Page 129 - Advanced thermodynamics for engineers

5.4 EXAMPLES 115

Temperature after compressor, at 2 is
w C ð 509:9Þ
T 2 ¼ T 1 ¼ 300 ¼ 807:6K
c p 1:0045
The energy added to the cycle is

q 23 ¼ c p T 3 T 2 ¼ 1:0045 1200 807:6 ¼ 394:2kJ kg:
The net work from the cycle is w net ¼ w T þ w C ¼ 693.2 þ ( 509.9) ¼ 183.3 kJ/kg and the thermal
w net 183:3
efficiency is h ¼ ¼ ¼ 0:465:
th
q 23 394:2
The maximum net work output is defined by
b w net ¼ b 3 b 2 :

Since both 2 and 3 are at the same pressure

T 3
b 3 b 2 ¼ c p ðT 3 T 2 Þ T 0 ln
T 2
Thus

1200
b w net ¼ 1:0045 ð1200 807:6Þ 300 ln ¼ 273:6kJ=kg:
807:6
The rational efficiency of the cycle based on these dead-state conditions is
w net 183:3
h ¼ ¼ ¼ 0:670:
R
b w net 273:6
The net work output of the device is made up of

w net ¼ b w net ½ b w net Š rejected T 0 s 2 s 2s ¼ 273:6 50:9 40:2 ¼ 182:5kJ=kg:
In this case, the inefficiency of the compressor has introduced a quantity of unavailable energy
T 0 (s 2 s 2s ), which is depicted on Fig 5.7.
(c) Compressor isentropic efficiency, h C ¼ 80% and turbine isentropic efficiency, h T ¼ 80%.
Thiscyclecombinesthetwoinefficienciesconsideredabove.Hence,thenetworkoutputofthecycleis

w net ¼ w T þ w C ¼ 554:6 þð 509:9Þ¼ 44:7kJ=kg:
Net heat addition q 23 ¼ 394.2 kJ/kg.
Hence, thermal efficiency is

w net 44:7
h ¼ ¼ ¼ 0:113:
th
q 23 394:2
The net work output of this cycle is made up in the following way

w net ¼ b w net ½ b w net Š rejected T 0 s 4 s 4s T 0 s 2 s 2s
¼ 273:6 117:4 72:2 40:2 ¼ 43:8kJ=kg