PY 410, Statistical and Thermal Physics, Spring 2010
Homework 1 (Due Feb. 2nd), problems from Reif: 1.1; 1.4 (analyze the answer at large N), 1.5, 1.9, 1.10, 1.12, 1.14. Solution
Homework 2 (Due Feb. 9th), problems from Reif: 1.16; 1.17, 1.18, 1.23; *1.26, *1.28 (for the last two problems you need to read Sec. 1.10) Solution
Homework 3 (Due Feb. 18th), problems from Reif: 2.1; 2.2, 2.4, 2.8; 2.10 Solution
Lecture8 Additional reading: Chapter 3 from Reif.
Homework 4 (Due Feb. 23rd), problems from Reif: 3.1, 3.3, 3.4.
Repeat the problem considered in the notes but for spin 1 particles. I.e. assume that we have a system of large number
N of noninteracting particles described by the
, where .
Find the approximate expressions for the density of states and then find the temperature as a function of the energy and the magnetic field. Invert this relation and express energy in the system as the function of temperature. Show that your result is consistent with the Boltzmann distribution where the probabilities of spins to be in one of the three possible states are
Hint: number of configurations such that .spins have magnetization 1, .- have magnetization 0, and .have magnetization -1 is given by the polynomial distribution
where . Because the total energy is fixed we have an additional constraint. Using Stirling’s approximation maximize the number of configurations with respect to remaining variable. This is approximately you need to find. Solution
Lecture9 additional reading Chapter 3
Homework 5 (Due March 2nd); problems from Reif 2.7 (compare your result with the force exerted on a wall by a classical particle with the same energy), 2.11, 3.5, 3.6 Solution
Homework 6 (Due March 4th, before Spring break!) – see problem 1 on page 5, problem 4 on page 6, and problem 3 on page 7 in the notes (lecture 11). Solution
Homework 7 (Due March 23rd); problems from Reif 4.1, 4.2, 5.1, 5.2, 5.3, 5.4
Lecture14 , Additional reading: Reif: Chapter 5
Homework 8 (Due Marh 31st); problems from Reif: 5.5, 5.7, 5.8 (hint: consider a small volume with a gas. Use Newton’s equations of motion and express force through pressure gradient. In addition use continuity equation), 5.9, prove that the Carnot engine has the maximum possible efficiency of 1-T2/T1.