9-77
9-102 A modified Brayton cycle with air as the working fluid operates at a specified pressure ratio. The T-s diagram is to be
sketched and the temperature and pressure at the exit of the high-pressure turbine and the mass flow rate of air are to be
determined.
Assumptions 1 Steady operating conditions exist. 2 The air-standard assumptions are applicable. 3 Kinetic and potential
energy changes are negligible. 4 Air is an ideal gas with constant specific heats.
Properties The properties of air are given as cv = 0.718 kJ/kg·K, cp = 1.005 kJ/kg·K, R = 0.287 kJ/kg·K, k = 1.4.
Analysis (b) For the compression process,
P
T2  T1  2
 P1



( k 1) / k
T
 (273 K)(8) 0.4/1.4  494.5 K
The power input to the compressor is equal to the power output
from the high-pressure turbine. Then,
P3 = P2
3
1500 K
P4
2
4
W Comp,in  W HP Turb,out
P5
5
m c p (T2  T1 )  m c p (T3  T4 )
273 K
T2  T1  T3  T4
1
s
T4  T3  T1  T2  1500  273  494.5  1278.5 K
The pressure at this state is
P4  T4

P3  T3




k /( k 1)
T

 P4  rP1  4
 T3




k /( k 1)
 1278.5 K 
 8(100 kPa)

 1500 K 
1.4 / 0.4
 457.3 kPa
(c) The temperature at state 5 is determined from
P
T5  T4  5
 P4



( k 1) / k
 100 kPa 
 (1278.5 K)

 457.3 kPa 
0.4/1.4
 828.1 K
The net power is that generated by the low-pressure turbine since the power output from the high-pressure turbine is equal
to the power input to the compressor. Then,
W LP Turb  m c p (T4  T5 )
m 
W LP Turb
200,000 kW

 441.8 kg/s
c p (T4  T5 ) (1.005 kJ/kg  K )(1278.5  828.1)K
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.