PHYSICS 313
Problem set 3 2002
Given Sept 23
Due Oct 2

Problem 1: One million pennies lie flat on a large table.
a: In how many ways can one obtain a macrostate in which there are exactly 500 000 heads and an equal number of tails?
b: What is the probability after 1 million coin tosses with a fair coin to get exactly 500 000 heads?
c: What is the entropy (in units of the Boltzmann constant $k$) of the state with 500 000 heads and an equal number of tails.
Problem 2:
An Einstein solid has on the average 1 vibrational quantum excited per oscillator.
a: What is the entropy per oscillator?
b: What is the temperature? Give your answer in units of the Einstein temperature

$$T_E=\frac{\hbar\omega}{k}$$

Problem 3:Two Einstein solids have the same total number of oscillators. One solid has on the average one half vibrational quantum excited per oscillator the other has two.
a: What are the temperatures of the two solids? Give your answer in units of the Einstein temperature
b: What is the temperature if the two solids are joined and brought to thermal equilibrium?