690 ENGINEERING THERMODYNAMICS

dharm
\M-therm\Th13-6.pm5

For compression process : cp = 1.005 kJ/kg K, γ = 1.4

For expansion process : cp = 1.11 kJ/kg K, γ = 1.333

2 ′ 3

Generator

1 4 ′

C.C.

T = 15 + 273

= 288 K

1

(a)

T = 610 + 273

= 883 K

3

T(K)

288

(b)

1

2 2 ′ 4 ′

4

3

s

p^1

p^2

883

Fig. 13.60
In order to evaluate the net work output it is necessary to calculate temperatures T 2 ′ and
T 4 ′. To calculate these temperatures we must first calculate T 2 and then use the isentropic efficiency.

For an isentropic process, T

T

p

p

2

1

2

1

(^1) 14 1
=F 6 14
HG
I
KJ

γ− −
γ
()
.

. = 1.67

∴ T 2 = 288 × 1.67 = 481 K

Also, ηcompressor =

TT

TT

21

21

−

′−

0.8 = 481 288

21

−

TT′−

∴ T 2 ′ = 481 288

08

−

.

+ 288 = 529 K

Similarly for the turbine,

T

T

p

p

p

p

3

4

3

4

1

2

1

(^1) 1 333 1
=F 6 1 333
HG
I
KJ

F
HG
I
KJ

γ−−−
γ
γ
γ
()
.

. = 1.565

∴ T 4 = T^3

5651.

883

1.565

= = 564 K

Also, ηturbine =

TT

TT

34 T

34

(^8834)
883 564
−′
−
= −′
−
∴ 0.82 =
883
883 564
−′ 4
−
T
∴ T 4 ′ = 883 – 0.82 (883 – 564) = 621.4 K