TITLE.PM5

702 ENGINEERING THERMODYNAMICS

dharm

\M-therm\Th13-6.pm5

(b)

T(K)

293

3

4 4 ¢

7

1

2 ¢

2

5

7 ¢

68

9 ¢

9

10

898

s

Fig. 13.67

Also, T

T

p

p

2

1

2

1

1

=

F

HG

I

KJ

−γ

γ

and p

p

2

1

= 9 = 3

∴ T 2 = (20 + 273) × ()

.

3.

14 1

14

−

= 401 K

Now, ηcompressor (L.P.) =

TT

TT

21

21

−

′−

0.8 =

401 293

2 293

−

T′−

i.e., T 2 ′ =

401 298

08

−

. + 293 = 428 K
Work input per compressor stage
= cpa(T 2 ′ – T 1 ) = 1.005 (428 – 293) = 135.6 kJ/kg
The H.P. turbine is required to drive both compressors and to overcome mechanical friction.

i.e., Work output of H.P. turbine =
2 135 6
095

×.

.

= 285.5 kJ/kg

∴ cpg (T 6 – T 7 ′) = 285.5

i.e., 1.15 (898 – T 7 ′) = 285.5

∴ T 7 ′ = 898 –

285.5

1.15 = 650 K

Now, ηturbine (H.P.) =

TT

TT

67

67

−′

− ; 0.85 =

898 650

(^8987)
−
−T