Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 2.6-3

SOME FORMAL RELATIONSHIPS, AND SAMPLE SYSTEMS

Physics — Statistical Mechanics · thermal-equilibrium-two-systems

Problem

Two particular systems have the following equations of state:

\frac{1}{T^{(1)}} = \frac{3}{2}R\frac{N^{(1)}}{U^{(1)}}

and

\frac{1}{T^{(2)}} = \frac{5}{2}R\frac{N^{(2)}}{U^{(2)}}

where

R

is the gas constant (Problem 2.6-2). The mole number of the first system is

N^{(1)} = 2

and that of the second is

N^{(2)} = 3

. The two systems are separated by a diathermal wall, and the total energy in the composite system is

2.5 \times 10^3

J. What is the internal energy of each system in equilibrium? Answer:

U^{(1)} = 714.3