Thermodynamics, Statistical Physics, and Quantum Mechanics

36 PROBLEMS

a)Derive the average number of photons in the box.

Hint:

b)

c)

d)

e)

What is the total energy of the radiation in the box for

What is the entropy of the radiation for

Assume that photons can create neutral particles of mass and zero

spin and that these neutral particles can create photons by anni-

hilation or some other mechanism. The cavity now contains photons

and particles in thermal equilibrium at a temperature Find the

particledensity Consider only the process where a single

photon is emitted orabsorbed bymaking asingleparticle.

Hint: Minimize the free energy.

Now, instead of neutral particles, consider the creation of electron-positron

pairs.

What is the total concentration of electrons and positrons inside the

box when

What is the total concentration of electrons and positrons when

4.75 D-Dimensional Blackbody Cavity (MIT)

Consider aD-dimensional hypercube blackbody cavity. What is the energy

density as a function of temperature? It is not necessary to derive the

multiplicative constant. Assume that the radiation is in quanta of energy

4.76 Fermi and Bose Gas Pressure(Boston)

For a photon gas the entropy is

where is the angular frequency of the mode. Using (P.4.76.1):

Hint:

f)