Number of photons in a photon gas.

(a) Show that the number of photons in equilibrium in a box of volume V at temperature T is

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 temperatures 300 K; 1500 K (a typical kiln); 2.73 K (the cosmic background radiation).

Ch 16 Spontaneity, Entropy, and Free Energy I. 16.1: Spontaneous Processes and Entropy a. A process is said to be spontaneous if it occurs without outside intervention. May be fast or slow. Thermodynamics can tell us the direction in which a process will occurs but can say nothing about the speed. i. Rate of reactions depends on many factors life activation energy, temperature, concentration and catalysts: can be explained by using a simple collision model b. The driving force for spontaneous processes is an increase in the entropy of the universe i. Entropy can be viewed as a measure of molecular randomness