Problems and Solutions on Thermodynamics and Statistical Mechanics

Statistical Phyaics 187

Solution:
For a single atom, we have

For the system, we have

Since = q' GI it follows

2027

Obtain the temperature of each system:

(a) 6.0 x atoms of helium gas occupy 2.0 litres at atmospheric

pressure. What is the temperature of the gas?

(b) A system of particles occupying single-particle levels and obeying

Maxwell-Boltzmann statistics is in thermal contact with a heat reservoir at

temperature T. If the population distribution in the non-degenerate energy

levels is as shown, what is the temperature of the system?

Energy (eV) population

30.1 x lob3 3.1%

21.5 x 8.5%

12.9~ 23%

4.3 x 10-3 63%

(c) In a cryogenic experiment, heat is supplied to a sample at the

constant rate of 0.01 watts. The entropy of the sample increases with time

as shown in the table. What is the temperature of the sample at t = 500 sec?

Time: 100 200 300^400 500 600 700 (sec)

Entropy: 2.30 2.65 2.85 3.00 3.11 3.20 3.28 (J/K)

(UC, Berkeley)