Homework 3.
Problem 1.
Evaluate multidimensional integral VN = . dx1.dx N where the integration area is
N
restricted by 0 xr L and all xr are positive.
r =1
Solution.
The easiest way to solve the problem is to consider N=1,2,3 and then guess the answer by
Homework 4
Problem 1. (see Pathria, 3.15)
Consider classical gas of N relativistic indistinguishable particles in volume V each
described by the Hamiltonian H(p,q)=pc. Using canonical ensemble theory calculate
1.
2.
3.
4.
5.
Partition function of the gas
Problem I (10 points). Ideal Gas in 1 Dimension.
Consider an ideal gas of classical non-relativistic indistinguishable particles living in a
thin long cylinder of the length L, that is each particle can essentially move only along
the cylinder axis only.
Homework 8.
Problem 1.
Consider a gas of free electrons in volume V. Assume the limit of high temperatures so
that the Maxwell Boltzmann statistics can be applied instead of Fermi Dirac statistics.
1. Find the dependence of the magnetization of the gas as
Homework 7.
Problem 1. (Pathria 7.13)
Consider an ideal Bose gas confined to a region of area A in two dimensions.
1. Express the number of particles in the excited states, Ne, and the number of
particles in the ground state, N0, in terms of (z,T,A)
2. Sh
Homework 6
Problem 1
Consider a diatomic molecule with two identical atoms (each of mass m) separated by
distance D. The kinetic energy of the molecule is the sum of kinetic energies of two
atoms
T=
2
mv12 mv2
p2 p2
+
= 1+ 2
2
2
2m 2m
Consider the portion
Homework 5
Problem 1.
An extreme relativistic gas of indistinguishable particles in a volume V is characterized
by the single particle energy states
(p)=pc
where c is the light velocity. Assume the particles can leave the volume to the reservoir
and back
Homework 2
Problem I.
Consider a system of three particles. Assume each particle can occupy either of 3 energy
levels, , 2, and 3.
1. What are the possible values of the total energy E of this system?
2. What is the number of microstates dist (E) availabl
Homework 1
1. A cube of ice having temperature Tice<273K is placed into the lake with Tlake>273K.
Calculate the change in the entropy of the cube-lake system as it comes to the thermal
equilibrium. Assume the specific heat of ice Cice, the water Cw and th