Page 72 - Advanced thermodynamics for engineers

56 CHAPTER 3 ENGINE CYCLES AND THEIR EFFICIENCIES

Heat extracted from the evaporator (cold reservoir)
Q C ¼ Q 41 ¼ h 4 h 1 ¼ h 4 h 2 ¼ 1137 313:4 ¼ 823:6kJ=kg:
h 4 h 1 823:6
Hence, coefficient of performance of refrigerator, b ¼ ¼ 336:3 ¼ 2:449:
Heat transferred from the condenser (hot reservoir) h 3 h 4
Q H ¼ Q 32 ¼ h 2 h 3 ¼ 313:4 1473:3 ¼ 1159:9kJ=kg
h 2 h 3 1159:9
0 ¼ 3:449:
Hence, coefficient of performance of heat pump, b ¼ ¼
h 4 h 3 336:3
Thus, both the coefficients of performance are greater than unity, and the coefficient of perfor-
mance of the heat pump is one greater than that of the refrigerator – even though the devices are not
reversible. If the devices had been reversible, i.e. had followed the reversed Carnot cycle, then the
values would have been
T C T 1 233
b ¼ ¼ ¼ ¼ 2:913
T H T C T 3 T 1 313 233
T H T 3 313
0
b ¼ ¼ ¼ ¼ 3:913
T H T C T 3 T 1 313 233
It can be seen that the reversible reversed heat engines, operating on the Carnot cycle, have higher
coefficients of performance than those undergoing cycles with irreversibilities.

3.5 CONCLUDING REMARKS
This chapter has introduced a range of different cycles, from the fundamental Carnot cycle through
more realistic cycles for simulating actual power plant. It is possible to evaluate the thermal efficiency
of these cycles, and these efficiencies can be compared to that of the Carnot cycle. The Carnot cycle is
shown to be the most efficient cycle operating between two temperature levels, simply because it is
able to receive and reject energy at the upper and lower temperatures. None of the other cycles can
achieve this, although the basic Rankine cycle can come close.
Air-standard cycles have been introduced, and cycles that can be used to analyse reciprocating
engines, e.g. spark-ignition and diesel engines and gas turbines have been described. It has been
explained that engines following these cycles are usually not heat engines because working fluid flows
across their boundaries. It has also been demonstrated that they can never achieve the Carnot efficiency
because the energy addition and rejection occurs at varying temperature, and the efficiency of the
cycles is related to the mean temperatures of energy addition and rejection.
Finally, reversed heat engine cycles, i.e. refrigerators and heat pumps, have been introduced and
their ‘efficiency’ has been defined as the coefficient of performance. Reciprocating engines and gas
turbines will be discussed further in Chapters 16 and 17 respectively.

3.6 PROBLEMS
P3.1 A steam turbine operates on a Carnot cycle, with a maximum pressure of 20 bar and a
condenser pressure of 0.5 bar. Calculate the salient points of the cycle, the energy addition and
work output per unit mass, and hence the thermal efficiency of the cycle.