Black-Body Radiation. Solids.
Test 5
Stat Physics
(Dated: 05-20-2008)
1
1. For a d-dimensional solid, nd how the low temperature specic heat scales with
temperature.
Solution
Energy of the solid
Z1
z d dz
! d d!
d+1
/T
E/
exp (~!=T ) 1
exp z 1
0
0
Z1
z d
Quantum Gases. BE Condensation.
Test 4
Stat Physics
(Dated: 04-29-2008)
1
1. For a non relativistic, degenerate Bose gas, show that, in three and four dimensions,
(@N=@ )V;T diverges at the temperature of Bose-Einstein condensation, T0 .
Bonus : Close to
Degenerate Electron Gas
Test 3
Stat Physics
(Dated: 04-22-2008)
1
1. For a relativistic, two-dimensional, completely degenerate electron gas, evaluate the
dependence of the Fermi energy on the areal density of electrons. Evaluate the mean
energy per elect
Gibbs Distribution
Test 2
Stat Physics
(Dated: 02-26-2008)
1
1. N diatomic molecules are stuck to the metal surface of cubic crystal symmetry (square
on the surface). Each molecule can either lie at on the surface, in which case it will
be aligned to one
Ideal Gas
Final
Stat Physics
(Dated: 03-20-2008)
Abstract
Euler-Maclaurin formula
n1
k =1
n1
k =0
n
f (k )
f (k) dk
0
1
1
1
[f (n) + f (0)] +
f (n) f (0)
f (n) f (0) + . . .
2
12
720
f (k) dk
1
1
1
[f (n) f (0)] +
f (n) f (0)
f (n) f (0) + . . .
2
12
Thermodynamics
Test1
Stat Physics
(Dated: 02-07-2008)
1
1. An ideal, monatomic gas of N atoms,
P V = NT
with initial volume and pressure V0 and P0 respectively, is placed in a thermally isolated
shaft. On top, it is separated by a massless lid of area A,