy generation rate by
E D = T 0 S gen (12.14)
˙
˙
The specific exergy transfer terms e i and e e are expressible in terms of four components: physical exergy
PH
CH
KN
PT
e , kinetic exergy e , potential exergy e , and chemical exergy e :
e = e PH + e KN + e PT + e CH (12.15a)
The first three components are evaluated as follows:
PH
(
e = ( hh 0 ) T 0 ss 0 ) (12.15b)
–
–
–
KN 1 2
e = --v (12.15c)
2
PT
e = gz (12.15d)
In Eq. (12.15b), h 0 and s 0 denote, respectively, the specific enthalpy and specific entropy at the restricted
dead state. In Eqs. (12.15c) and (12.15d), v and z denote velocity and elevation relative to coordinates
in the environment, respectively.
To evaluate the chemical exergy (the exergy component associated with the departure of the chemical
composition of a system from that of the environment), alternative models of the environment can be
employed depending on the application; see for example Moran (1989) and Kotas (1995). Exergy analysis
is facilitated, however, by employing a standard environment and a corresponding table of standard

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