GAS POWER CYCLES 703

dharm
\M-therm\Th13-6.pm5

∴ T 7 = 898 –

898 650

085

F −

HG

I

. KJ = 606 K

Also, T

T

p

p

6

7

6

7

1

=

F

HG

I

KJ

−γ

γ

or p
p

T

T

6

7

6

7

1

1 333

898 0 333

606

= 482

F

HG

I

KJ

=F

HG

I

KJ

=

−

γ

γ

.

..

Then,

p

p

8

9

9

482

=

. = 1.86

Again, T

T

p

p

8

9

8

9

(^1) 1333 1
=F^133316
HG
I
KJ

γ− −
γ
()
.
1.86. 1.
∴ T 9 = T^8
16
898

1. 
   
   
   
   1. 16
      = = 774 K
   
   
   
   

Also, ηturbine (L.P.) =

TT

TT

89

89

−′

− ; 0.85 =

898

898 774

−′ 9

−

T

∴ T 9 ′ = 898 – 0.85 (898 – 774) = 792.6 K

∴ Net work output = cpg(T 8 – T 9 ′) × 0.95

= 1.15 (898 – 792.6) × 0.95 = 115.15 kJ/kg

Thermal ratio or effectiveness of heat exchanger,

ε=

−′

′− ′

= −

−

TT

TT

54 T

94

5 428

792.6 428

i.e., 0.8 =
T 5 428
792 6 428

−

. −
∴ T 5 = 0.8 (792.6 – 428) + 428 = 719.7 K
Now, Heat supplied = cpg(T 6 – T 5 ) + cpg(T 8 – T 7 ′)
= 1.15 (898 – 719.7) + 1.15 (898 – 650) = 490.2 kJ/kg

∴ ηthermal =

Net work output

Heat supplied

=

115 15

490 2

.

.

= 0.235 or 23.5%. (Ans.)

(ii)Work ratio :

Gross work of the plant = Wturbine (H.P.) + Wturbine (L.P.)

= 285.5 +

115 15

095

.

.

= 406.7 kJ/kg

∴ Work ratio ==

Net work output

Gross work output

115 15

406 7

.

.

= 0.283. (Ans.)

(iii)Mass flow rate, m& :

Let the mass flow be m&, then

m& × 115.15 = 4500