Lecture 4
Thermodynamic processes
Equilibrium thermodynamics only provides a description of equilibrium
states, so its not possible within this model to precisely describe whats
happening to a system for times at which it has not relaxed to equilibrium.
N

Physics 112 - Fall 2015
Midterm Exam #2
Some potentially useful facts
NOTE: These facts are all approximate, and some of them are rather rough approximations, but you may treat them as exact for the sake of computational simplicity on this exam.
One vibra

Physics 112 Winter 2016
Assignment 7: Chapter 4,5
Due in lecture Thursday, November 10th
1. DS Problem 4.6
2. DS Problem 4.15
3. DS Problem 4.20
4. DS Problem 4.26
5. DS Problem 5.4
6. DS Problem 5.6
7. DS Problem 5.11
8. Extra Credit: Consider thermodyna

Physics 112 Fall 2016
Assignment 5: Chapter 3
Due in lecture Thursday, October 27
1. DS Problem 2.42
2. DS Problem 3.7
3. DS Problem 3.10
4. DS Problem 3.13
5. DS Problem 3.15
6. Extra Credit: Consider ideal gas with f = const degrees of freedom for which

Physics 112 Fall 2016
HA 1: Chapter 1
Due in lecture Thursday, September 29
1. DS Problem 1.1 and Problem 1.3
2. DS Problem 1.12 and Problem 1.13
3. DS Problem 1.16
4. DS Problem 1.17
5. DS Problem 1.20
6. DS Problem 1.22 (in 1.22b
q compute jvx j using M

Physics 112 Spring 2016
Assignment 4: Chapter 2,(3)
Due in lecture Thursday, October 20
1. DS Problem 2.26, 2.32
2. DS Problem 2.29
3. DS Problem 2.22
4. DS Problem 2.30
5. DS Problem 2.37,
6. DS Problem 2.38
7. Extra Credit: Consider monatomic ideal gas

Physics 112 Fall 2016
Assignment 3: Chapter 1,2
Due in lecture Thursday, October 13
1. DS Problem 1.50
2. DS Problem 1.55
3. Please Read DS Chapter 1.7 and solve DS Problem 1.70
4. DS Problem 2.8
5. DS Problem 2.17
6. DS Problem 2.19
7. DS Problem 2.24
8.

Physics 112
Fall 2016
Assignment 2: Chapter 1
Due in lecture Thursday, October 6
1. DS Problem 1.29
2. DS Problem 1.34
3. DS Problem 1.36
4. DS Problem 1.39
5. DS Problem 1.40
6. DS Problem 1.45
7. DS Problem 1.46
8. DS Problem 1.47
1

Physics 112 Fall 2016
Assignment 6: Chapter 3,4
Due in lecture Thursday, November 3
1. DS Problem 3.14
2. DS Problem 3.21
3. DS Problem 3.31
4. DS Problem 3.34
5. DS Problem 3.37
6. DS Problem 3.39
7. DS Read Chapter 4
8. Extra Credit: Suppose you are giv

PHYSICS 112 SPRING 2016
Homework assignment #2
Due: Tuesday, April 12
From Reif Chapter 2: 2.3, 2.4, 2.6, 2.7, 2.8
A. Determine the total number of states having energy E within a band dE, i.e., (E) for
a 2-dimensional ideal gas of N particles constrained

Discussion 1 solutions
Problem 0. This problem has no well-dened answer. The change in the triangles area when b is changed
depends on what other aspects of the triangle are being held xed.
Problem 1.
The derivatives requested in parts (a) through (d) are

Physics 112 Midterm 1 Review Session
Problem 1. Heating at constant pressure. An ideal gas of N particles at temperature T
has energy U = cN kB T . N particles of the gas are contained in a thermally insulating balloon
inside a room where the pressure P i

Lecture Supplement
Statistical Mechanics Examples
We illustrate how to do some basic statistical mechanical computations
on some simple physical systems. All examples will consist of systems whose
microscopic descriptions we take to be quantum mechanical.

Lecture Supplement
Statistical mechanics
Over the centuries, we scientists have often relied on a particular strategy
to understand physical systems better use more and more powerful microscopes. Put another way, we often look to smaller and smaller lengt

Lecture 1
Thermodynamics Primer
1
Basic problems of thermodynamics
Evolution of macroscopic systems (toward equilibrium)
Gas in a cylinder with a partition in dierent cases (dierent
constraints) what will happen.
Computing properties of materials
Vari

Lecture Supplement
Indistinguishable particles
In these notes, we show how one can compute microstate probabilities
for a system of indistinguishable particles in thermal equilibrium with a heat
bath. The main dierence between computing these probabilitie

Lecture Supplement
The Einstein Model of a Solid
Our objective is to articulate the Einstein model of a solid, a certain
simple microscopic model, and to show how statistical mechanics can be
used to determine the thermodynamics of an Einstein solid.
A re

Lecture Supplement
The classical ideal gas
In the context of thermodynamics, all behaviors of a given system are
determined by the entropy as a function of U and other extensive thermodynamic variables that characterize the equilibrium states of the syste

Lecture 2
Introduction to Equilibrium
Thermodynamics
1
Thermodynamic systems
A physical system is said to be macroscopic roughly if it is on the scale
of humans. In this course, this means that the system contains roughly an
Avogradros number of particles

Physics 112 - Fall 2015
Midterm Exam #1
Problem 1.
A certain sample of classical ideal gas, which we call sample A, is put into a rigid,
hermetic, cylinder whose bottom is thermally conducting but the rest of which is thermally
insulating. An identical sa

Physics 112 Discussion 8
TA info
Name: River Snively
Oce hours: Tuesday 11-12, Thursday 2-3
Oce hours location: 1-704A PAB
email: river@physics.ucla.edu (Questions: please post on Piazza.)
Problem 1. Two-dimensional box of particles. Consider N distinguis

PHYSICS 112
Practice Midterm
Real Exam: Thursday April 30th, 2015, 9.30am-10.45am, PAB 1-434
Topics for the midterm: All material covered up to (and including) April 23rd, and
topics covered in homework and discussion problems. Emphasis will be on calcul

112 Homework 7 Solutions
May 27, 2015
0.1
Problem 1: Schroeder 6.18
It is easiest to start with the second derivative of the partition function.
X
@2Z
=
E(s)2 e
2
@
s
E(s)
= ZE2
(1)
Note that the bar is over the E 2 , and not just E. Next, we look to nd t

PHYSICS 112
Practice Final
Real Final: Tuesday June 9th, 2015, 3pm-6pm, PAB 1-434
Topics for thenal: All material covered up to (and including) last lecture on June 4th,
and topics covered in homework and discussion problems. Emphasis will be on statisti

Thermodynamics and Statistical Mechanics: Physics 112
Problem Set # 7
Due Tuesday May 19th, In class
Problem 1 [10 pts]: Schroeder Problem 2.26
Problem 2 [10 pts]: Schroeder Problem 2.29
Problem 3 [10 pts]: Schroeder Problem 2.32
Problem 4 [10 pts]: Schro

112 Homework 4 Solutions
April 28, 2015
0.1
Problem 1: Schroeder 3.14
We can integrate the heat capacity divided by the temperature to nd the change in entropy.
S=
Z
Tf
0
CV
b 3
dT = aTf + Tf
T
3
(1)
We can then nd the entropy at 1 and 10 Kelvin.
1
S(1 K)

112 Homework 2 Solutions
April 13, 2015
0.1
0.1.1
Problem 1: Schroeder 1.31
(a)
Figure 1: Pressure vs volume.
0.1.2
W =
(b)
R
P dV . Since it is linear, we can take the average pressure.
W =
0.1.3
(2 105 Pa)(2 10
(2 atm)(2 liters) =
3
m3 ) =
400 J
(1)
(c)

112 Homework 3 Solutions
April 20, 2015
0.1
0.1.1
Problem 1: Work of adiabatic and isothermal transitions
(a)
We can calculate the work done by integrating
W =
0.1.2
Z
VB
P dV =
VA
Z
VB
VA
P over dV , using the fact that P V = c.
c
dV =
V
cV 1
1
VB
=
PA V

Thermodynamics and Statistical Mechanics: Physics 112
Problem Set # 4
Due Tuesday April 28th, In class
Problem 1 [10 pts]: Schroeder Problem 3.14
Problem 2 [20 pts]: Schroeder Problem 3.32
Problem 3 [30 pts]: Schroeder Problem 3.34
Problem 4 [20 pts]:
fun

Thermodynamics and Statistical Mechanics: Physics 112
Problem Set # 5
Due Tuesday May 5th, In class
Problem 1 [10 pts]: Schroeder Problem 5.13
Problem 2 [20 pts]: Schroeder Problem 5.23
Problem 3 [20 pts]: Schroeder Problem 5.32
Problem 4 [10 pts]: Schroe