1. The problem statement, all variables and given/known data A two component gaseous system has a fundamental equation of the form S=AU1/3V1/3N1/3 + (BN1N2)/N N=N1+N2 where A and B are positive constants. V is volume , S is entropy, U is internal energy, N is mole number. A closed cylinder of total volume 2V0 is separated into two equal subvolumes by a rigid diathermal partition permeable only to the first component. One mole of the first component at a temperature Tl is introduced in the left subvolume and a mixture of 1/2 mole of each component is introduced in the right subvolume at a temperature Tr. Find the equilibrium Te and the mole numbers in each subvolume. 2. Relevant equations At equilibrium the chemical potentials of species 1 on right and left chambers are equal and also temperatures are equal. 3. The attempt at a solution The main issue is that whenever I compute the chemical potential of species 1 in the left chamber or the right chamber and equate them (∂S/∂N1)left=(∂S/∂N1)right I end up getting 0 = 0. I expected to obtain an expression that helps in evaluate the amount of species (1) in the left and right chamber. Am I missing something? Help is appreciated.