Page 72 - Advanced Thermodynamics for Engineers, Second Edition

3.6 PROBLEMS 57

Compare this value to the Carnot efficiency based on the temperatures of energy addition and
rejection.
[26.98%; 27.0%]
P3.2 A steam power plant operating on a basic Rankine cycle has the following parameters: maximum
(boiler) pressure 20 bar; minimum (condenser) pressure 0.5 bar. Calculate the thermal efficiency
of the cycle, and compare it to that of a Carnot cycle operating between the same temperature
limits (see P3.1). Calculate the specific power output and the back work ratio (defined as _ w P = _ w T )
for the cycle in this question and that in P3.1. Comment on the results obtained.
(Assume the pump and turbine operate isentropically.)
[24.26%; 27.0%; 598.5 kW/(kg/s); 0.34%; 14.7%]
P T
P3.3 Recalculate P3.1 assuming that the pump efficiency, h ¼ 0:8, and the turbine efficiency, h ¼
0:9: Comment on the effect on the thermal efficiency of the plant, and also the back work ratio.
[22.64%; 20.48%]
P T
P3.4 Recalculate P3.2 assuming that the pump efficiency h ¼ 0:8, and the turbine efficiency h ¼
0:9: Comment on the effect on the thermal efficiency of the plant, and also the back work ratio.
[21.81%; 0.47%]
P3.5 The engine designed by Lenoir was essentially an atmospheric engine based on the early steam
engines. In this, a combustible mixture was contained in a cylinder: it was ignited and the pressure
increased isochorically to the maximum level. After this the gas expanded isentropically through
an expansion ratio, r e , during which it produced work output. The air-standard cycle returned the
gas to state 1 through an isochoric expansion to p 1 and an isobaric compression to V 1 .
Assume p 1 ¼ 1 bar, T 1 ¼ 15 C, p 2 ¼ 10 bar and the expansion ratio, r e ¼ 5. Calculate the

specific work output and thermal efficiency of this cycle. How does this compare with the
efficiency of an equivalent Carnot cycle?
[650.30 kJ/kg; 34.97%; 90.0%]
P3.6 A Lenoir engine (described in P3.5) operates with inlet conditions of p 1 ¼ 1 bar and
T 1 ¼ 27 C. The energy added to the charge is 1000 kJ/kg, and the expansion ratio, r e , is 3.0.

Calculate the maximum pressure and temperature achieved in the cycle and its thermal
efficiency.
[5.65 bar; 1422 C; 26.00%]

P3.7 A cycle is proposed as a development of the Lenoir cycle, in which the working fluid is
expanded isentropically from its peak pressure down to a point where its temperature is equal
to T 1 , the initial temperature. The gas is then compressed isothermally back to the initial
pressure. Prove that the thermal efficiency of the cycle is given by

T 1 T 2
th
h ¼ 1 ln
T 2 T 1 T 1
where T 2 is the maximum temperature achieved in the cycle.
Calculate the thermal efficiency of the cycle if the initial pressure is 10 bar and the
maximum pressure is 35 bar. Compare this to the Carnot efficiency achievable between the
temperature limits and explain why this cycle would not be used in practice.
[49.9%; 71.4%]