680 ENGINEERING THERMODYNAMICS

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\M-therm\Th13-6.pm5

Example 13.32. Air enters the compressor of a gas turbine plant operating on Brayton
cycle at 101.325 kPa, 27°C. The pressure ratio in the cycle is 6. Calculate the maximum tempera-
ture in the cycle and the cycle efficiency. Assume WT = 2.5 WC , where WT and WC are the
turbine and the compressor work respectively. Take γ = 1.4. (P.U.)
Solution. Pressure of intake air, p 1 = 101.325 kPa
Temperature of intake air, T 1 = 27 + 273 = 300 K
The pressure ratio in the cycle, rp = 6
(i)Maximum temperature in the cycle, T 3 :
Refer Fig. 13.52.

T

s

p = C

p = C

3

(^24)
1
Fig. 13.52
T
T
p
p
(^2) rp
1
2
1
(^1111)
=F 6 1
HG
I
KJ

γ− − −
γ
γ
()γ ()
.4
.4 = 1.668
∴ T 2 = 1.668 T 1 = 1.668 × 300 = 500.4 K
Also, T
T
(^3) rp
4
(^1) 14 1
== 6 14
− −
() ()
.
.
γ
γ = 1.668
∴ T 4 = T^3
1 668.
But, WT = 2.5 WC (given)
∴ mcp (T 3 – T 4 ) = 2.5 mcp (T 2 – T 1 )
or, T 3 –
T 3
1 668.
= 2.5 (500.4 – 300) = 501 or T 3 1
1
1 668
FHG − IKJ
.
= 501
∴ T 3 =
501
1 1
1 668
F −
HG
I

. KJ

= 1251 K or 978°C. (Ans.)

(ii)Cycle efficiency, ηcycle :

Now, T 4 =

T 3

668

1251

1. 
   
   
   
   1. 668
   
   
   
   

= = 750 K