GAS POWER CYCLES 621

dharm
\M-therm\Th13-2.pm5

p (bar)

V(m )^3

Adiabatic

compression

Heat addition at

constant volume

3

7 2

1 1

p-Vdiagram T-sdiagram

s(kJ/kg K)

Adiabatic

Constant volume

3

2

T(K)

1262.3

603.7

(^3431)
Fig. 13.10
or
V
V
1
2
F
HG
I
KJ
γ
= p
p
2
1
or ()rγ = p
p
2
1
Q V
V
(^1) r
2

F
HG
I
KJ
or r = p
p
2
1
1
F
HG
I
KJ
γ
=^7
1
1
F^41
HG
I
KJ

1. = (7)0.709 = 3.97

Hence compression ratio of the engine = 3.97. (Ans.)

(ii)Temperature at the end of compression, T 2 :

In case of adiabatic compression 1-2,

T

T

2

1

=

V

V

1

2

F^1

HG

I

KJ

−γ

= (3.97)1.41 – 1 = 1.76

∴ T 2 = 1.76 T 1 = 1.76 × 343 = 603.7 K or 330.7°C

Hence temperature at the end of compression = 330.7°C. (Ans.)

(iii)Temperature at the end of heat addition, T 3 :

According to constant volume heating operation 2-3

Qs = cv (T 3 – T 2 ) = 465

0.706 (T 3 – 603.7) = 465

or T 3 – 603.7 =

465

7060.

or T 3 =^465
7060.

• 603.7 = 1262.3 K or 989.3°C
  Hence temperature at the end of heat addition = 989.3°C. (Ans.)
  Example 13.12. In a constant volume ‘Otto cycle’, the pressure at the end of compression
  is 15 times that at the start, the temperature of air at the beginning of compression is 38°C and
  maximum temperature attained in the cycle is 1950°C. Determine :