Page 100 - Advanced thermodynamics for engineers

4.9 EXERGY 85

Equation (4.49) is the unsteady flow availability equation that is the availability equivalent of the
unsteady flow energy equation. Many of the processes considered in engineering are steady state ones,
which means that the conditions in the control volume do not change with time. This means that
dA cv =dt ¼ 0 and dV=dt ¼ 0; and then Eqn (4.49) can be simplified to

X T 0 _ _ X _ X _
0 ¼ 1 Q W þ m i a f i m e a f e T 0 _ s cv
T
j i e

T 0
X X X
_
_
_
_
_
¼ 1 Q W þ m i a f i m e a f e I cv (4.50)
T
j i e
Example 4.8.1: steady flow availability
Superheated steam at 30 bar and 250 C flows through a throttle with a downstream pressure of

5 bar. Calculate the change in flow availability across the throttle, neglecting the kinetic and potential
terms, if the dead-state condition is t 0 ¼ 25 C and p 0 ¼ 1 bar.

A throttle does not produce any work, and it can be assumed that the process is adiabatic (see
_
_
Chapter 1, Section 1.5.8.3), i.e. Q ¼ 0; W ¼ 0:
Hence, Eqn (4.50) becomes, taking into account there is only one inlet and outlet
_ _ _
0 ¼ m i a f i m e a f e I cv
The conditions at inlet, i, are
h i ¼ 2858 kJ=kg; s i ¼ 6:289 kJ=kg K;
and the conditions at exhaust, e, are
h e ¼ 2858 kJ=kg; s e ¼ 7:0650 kJ=kg K:
Hence the irreversibility per unit mass is
_ I cv
_
i cv ¼ ¼ðh i T 0 s i Þ ðh e T 0 s e Þ¼ð2858 298 6:289Þ ð2858 298 7:0650Þ
m _
¼ 231:28 kJ=kg
The significance of this result is that although energy is conserved in the flow through the throttle
the ability of the fluid to do work is reduced by the irreversibility. In this case, because the enthalpy
does not change across the throttle, the irreversibility could have been evaluated by

T 0 ðs 2 s 1 Þ¼ 298 ð7:065 6:289Þ¼ 231:28 kJ=kg:

4.9 EXERGY

Exergy is basically the available energy based on datum conditions at a dead state; it was introduced in
Example 4.3.3. An obvious datum to be used in most calculations is the ambient condition, say p 0 , T 0 .
This datum condition can be referred to as the dead state and the system reaches this when it is in
thermal and mechanical equilibrium with it. A state of thermal and mechanical equilibrium is reached