Consider a two level system of N distinguishable particles. We want to find the Energy of the system as a function of the Temperature. The first energy level is E1 and the second is E2. I computed the entropy. Now if we take a derivative with respect to Energy, we have 1/T = dS/dE where S = f(N,N1) or f(N,N2) depending on how we substitute. Consider another problem, namely dipoles in a uniform magnetic field, then E=M*Eo , where M = N+ - N- Then, 1/T = dS/dE= 1/Eo*dS/dM We can easily calculate dS/dM and rearrange stuff. The problem i'm having is how to take dS/dE when E=N1*E1 + N2*E2.