Homework 3.
Problem 1.
Evaluate multidimensional integral VN = . dx1.dx N where the integration area is restricted by 0 xr L and all xr are positive.
r =1 N
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)
Consider a system of N distinguishable particles. Each particle can occupy only one of the two levels 1 or 2, where 1< 2. Assume N is very large. You can distribute the particles in such way that n particles reside on level 2 while N
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
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
Power Law
y=a*x^k
Observations
x
y
0.050
0.500
0.666
0.950
Calculations
ln(x)
ln(y)
-2.996
-0.693
Solve for k:
ln(y) = ln(a) + k * ln(x)
ln(0.666) = ln(a) + k * ln(0.05)
ln(0.95) = ln(a) + k * ln(0.5)
ln(a) = ln(0.95) k * ln(0.5)
ln(0.666) = ln(0.95) k *