Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 7.4-24

FIRST-ORDER PHASE TRANSITIONS

Physics — Statistical Mechanics · joule-thomson-expansion-final-temperature

Problem

A nonideal gas undergoes a throttling process (i.e., a Joule--Thomson expansion) from an initial pressure

P_0

to a final pressure

P_f

. The initial temperature is

T_0

and the initial molar volume is

v_0

. Calculate the final temperature

T_f

if it is given that

\kappa_T = \frac{A}{v^2} \text{ along the } T = T_0 \text{ isotherm } (A > 0)

\alpha = \alpha_0 \text{ along the } T = T_0 \text{ isotherm}

and

c_p = c_p^0 \text{ along the } P = P_f \text{ isobar}

What is the condition on

T_0

in order that the temperature be lowered by the expansion?