Problems and Solutions on Thermodynamics and Statistical Mechanics

Statistical Physics 247

The total number of photons is

The total energy is

w 2.6 x ergs ,

(b) The Fermi momentum of the electrons is

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An n-dimensional universe.

In our three-dimensional universe, the following are well-known results

from statistical mechanics and thermodynamics:

(a) The energy density of black body radiation depends on the tem-

perature as TQ, where a = 4.

(b) In the Debye model of asolid, the specific heat at low temperatures

(c) The ratio of the specific heat at constant pressure to the specific

Derive the analogous results (i.e., what are 7, a and /I) in the universe

depends on the temperature as Tfl, where /I = 3.

heat at constant volume for a monatomic ideal gas is 7 = 5/3.

with n dimensions.

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