10-95
10-90 A combined gas-steam power plant is considered. The topping cycle is a gas-turbine cycle and the bottoming
cycle is a nonideal reheat Rankine cycle. The moisture percentage at the exit of the low-pressure turbine, the steam
temperature at the inlet of the high-pressure turbine, and the thermal efficiency of the combined cycle are to be
determined.
Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential energy changes are negligible. 3 Air is an ideal gas
with variable specific heats.
Analysis (a) We obtain the air properties from EES. The analysis of gas cycle is as follows
 h7  288.50 kJ/kg
T7  15C 
T7  15C

s 7  5.6648 kJ/kg
P7  100 kPa 
P8  700 kPa 
h8 s  503.47 kJ/kg
s8  s 7

C 
Combustion
chamber
8
9
Compressor
h8 s  h7

 h8  h7  h8 s  h7  /  C
h8  h7
 290.16  503.47  290.16 / 0.80 
 557.21 kJ/kg
Gas
turbine
7
11
10
Heat
exchanger
3
 h9  1304.8 kJ/kg
T9  950C 
T9  950C 
s 9  6.6456 kJ/kg
P9  700 kPa 
Steam
turbine
4
6
P10  100 kPa 
h10 s  763.79 kJ/kg
s10  s 9

h h
 T  9 10  h10  h9   T h9  h10 s 
h9  h10 s
 1304.8  0.80 1304.8  763.79 
5
Condenser
pump
2
1
 871.98 kJ/kg
 h11  475.62 kJ/kg
T11  200 C 
From the steam tables (Tables A-4, A-5, and A-6
or from EES),
h1  h f
v1  v f
@ 10 kPa
@ 10 kPa
9
950C
·
Qin
 191.81 kJ/kg
 0.00101 m3 /kg
wpI,in  v1 P2  P1  /  p

T
10

 1 kJ 
 / 0.80
 0.00101 m 3 /kg 6000  10 kPa 
1 kPa  m 3 

 7.56 kJ/kg
8s
P6  10 kPa  x 6 s

s 6s  s5
h
6s
6 MPa
3
1 MPa
5
15C
7
2
1
7.4670  0.6492


 0.9091
s fg
7.4996
 h f  x 6 s h fg  191.81  0.90912392.1  2366.4 kJ/kg
s 6s  s f
10s
8
h2  h1  wpI,in  191.81  7.65  199.37 kJ/kg
P5  1 MPa  h5  3264.5 kJ/kg
T5  400C  s 5  7.4670 kJ/kg  K
GAS
CYCLE
11 STEAM
4
CYCLE 4s
10 kPa
·
6s 6
Qout
s
PROPRIETARY MATERIAL. © 2011 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course
preparation. If you are a student using this Manual, you are using it without permission.
10-96
T 
h5  h6

 h6  h5   T h5  h6 s 
h5  h6 s
 3264.5  0.80 3264.5  2366.4
 2546.0 kJ/kg
P6  10 kPa

x  0.9842
h6  2546.5 kJ/kg  6
Moisture Percentage  1  x 6  1  0.9842  0.0158  1.6%
(b) Noting that Q  W  Δke  Δpe  0 for the heat exchanger, the steady-flow energy balance equation yields
E in  E out
 m h   m h
i i
e e
m s h3  h2   m s h5  h4   m air h10  h11 
(1.15)(3346.5  199.37)  (3264.5  h4 )  (10)(871.98  475.62) 
 h4  2965.0 kJ/kg
Also,
P3  6 MPa  h3 

T3  ?
 s3 
T 
P4  1 MPa 
 h4 s 
s 4s  s3

h3  h4

 h4  h3   T h3  h4 s 
h3  h4 s
The temperature at the inlet of the high-pressure turbine may be obtained by a trial-error approach or using EES from the
above relations. The answer is T3 = 468.0ºC. Then, the enthalpy at state 3 becomes: h3 = 3346.5 kJ/kg
(c)
W T,gas  m air h9  h10   10 kg/s 1304.8  871.98 kJ/kg  4328 kW
W C,gas  m air h8  h7   10 kg/s 557.21  288.50  kJ/kg  2687 kW
W net,gas  W T,gas  W C,gas  4328  2687  1641 kW
W T,steam  m s h3  h4  h5  h6   1.15 kg/s 3346.5  2965.0  3264.5  2546.0 kJ/kg  1265 kW
W P,steam  m s w pump  1.15 kg/s 7.564 kJ/kg  8.7 kW
W net,steam  W T,steam  W P,steam  1265  8.7  1256 kW
W net,plant  W net,gas  W net,steam  1641  1256  2897 kW
(d)
Q in  m air h9  h8   10 kg/s 1304.8  557.21 kJ/kg  7476 kW
 th 
W net,plant 2897 kW

 0.388  38.8%
7476 kW
Q in
PROPRIETARY MATERIAL. © 2011 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course
preparation. If you are a student using this Manual, you are using it without permission.