Energy of an ideal gas given its multiplicity

[felipedc]

Question:
The multiplicity of an ideal gas is given by g(U) = A.U^3N/2, where U is the energy of the gas, A is a constant and N is the number of particles in the gas.
Prove that the energy of the gas given a temperature T is U = (3/2).N.kb.T

Attempts:
My first thought was to work with the entropy equation (S = kb * ln(g(U))) , but after isolating the variable U from the equation, I see no other way out.
Then I thought I should start by finding the probability of a system having energy U, and find the mean of all possibles energies. But that does not depend on variable g(U).

How should i proceed?

 

[king vitamin]

My first thought was to work with the entropy equation (S = kb * ln(g(U))) , but after isolating the variable U from the equation, I see no other way out.

This is the correct first step.

Do you know how the temperature is related to the entropy?