GAS POWER CYCLES 697

dharm
\M-therm\Th13-6.pm5

T(K)

288

s

459

626

673

873

3

4 ′

4

5

2 ′

2

1

Fig. 13.64

Considering the isentropic expansion process 3-4 :

T

T

p

p

3

4

3

4

(^111)
=F 4)^1
HG
I
KJ

γ− −
γ
(
.4
.4 = 1.486
∴ T 4 =
T 3
486
873

1. 
   
   
   
   1. 486
   
   
   
   

= = 587.5 K.

Again, ηturbine =

TT

TT

34 T

34

(^8734)
873 587 5
−′
−

−′
−.
i.e., 0.70 =
873
873 587 5
−′ 4
−
T
.
∴ T 4 ′ = 873 – 0.7(873 – 587.5) = 673 K
Wcompressor = cp(T 2 ′ – T 1 )
But cp = R ×
γ
γ− 1 = 0.287 ×
1.4
1.4 1− = 1.0045 kJ/kg K
∴ Wcompressor = 1.0045(459 – 288) = 171.7 kJ/kg
Wturbine = cp(T 3 – T 4 ′) = 1.0045(873 – 673) = 200.9 kJ/kg
∴ Net work = Wturbine – Wcompressor = 200.9 – 171.7 = 29.2 kJ/kg.
Effectiveness for heat exchanger, ε =
TT
TT
52
42
−′
′− ′
i.e., 0.78 =
T 5 459
673 459
−
−
∴ T 5 = (673 – 459) × 0.78 + 459 = 626 K