Page 125 - Advanced thermodynamics for engineers

5.4 EXAMPLES 111

The rational efficiency is
½w net Š actual ½w net Š actual 956 2:11
R
h ¼ ¼ ¼ y1:00
b 4 b 2 b w net 955:2

(a) Turbine efficiency, h T ¼ 80%.

w T ¼ h ðw T Þ isen ¼ 0:80 956 ¼ 764:8kJ kg:
T
w net w T þ w P 764:8 2:0
Hence, the thermal efficiency of the cycle is h ¼ ¼ ¼ ¼ 0:234
th
The rational efficiency is q in h 4 h 2 3601 342:0
½w net Š actual ½w net Š actual 764:8 2:0
h ¼ ¼ ¼ ¼ 0:799 :
R
b 5 b 2 b w net 955:2
Hence, again, the effect of the turbine efficiency is to reduce the rational efficiency by an amount
almost equal to its isentropic efficiency.
(b) Feed pump efficiency, h P ¼ 70%.

The effect on the feed pump work is the same as above, and the thermal efficiency of the cycle
becomes

w net w T þ w P 956 2:86
h ¼ ¼ ¼ ¼ 0:293:
th
q in h 4 h 2 0 3601 342:8
The rational efficiency is
½w net Š actual ½w net Š actual 956 2:86
h ¼ ¼ ¼ ¼ 0:998
R
b 5 b 2 0 b w net 910:8 ð 43:7Þ
Again, the reduction in thermal efficiency is small and the rational efficiency is almost 1.
(c) Turbine efficiency, h ¼ 80%; feed pump efficiency, h P ¼ 70%.
T
w net w T þ w P 764:8 2:86
The thermal efficiency is h ¼ ¼ ¼ ¼ 0:234
th
q in h 5 h 2 0 3601 342:8
½w net Š actual ½w net Š actual 764:8 2:86
The rational efficiency is h ¼ ¼ ¼ ¼ 0:798
R
b 5 b 2 0 b w net 955:2
It can be seen that both the basic and superheated Rankine cycles are equally affected by
inefficiencies in the individual components. The rational efficiency is an estimate of how close the
cycle comes to the internally reversible cycle.
Q4. Gas turbine cycle
A gas turbine operating on an ideal Joule cycle, has a pressure ratio of 20:1, and a peak temperature
of 1200 K. Calculate the net work output, the maximum work output, the thermal efficiency and the
rational efficiency of the cycle. Assume that the working fluid is air with a value of k ¼ 1.4 and a
specific gas constant R ¼ 0.287 kJ/kg K. The inlet conditions at 1 are 1 bar and 300 K, and these
should be taken as the dead-state conditions also.