TITLE.PM5

THERMODYNAMIC RELATIONS 353

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or

∂

∂

F

HG

I

KJ

v

T p =

R

p =

v

T

∴μ =^1

c

T v

T

v

p

FHG ×−IKJ = 0.

Therefore, if an ideal gas is throttled, there will not be any change in temperature.

Let h = f(p, T)

Then dh =

∂

∂

F

HG

I

KJ

h

pT^ dp +

∂

∂

F

HG

I

KJ

h

T p^ dT ...(7.47)

But

∂

∂

F

HG

I

KJ

h

T p = cp

∴ dh =

∂

∂

F

HG

I

KJ

h

pT^ dp + cp dT

For throttling process, dh = 0

∴ 0 =

∂

∂

F

HG

I

KJ

∂

∂

F

HG

I

KJ

h

p

p

T T h + cp ...(7.48)

or cp = –^1

μ

∂

∂

F

HG

I

KJ

h

pT

...(7.49)

∂

∂

F

HG

I

KJ

h

pT is known as the constant temperature co-efficient.

7.7. Clausius-Claperyon Equation

Clausius-Claperyon equation is a relationship between the saturation pressure, tempera-

ture, the enthalpy of evaporation, and the specific volume of the two phases involved. This equa-

tion provides a basis for calculations of properties in a two-phase region. It gives the slope of a

curve separating the two phases in the p-T diagram.

Fusion

Liquid

Vapour

Critical point

Triple point

Sublimation

curve

Vapourisation

Solid

p

T

curve

curve

Fig. 7.4. p-T diagram.