PY 410, Statistical and Thermal
Physics, Spring 2010

Homework 1 (Due Feb. 2^{nd}),
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. 9^{th}),
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. 18^{th}),
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. 23^{rd}),
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
Hamiltonian:

, 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 2^{nd});
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 4^{th}, **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 23^{rd});
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
31^{st}); 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-T_{2}/T_{1}.