Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 7.4-20

FIRST-ORDER PHASE TRANSITIONS

Physics — Statistical Mechanics · temperature-along-locus

Problem

A system is composed of 1 mole of a particular substance. In the

P

v

plane two states (

A

and

B

) lie on the locus

Pv^2 = \text{constant}

, so that

P_A v_A^2 = P_B v_B^2

. The following properties of the system have been measured along this locus:

c_p = Cv^2

\alpha = D/v

, and

\kappa_T = Ev

, where

C

D

, and

E

are constants. Calculate the temperature

T_B

in terms of

T_A

P_A

v_A

v_B

, and the constants

C

D

, and

E

. Answer:

T_B = T_A + (v_B - v_A)/D + 2EP_A v_A^2 D^{-1}\ln(v_B/v_a)