(a) Show that the number of photons in equilibrium in a box of volume V at temperature T is N = 8rV ()" dr. KT 3 dx. hc The integral cannot be done analytically; either look it up in a table or evaluate it numerically. (b) How does this result compare to the formula derived in the text for the entropy of a photon gas? (What is the entropy per photon, in terms of k?) (c) Calculate the number of photons per cubic meter at the following temper- atures: 300 K; 1500 K (a typical kiln); 2.73 K (the cosmic background radiation).
(a) Show that the number of photons in equilibrium in a box of volume V at temperature T is N = 8rV ()" dr. KT 3 dx. hc The integral cannot be done analytically; either look it up in a table or evaluate it numerically. (b) How does this result compare to the formula derived in the text for the entropy of a photon gas? (What is the entropy per photon, in terms of k?) (c) Calculate the number of photons per cubic meter at the following temper- atures: 300 K; 1500 K (a typical kiln); 2.73 K (the cosmic background radiation).
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Number of photons in a photon gas.
Transcribed Image Text:(a) Show that the number of photons in equilibrium in a box of volume V at
temperature T is
N = 8rV ()" dr.
KT 3
dx.
hc
The integral cannot be done analytically; either look it up in a table or
evaluate it numerically.
(b) How does this result compare to the formula derived in the text for the
entropy of a photon gas? (What is the entropy per photon, in terms of k?)
(c) Calculate the number of photons per cubic meter at the following temper-
atures: 300 K; 1500 K (a typical kiln); 2.73 K (the cosmic background
radiation).
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