1. The problem statement, all variables and given/known data Expression for the entropy and internal energy of black body radiation. Using the below relations: 2. Relevant equations Total free energy for black body: $$ F = (k_b TV/\pi^2) \int k^2 ln[1-exp(-\hbar ck/k_b T)]dk $$ Relationship between partition function and internal energy: $$ E = -\partial ln(z)/ \partial \beta $$ Where ##\beta## is the inverse temperature given by: $$ \beta = (1/k_b T) $$ Relationship between the free energy, internal energy and entropy: $$ F = E - TS $$ 3. The attempt at a solution If I use ## F = E - TS## rearranged to $$ S = (E-F)/T $$ Then substitute the relations in and calculate. I make a little progress until I hit the ## F ## part, the integral gives me some problems as I am having trouble calculating it, I tried using Wolfram Alpha as a guide but it won't actually give me an answer which suggested to me that I'm going about it the wrong way.