31 Consider a Bose gas composed of N free, spinless particles, with mass m, restricted to a volume V, and subjected to a

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31 Consider a Bose gas composed of N free, spinless
particles, with mass m, restricted to a volume V, and subjected to
a temperature T.
a) Find an expression for the density of states of a simple
particle as a function of the energy of a particle;
b) Write an expression for the average occupancy of a state by a
single particle as a function of single particle energy, chemical
potential, and temperature;
c) Determine the chemical potential as a function of temperature
for this system;
d) Determine the expression for the Bose-Einstein transition
temperature.