8.333: Statistical Mechanics I
Problem Set # 4
Due: 11/9/15
Non-interacting particles
1. Rotating gas:
Consider a gas of N identical atoms confined to a spherical harmonic
trap in three dimensions, i.e. the particles are subject to the Hamiltonian
N 2
X
p

8.333: Statistical Mechanics I
Fall 2015
Test 3
Review Problems
The third in-class test will take place on Monday 11/23/15 in room 4-163 from 2:30
to 4:00 pm. There will be a recitation with test review on Friday 11/20/15.
The test is closed book, but if

8.333: Statistical Mechanics I
Fall 2015
Test 2
Review Problems
The second in-class test will take place on Monday 10/26/15 in room 4-163 from
2:30 to 4:00 pm. There will be a recitation with test review on Friday 10/23/15.
The test is closed book, but if

8.333: Statistical Mechanics I
Fall 2015
Test 1
Review Problems
The first in-class test will take place on Wednesday 9/30/15 in room 4-163 from
2:30 to 4:00 pm. There will be a recitation with test review on Friday 9/28/15.
The test is closed book, but if

8.333: Statistical Mechanics I
Problem Set # 5
Due: 11/20/15
Interacting particles & Quantum ensembles
1. Surfactant condensation:
N surfactant molecules are added to the surface of water
over an area A. They are subject to a Hamiltonian
H=
N
!
pi 2
i=1
2

8.333: Statistical Mechanics I
Problem Set # 6
Due: 12/4/15 @ mid-night
According to MIT regulations, no problem set can have a due date later than 12/4/15,
and I have extended the due date to the last possible minute! However, you can be (and
will be!)

8.333: Statistical Mechanics I
Problem Set # 3
Due: 10/19/2015
Kinetic Theory
1. Poisson Brackets:
(a) Show that for observable O(p(), q(), dO/dt = cfw_O, H, along the time trajectory of
any micro state , where H is the Hamiltonian.
(b) If the ensemble av

8.333: Statistical Mechanics I
Problem Set # 2
Due: 10/7/15
Probability
1. Random deposition: A mirror is plated by evaporating a gold electrode in vaccum by
passing an electric current. The gold atoms fly o in all directions, and a portion of them
sticks

8.333: Statistical Mechanics I
Problem Set # 1
Due: 9/23/15
Thermodynamics
1. Non-Carnot Engine: Consider an engine that operates between a set of temperatures
Tmax = T1 > T2 > T3 > > Tn = Tmin . For a subset of these temperatures cfw_T+ ,
the engine take

8.333: Statistical Mechanics I
Re: 2015 Final Exam
Review Problems
The final exam will take place on Monday 12/14/2015, from 1:30pm to 4:30pm
in Walker. All topics presented in the course will be covered, with emphasis on the second
half. It will be a clo