Problem set 5, Physics 211, University of California, Berkeley
6 problems; due Friday, April 16, 5 pm in Physics 211 box in 251 Le Conte
1. Reif 5.19 (The van der Waals equation.)
2. Reif 5.24 (The la
Notes for Physics 211, University of California, Berkeley
Week I: We covered mostly Reif 2.1-2.4 plus a few things (below). The random walk and
Gaussian examples are discussed in detail in Reif chapte
Notes for Physics 211, University of California, Berkeley
The rst lecture (reservoir derivation of the canonical ensemble) is similar to Reif 6.2, and the
example mentioned is discussed in Reif 3.8. T
Notes for Physics 211, University of California, Berkeley
Week IV: Last week we covered some topics that are not in Reif (e.g., proof of the Central
Limit Theorem via cumulants). Today we return to Re
Physics 211 (Moore) Spring 2010
Problem Set #1 Solution
February 21, 2010
1. St. Petersburg Lottery
a. The expectation value of your return equals
x =
xn pn
n=1
where xn is the return in outcome n and
Physics 211 (Moore) Spring 2010
Problem Set #5 Solution
April 22, 2010
1. Reif 5.19
a. The equation of state reads (p + av 2 )(v b) = RT . We want to solve for the critical point in terms
of a and b.
Physics 211 (Moore) Spring 2010
Problem Set #3 Solution
March 14, 2010
1. Gibbs free energy and chemical potential
a. For large systems, entropy is extensive, meaning that if we scale the system with
Physics 211 (Moore) Spring 2010
Problem Set #2 Solution
March 5, 2010
1.
a. We have a particle of mass m and a probability distribution for pz of the form
P (pz ) =
1
exp(p2 /2mkT )
z
2mkT
where T =
Physics 211 (Moore) Spring 2010
Problem Set #6 Solution
April 29, 2010
log Z
1
1. Reif 11.1 This is pretty trivial. M = 1
=
H
Z
indeed M .
r
Er Er
1
e
=
H
Z
r
Mr eEr which is
2. Units check The Josep
Notes for Physics 211, University of California, Berkeley
Week II: We covered mostly topics in Reif, starting with the later part of chapter 2. We started
on chapter 3 but skipped 3.1 and 3.2 now as w
Physics 211 (Moore) Spring 2010
Midterm Solution
April 2, 2010
1.
a. F = kB T log Z, where
Z = eE1 + eE2 .
(1)
b. The mean energy is
E=
log Z
E1 + E2 e(E2 E1 )
.
=
1 + e(E2 E1 )
(2)
The entropy is
S=
Department of Physics
University of California, Berkeley
Physics 211 Final Examination
Monday, May 10, 2010
7 pm - 10 pm
Brief solutions (JEM)
1. (a) S = kB (p1 log p1 + p2 log p2 ), with
p1 =
eB/kB T
Problem set 4, Physics 211, University of California, Berkeley
6 problems; due Friday, April 2, 5 pm in Physics 211 box in 251 Le Conte
1. Compute a simplied version of the Chandrasekhar limit (the ma
Problem set I, Physics 211, University of California, Berkeley
Due Friday, Feb 5, 5 pm in 251 Le Conte (see box)
1. St. Petersburg lottery: Suppose that you pay a xed fee of x dollars to enter the fol
Problem set 6, Physics 211, University of California, Berkeley
6 problems; due Friday, April 30, 5 pm in Physics 211 box in 251 Le Conte
This set should be less time-consuming than others.
1. Reif 11.
Problem set 3, Physics 211, University of California, Berkeley
7 problems; due Friday, March 5, 5 pm in Physics 211 box in 251 Le Conte
1. Gibbs free energy and chemical potential: (a) Use that entrop
Problem set 2, Physics 211, University of California, Berkeley
7 problems; due Friday, Feb 19, 5 pm in 251 Le Conte (see box)
1. Planetary atmospheres (from Sethna): Treat diatomic oxygen for now as a
Department of Physics, University of California, Berkeley
Physics 211 Final Examination, Monday, May 10, 2010, 7 pm - 10 pm
There are 6 problems; all count equally. No books, notes, or calculators are
Physics 211 Spring 2010
Take-home midterm
Due in box (or by electronic submission), 5 pm, Friday March 19
You must complete this midterm in one two-hour period.
Reminder: No lectures Mon, Wed; will ma
Physics 211 (Moore) Spring 2010
Problem Set #4 Solution
April 22, 2010
1. Chandrasekhar limit
a. Consider a sphere of density and radius r. We would like to bring in a small mass dm in the form of
a t