Modern Engineering Thermodynamics

352 CHAPTER 10: Availability Analysis
Some of the more important equations introduced in this chapter are (recall that the thermodynamic properties
of the local environment or ground state are written as T 0 , p 0 , V 0, v 0 , U 0 , u 0 , H 0 , h 0 , S 0 and s 0 ) follow.
1. The maximum reversible work that a closed system can perform is given by Eq. (10.1) as
ðWÞ maximum
reversible
= E − E 0 − T 0 ðS − S 0 Þ
and the maximum reversible useful work that a closed system can perform is given by Eq. (10.2) as
ðWÞmaximum
reversible
useful
= ðWÞ maximum
reversible
− ðWÞreversible = E − E 0 + p 0 ðV − V 0Þ − T 0 ðS − S 0 Þ
moving
boundary
2. The total availability A of a closed system is given by Eq. (10.3) as
A = ðWÞmaximum
= E − E
reversible
0 + p 0 ðV − V 0Þ − T 0 ðS − S 0 Þ
useful
= mu− u 0 + p 0 ðv − v 0 Þ − T 0 ðs − s 0 Þ + V 2 /2g c + gZ/g c
and the specific availability, a, of a closed system is given by Eq. (10.4) as
a = A/m = u − u 0 + p 0 ðv − v 0 Þ − T 0 ðs − s 0 Þ + V 2 /2g c + gZ/g c
3. The change in total and specific availability of a closed system as it passes from state 1 to state 2 is given by
Eqs. (10.5) and (10.6) as
and
A 2 − A 1 = E 2 − E 1 + p 0 ðV 2 − V 1Þ − T 0 ðS 2 − S 1 Þ
= m½u 2 − u 1 + p 0 ðv 2 − v 1 Þ − T 0 ðs 2 − s 1 Þ + ðV 2 2 − V2 1 Þ/2g c + gðZ 2 − Z 1 Þ/g c Š
a 2 − a 1 = u 2 − u 1 + p 0 ðv 2 − v 1 Þ − T 0 ðs 2 − s 1 Þ + ðV 2 2 − V 2 1 Þ/2g c + gðZ 2 − Z 1 Þ/g c
4. The irreversibility I and the irreversibility rate _ I that occur inside a system are given by Eqs. (10.14) and
(10.15) as
and
1I 2 = T 01 ðS P Þ 2
≥ 0
_I = T 0
_S P ≥ 0
5. The availability balance (AB) and availability rate balance (ARB) for a closed system with a single heat
transfer mode occurring at a constant system boundary temperature T b is given by Eqs. (10.18) and
(10.19) as
1 − T
0
ð 1 Q 2 Þ − 1W 2 + p 0 ðV 2 − V 1Þ − 1 I 2 = ðA 2 − A 1 Þ
T system = ½mða 2 − a 1 ÞŠ system
bi
and
1 − T
0
dV
_Q − _W + p 0
T b
dt − _I =
dA
dt
system
6. The specific flow availability of mass crossing a system boundary is defined by Eq. (10.20) as
a f = h − h 0 − T 0 ðs − s 0 Þ + V2
2g c
+ gZ
g c