Page 132 - Mechanical Engineers' Handbook (Volume 4)

2 Exergy Analysis 121

dV
˙
˙
E W P 0
W
dt
The first and second laws of thermodynamics can be combined to show that the available
work transfer rate from the system of Fig. 1 is given by the equation 1
n
d (E TS PV)
T
˙
˙
E 1 0 Q
W 0 0 i
dt i 1 T i
Accumulation Exergy transfer
of nonflow exergy via heat transfer
˙ m(h Ts) ˙ m(h T s) TS ˙
in 0 out 0 0 gen
Intake of Release of Destruction
flow exergy via
flow exergy via of exergy
mass flow
mass flow
where E, V, and S are the instantaneous energy, volume, and entropy of the system, and h
is shorthand for the specific enthalpy plus the kinetic and potential energies of each stream,
h h – 1 2 V gz. The first four terms on the right-hand side of the E ˙ W equation represent
2
the exergy rate delivered as useful power (to an external user) in the limit of reversible
˙
operation (E ˙ W,rev , S ˙ gen 0 ). It is worth noting that the E W equation is a restatement of the
Gouy-Stodola theorem (see Section 5), which is the proportionality between the rate of
exergy destruction and the rate of entropy generation
˙
E ˙ W,rev E TS ˙
0gen
W
A special exergy nomenclature has been devised for the terms formed on the right side of
the E ˙ W equation. The exergy content associated with a heat transfer interaction (Q , T ) and
i
i
the environment (T ) is the exergy of heat transfer,
0
Q 1
E Qi i T 0
T
i
This means that the heat transfer with the environment (Q , T ) carries zero exergy.
0
0
Associated with the system extensive properties (E, S, V) and the two specified intensive
properties of the environment (T , P ) is a new extensive property: the thermomechanical or
0
0
physical nonflow availability,
A E TS PV
0
0
a e Ts P v
0
0
Let A represent the nonflow availability when the system is at the restricted dead state (T ,
0 0
P ), that is, in thermal and mechanical equilibrium with the environment, A E T S
0 0 0 0 0
P V . The difference between the nonflow availability of the system in a given state and
0 0
its nonflow availability in the restricted dead state is the thermomechanical or physical non-
flow exergy,

A A E E T (S S ) P (V V )
0
0
0
0
0
0
a a e e T (s s ) P (v v )
0
0
0
0
0
0
The nonflow exergy represents the most work that would become available if the system
were to reach its restricted dead state reversibly, while communicating thermally only with