1000 Solved Problems in Modern Physics

4.2 Problems 253

4.2.2 Maxwell’s Thermodynamic Relations ..............

4.21 Obtain Maxwell’s Thermodynamic Relations

(a)

(

∂s

∂V

)

T

=

(

∂P

∂T

)

V

(b)

(

∂s

∂P

)

T

=−

(

∂V

∂T

)

P

4.22 Obtain Maxwell’s thermodynamic relation.
(
∂T
∂V

)

S

=−

(

∂p

∂S

)

V

4.23 Obtain Maxwell’s thermodynamic relation.
(
∂T
∂P

)

S

=

(

∂V

∂S

)

P

4.24 Using Maxwell’s thermodynamic relations deduce Clausius Clapeyron equa-
tion(
∂p
∂T

)

saturation

=

L

T(ν 2 −ν 1 )

whereprefers to the saturation vapor pressure,Lis the latent heat,Tthe

temperature,ν 1 andν 2 are the specific volumes (volume per unit mass) of the

liquid and vapor, respectively.

4.25 Calculate the latent heat of vaporization of water from the following data:
T= 373 .2K,ν 1 =1cm^3 ,ν 2 = 1 ,674 cm^3 ,dp/dT= 2 .71 cm of mercury
K−^1

4.26 Using the thermodynamic relation
(
∂s
∂V

)

T

=

(

∂p

∂T

)

V

,

derive the Stefan-Boltzmann law of radiation.

4.27 Use the thermodynamic relations to show that for an ideal gas
CP−CV=R.

4.28 For an imperfect gas, Vander Waal’s equation is obeyed
(
p+

a

V^2

)

(V−b)=RT

with the approximationb/V1, show that

CP−CV∼=R

(

1 +

2 a

RT V

)

4.29 IfEis the isothermal bulk modulus,αthe coefficient of volume expansion
then show that
CP−CV=TEα^2 V