TITLE.PM5

262 ENGINEERING THERMODYNAMICS

dharm
/M-therm/th5-3.pm5

5.17.6. Polytropic process

Refer Fig. 5.29.
The expression for ‘entropy change’ in polytropic process (pvn = constant) can be obtained
from eqn. (5.28)

i.e., s 2 – s 1 = cv loge T
T

2

1

+ R loge v

v

2

1

Fig. 5.29. T-s diagram : Polytropic process.

Also p 1 v 1 n = p 2 v 2 n

or p
p

v

v

n

1

2

2

1

=

F

HG

I

KJ

...(i)

Again, as

pv

T

11

1

=

pv

T

22

2

or
p
p

1

2

=

v

v

T

T

2

1

1

2

× ...(ii)

From (i) and (ii), we get

v

v

n

2

1

F

HG

I

KJ

=

v

v

T

T

2

1

1

2

×

or

v

v

n

2

1

F^1

HG

I

KJ

−

=

T

T

1

2

or

v

v

2

1

=

T

T

1 n

2

1

F^1

HG

I

KJ

−

Substituting the value of

v

v

2

1 in eqn. (5.28), we get

s 2 – s 1 = cv loge

T

T

2

1

+ R loge

T

T

1 n

2

1

F^1

HG

I

KJ

−

= cv loge

T

T

2

1

+ R

1

n− 1

F

HG

I

KJ loge^

T

T

1

2