Modern Engineering Thermodynamics

Summary 353
7. The general open system availability rate balance is given by Eq. (10.21) as
∑ n
i=1
1 − T
0
T bi
_Q i − _W +∑ _ma f − ∑
inlet outlet
_ma f + p 0
_V − _I =
dA
dt
system
and the modified availability rate balance (MARB) for steady state, steady flow, single-inlet, singleoutlet,
constant volume, isothermal boundary (SS, SF, SI, SO, CV, IB) open systems is given by
Eq. (10.26) as
1 − T 0
T b
_Q − _W + _m½ða f Þ in
− ða f Þ out
Š − _I = 0
8. The second law efficiency (or effectiveness) is defined in Eq. (10.29) as
ε =
A desired
result
A initial or
net input
=
_A desired
result
_A initial or
net input
9. The second law availability efficiency of a heat engine is given by Eq. (10.30) as
ε HE =
1 − T
0
T H
_W
_Q H − 1 − T 0
T L
j _Q L j
which becomes ε HE = η T /η Carnot when T 0 = T L .
10. The second law availability efficiency of a heat pump is given by Eq. (10.32) as
ε HP =
1 − T
0 _Q
T H
H
j _W in j
= 1 − T
0
T H
_Q H
j _W in j
!
= 1 − T
0
COP actual
T H heat pump
which becomes ε HP = (COP) actual HP /(COP) Carnot HP when T 0 = T L .
11. The second law availability efficiency of a refrigerator or air conditioner is given by Eq. (10.34) as
ε R/AC =
1 − T 0
T L
_Q L
j _W in j
= 1 − T
0
T L
_Q L
j _W in j
!
= 1 − T
0
COP actual
T L ref or air cond
which reduces to ε R/AC = (COP) actual R/AC /(COP) Carnot R/AC when T 0 = T H .
12. The second law availability efficiency of a four flow stream nonmixing heat exchanger is given by
Eq. (10.36) as
ε nonmixing HX = _m Cða f 4 − a f 3 Þ
_m H ða f 1 − a f 2 Þ
and, for a three flow stream heat exchanger in which the fluids mix inside its boundaries, it is given by
Eq. (10.37) as
ε mixing HX = ð1 − yÞða f 3 − a f 2 Þ
yða f 1 − a f 3 Þ
where y is the hot mass fraction, y = _m hot / _m mixed :