Page 68 - Advanced thermodynamics for engineers

52 CHAPTER 3 ENGINE CYCLES AND THEIR EFFICIENCIES

3.3 GENERAL COMMENTS ON EFFICIENCIES
The efficiency of the Carnot cycle is directly related to the temperature ratio of the hot and cold
reservoirs. Examination of the other efficiencies will show that they are also related to temperature
ratios of the cycle. The efficiency of the Otto cycle is (Eqn (3.17))
1 T 1 T 4
h Otto ¼ 1 ¼ 1 ¼ 1 :
r ðk 1Þ T 2 T 3
The equation for the diesel engine is more complex and will not be considered here. However, the
k 1
k T 2
efficiency of the Joule cycle can also be related to the temperature ratio because r p ¼ , and hence
T 1
1 T 1 T 4
h Joule ¼ 1 k 1 ¼ 1 ¼ 1 ; in Fig. 3.17.
k T 2 T 3
r p
Hence, all heat engines have efficiencies of the form
T n
h ¼ 1 ;
th
T m
where T n and T m are particular temperatures relating to the individual cycle.

3.4 REVERSED HEAT ENGINES
Reversed heat engines were introduced in Section 2.7, and comprise refrigerators and heat pumps. The
objectives of these devices are to transfer energy from a low temperature reservoir to a higher tem-
perature one. In the case of the refrigerator, the aim is to cool the ice box and reject the energy
extracted from it into ambient conditions at a higher temperature. The purpose of the heat pump is to
warm a building by ‘pumping’ low-grade energy up to a higher temperature. Both of these devices
work by using power input to drive the processes: it is not possible, by the Second Law, for energy to
pass spontaneously from a low to a high-temperature reservoir. The cycles used to analyse reversed
heat engines are similar to those introduced above for heat engines producing power – the processes
are simply executed in reverse order.

3.4.1 REVERSED CARNOT CYCLE
If the Carnot cycle shown in Fig. 3.1 is operated in reverse, i.e. the arrows on the diagram are turned
round, as in Fig. 3.18, then the directions of the work and heat transfer terms are also reversed. This
means that net work is provided to the cycle during processes 1-2 and 3-4, and that energy (Q in )is
‘pumped’ from the low-temperature reservoir (T C ), and energy (Q out ) is delivered to the high-
temperature reservoir (T H ). Hence, the addition of work to the cycle is able to raise the ‘quality’ of
the energy in the low-temperature reservoir.

3.4.2 ACTUAL REFRIGERATOR AND HEAT PUMP CYCLES
A device which would execute this cycle is shown schematically in Fig. 3.19(a): in this case, unlike
that of the steam turbine, the pumping work is significantly larger than the work obtained from the