All questions are worth the same number of points.
Make sure that you include detailed working. Answers with zero working will garner zero points!
Question 1: Definitions
Give a succinct definition (with a very brief illustrative example,
if applicable) for the following five concepts.
A maximum of five
concise (non-rambling) sentences is allowed for each definition.
A
maximum of five concise sentences is allowed for each example, where
applicable.
Question 2: Energy Fluctuations
KK problem 3.4
Question 3: One-Dimensional Paramagnet
Consider a system of N nearly independent and distinguishable
quantum spins, each with magnetic moment m. The system is in a
magnetic field B. Take each spin to have three
possible components in the direction of the B-field, i.e.
s=-1,0,+1.
(a) How many possible states are there of this system?
(b) Suppose the system is closed, and there are N=8 of the
spins, and that the total energy is +mB. How many accessible
states does the system have?
(c) Now let us put the system in contact with a reservoir of
temperature T. Find the partition function Z for
general N, and use it to find the average energy, pressure, and
entropy depending on N. Start by finding Z for
N=1.
(d) Suppose we consider a (macroscopic) state of this system with
energy E, and the next lowest-energy state with energy
E-e. Is there any temperature for which the system is allowed
to have a higher probability of occupation of the state with energy
E than the state with energy E-e? Explain in detail.
Question 4.
Derive all interesting properties of a two-dimensional photon gas. Do not forget the average energy, entropy, and pressure; also find the relation of p/V to U.
Question 5: Heat Shields
KK questions 4.8 and 4.19.