# thermal efficiency of the cycle is to be determined. 3 k

9-101
9-134 A regenerative gas-turbine cycle with three stages of compression and three stages of expansion is considered. The
thermal efficiency of the cycle is to be determined.
Assumptions 1 The air standard assumptions are applicable. 2 Air is an ideal gas with constant specific heats at room
temperature. 3 Kinetic and potential energy changes are negligible.
Properties The properties of air at room temperature are cp = 1.005 kJ/kgK and k = 1.4 (Table A-2a).
Analysis The temperatures at various states are obtained as follows
T2  T4  T6  T1 r p( k 1) / k  (290 K)(4) 0.4/1.4  430.9 K
T
T7  T6  20  430.9  20  450.9 K
q in  c p (T8  T7 )
q in
T8  T7 
cp
 1
T9  T8 
 rp

T10  T9 




cp
 1
T11  T10 
 rp

T12  T11 
T13




q in
cp
 1
 T12 
 rp

 450.9 K 
( k 1) / k
q in




9
7
300 kJ/kg
 749.4 K
1.005 kJ/kg  K
6
290 K
1
 (749.4 K) 
4
 504.3 K 
( k 1) / k
 504.3 K
5
2
3
1
13
11
14
s
300 kJ/kg
 802.8 K
1.005 kJ/kg  K
1
 (802.8 K) 
4
 540.2 K 
( k 1) / k
0.4/1.4
4
12
1
8
0.4/1.4
 540.2 K
300 kJ/kg
 838.7 K
1.005 kJ/kg  K
1
 (838.7 K) 
4
0.4/1.4
 564.4 K
T14  T13  20  564.4  20  544.4 K
The heat input is
q in  300  300  300  900 kJ/kg
The heat rejected is
q out  c p (T14  T1 )  c p (T2  T3 )  c p (T4  T5 )
 (1.005 kJ/kg  K)(544.4  290  430.9  290  430.9  290) R
 538.9 kJ/kg
The thermal efficiency of the cycle is then
 th  1 
q out
538.9
1
 0.401  40.1%
900
q in
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