1000 Solved Problems in Modern Physics

254 4 Thermodynamics and Statistical Physics

4.30 Obtain the followingTdsequation
Tds=CVdT+TαETdV
where ET =−V

(∂P

∂V

)

T is the isothermal elasticity andα =

1

V

(∂V

∂T

)

P

is the volume coefficient of expansion,Sis the entropy andTthe Kelvin

temperature.

4.31 Obtain the equation
Tds=CpdT−TVαdp

4.32 Obtain the equation

Tds=CV

(

∂T

∂P

)

V

dP+CP

(

∂T

∂V

)

P

dV

4.33 Obtain the formula for the Joule–Thompson effect

ΔT=

[T(∂V/∂T)P−V]ΔP

CP

4.34 (a) Show that for a perfect gas governed by the equation of statePV=RT
the Joule-Thompson effect does not take place.
(b) Show that for an imperfect gas governed by the equation of state

(

P+

a

V^2

)

(V−b)=RT, the Joule-Thompson effect is given by

ΔT=

1

CP

(

2 a

RT

−b

)

ΔP.

4.35 Explain graphically the condition for realizing cooling in the Joule-Thompson
effect using the concept of the inversion temperature.

4.36 Prove that for any substance the ratio of the adiabatic and isothermal elastici-
ties is equal to the ratio of the two specific heats.

4.37 Prove that the ratio of the adiabatic to the isobaric pressure coefficient of
expansion is 1/(1−γ).

4.38 Show that the ratio of the adiabatic to the isochoric pressure coefficient is
γ/(γ−1).

4.39 IfUis the internal energy then show that for an ideal gas(∂U/∂V)T=0.
[Nagarjuna University 2004]

4.40 Find the change in boiling point when the pressure on water at 100◦Cis
increased by 2 atmospheres. (L =540 Calg−^1 , volume of 1 g of steam=
1 ,677 cc)
[Nagarjuna University 2000]

4.41 If 1 g of water freezes into ice, the change in its specific volume is 0.091 cc
Calculate the pressure required to be applied to freeze 10 g of water at− 1 ◦C.
[Sri Venkateswara University 1999]