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Fig. 1.2 - P-v and T-s diagrams of the Joule-Brayton cycle
4-1 Constant-pressure heat rejection.
The T-s and P-v diagrams of an ideal Brayton cycle are shown in Fig. 1.3. Large
amount of work is consumed in process 4-1 for a gas turbine cycle as the working
material (gas) is very compressible. The compressor needs to handle a large volume and
achieve large compression ratios.

Analysis. The heat input in a gas turbine cycle per 1 kg of work fluid is given by q in
= C p (T 3 – T 2) and the heat rejected q out = C p (T 4 – T 1). Thus the thermal efficiency is
given by
q T  T
  1 out →   1 4 1 ,
th th
q T  T
in 3 2

Since the adiabatic processes take place between the same pressures, the temperature
ratios are the same
k 1 k 1
T  P  k k 1 T  P  k k 1
2 2 k 3 3 k
     ;      ,
T  P  T  P 
1  1  4  4 
where β is the pressure ratio and k is the specific heat ratio. The pressure ratio β is a
fundamental quantity for the gas-turbine cycle.
Then
T  T 1 1
 th  1 k 1 4 1 k 1  1 k 1 ;  th  1 k 1 (1.1)
T   k  T   k  k  k
4 1
Equation 1.1 shows that under the cold-air-standard assumptions, the thermal
efficiency of an ideal Brayton cycle depends on the pressure ratio of the gas turbine and
the specific heat ratio of the working fluid. The thermal efficiency increases with both
of these parameters, which is also the case for actual gas turbines.

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