Problems and Solutions on Thermodynamics and Statistical Mechanics

242 Problems El Sdutio~ on Thermcdynam'cs El Statistical Mechanics

Solution:

of photons in the interval dadn:

Considering black body radiation in a cavity we get the number density

The number of photons in the laser beam flowing through an area A per

unit time is dn' = cAdn, and the output power is W = Edn'.

Introducing E = hc/X and dn = n(dO)2 into the expression, we obtain

where

Therefore

2 n A hc2 dX (do)

A5

w, =

T=--. hc^1

Xk ln($+l)

Using the known quantities, we get

WO = 3.60 x lo-' W , T =^6 x lo9 K.

2074

(a) Show that the number of photons in equilibrium at temperature T

in a cavity of volume V is N = V(kT/ft~)~ times a numerical constant.

(b) Use this result to obtain a qualitative expression for the heat ca-

(UC, Berkeley)

pacity of a photon gas at constant volume.

Solution:

(d) The density of states of the photon gas is given by