Modern Engineering Thermodynamics

2. The coefficient of performance of the reversed Carnot benchmark cycle:
and
3. The equation for assigning refrigerant numbers:
COP Carnot HP =
T H
T H − T L
COP Carnot R/AC =
T H − T L
R-ða − 1Þðb + 1Þd
Summary 583
T L
T g − T a
T a − T e
T 1 − T 4
1
PR ðk−1Þ/k − 1
where a = number of carbon atoms, b = number of hydrogen atoms, c = number of chlorine atoms, and
d = number of fluorine atoms in the refrigerant molecule. Note that when a = 1, the leading a − 1 = 0
number is omitted from the R number designation.
4. The coefficient of performance of a dual-cascade, vapor-compression refrigeration system:
COP dual
=
cascade
_m B ðh 1B − h 4hB Þ
_m A ðh 2sA − h 1A Þ/ðη s Þ c−A + _m B ðh 2sB − h 1B Þ/ðη s Þ c−B
5. The coefficient of performance of a dual-stage, vapor-compression refrigeration system:
ð1 − x flash Þðh 1B − h 4hB Þ
COP dual − stage =
ðh 2sA − h 1A Þ/ðη s Þ c−A
+ ð1 − x flash Þðh 2sB − h 1B Þ/ðη s Þ c−B
where x flash is the quality of the vapor leaving the flash chamber.
6. The coefficient of performance of a Carnot absorption refrigeration system:
ðCOPÞ Carnot
absorption
refrigerator
where T e is the evaporator temperature, T g is the gas generator temperature, and T a is the ambient
temperature.
7. The coefficient of performance of a reversed Brayton cycle heat pump:
COP reversed
=
Brayton cycle
HP
= T e
T g
and of a reversed Brayton cycle refrigerator or air conditioner:
COP reversed
=
Braytonc ycle
R/AC
T 2 − T 3
ðT 2s − T 1 Þ/ðη s Þ c
− ðT 3 − T 4s Þðη s Þ e
ðT 2s − T 1 Þ/ðη s Þ c − ðT 3 − T 4s Þðη s Þ e
If the reversed Brayton cycle operates on an air standard cycle (ASC), then these equations become
and
COP reversed
=
Brayton ASC
HP
COP reversed
=
Brayton ASC
R=AC
1
1 − PR ð1−kÞ/k
where PR is the compressor or expander pressure ratio.
8. The coefficient of performance of a reversed Stirling air standard cycle heat pump and refrigerator or air
conditioner is the same as the reversed Carnot cycle:
COP reversed Stirling
ASC HP
= T H