Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 2.8-2

SOME FORMAL RELATIONSHIPS, AND SAMPLE SYSTEMS

Physics — Statistical Mechanics · chemical-equilibrium-two-component

Problem

A two-component gaseous system has a fundamental equation of the form

S = AU^{1/3}V^{1/3}N^{1/3} + \frac{BN_1 N_2}{N}, \quad N = N_1 + N_2

where

A

and

B

are positive constants. A closed cylinder of total volume

2V_0

is separated into two equal subvolumes by a rigid diathermal partition permeable only to the first component. One mole of the first component, at a temperature

T_\ell

, is introduced in the left-hand subvolume, and a mixture of

\frac{1}{2}

mole of each component, at a temperature

T_r

, is introduced into the right-hand subvolume. Find the equilibrium temperature

T_e

and the mole numbers in each subvolume when the system has come to equilibrium, assuming that

T_r = 2T_\ell = 400

K and that

37B^2 = 100A^3V_0

. Neglect the heat capacity of the walls of the container! Answer:

N_{1\ell} = 0.9

Related theory

Chemical Equilibrium

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