Final - Statistical Physics
Winter Quarter 2004
1. Two identical ideal gases at pressures P1 and P2 and temperatures T1 and T2 are in
vessels of volumes V1 and V2 respectively. The vessels are then co
Quiz 1: Thermodynamics
1. A gas obeys the equation of state
P=
NT
N 2 (T )
+
V
V2
where (T ) is a function of the temperature T only. The gas is initially at temperature
T and volume V and is expanded
Quiz 2: Gibbs Distribution
1. Consider two electrons in a two-level atom in equilibrium at temperature T . The
level separation is .
a) Evaluate the partition function of this system and its free ener
Quiz 3: Quantum Gases
1. Determine the entropy and the heat capacity of a degenerate, extreme relativistic
( = pc) electron gas.
Hint:
0
0
f () d
exp [( ) /T ] + 1
N () h () d
exp [( ) /T ] + 1
F
0
2
Quiz 5: Blackbody Radiation. Debyes Theory.
1. Apply Debyes theory to a 2D solid. Specically, derive the temperature dependence
of the heat capacity in the limits of high and low temperature. For simp
Quiz 4: Quantum Gases
1. For a concentration n = N/A of extreme relativistic ( = pc) bosons in 2D, nd the
temperature of Bose-Einstein condensation.
Hint:
0
zdz
2
=
exp z 1
6
Solution
N=
d =
n=
g
2h2