Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 2.8-1

SOME FORMAL RELATIONSHIPS, AND SAMPLE SYSTEMS

Physics — Statistical Mechanics · chemical-equilibrium-matter-flow

Problem

The fundamental equation of a particular type of two-component system is

S = NA + NR\ln\frac{U^{3/2}V}{N^{5/2}} - N_1 R\ln\frac{N_1}{N} - N_2 R\ln\frac{N_2}{N}

N \equiv N_1 + N_2

where

A

is an unspecified constant. A closed rigid cylinder of total volume 10 liters is divided into two chambers of equal volume by a diathermal rigid membrane, permeable to the first component but impermeable to the second. In one chamber is placed a sample of the system with original parameters

N_1^{(1)} = 0.5

N_2^{(1)} = 0.75

V^{(1)} = 5

liters, and

T^{(1)} = 300

K. In the second chamber is placed a sample with original parameters

N_1^{(2)} = 1

N_2^{(2)} = 0.5

V^{(2)} = 5

liters, and

T^{(2)} = 250

K. After equilibrium is established, what are the values of

N_1^{(1)}

N_1^{(2)}

T

P^{(1)}

, and

P^{(2)}

? Answer:

T = 272.7

Related theory

Chemical Equilibrium

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