For a given system in the microcanonical ensemble, the number of allowed mi- crostates takes the form 12 - exp (9(N)+ ( =)). where g(N) > 0, N the number of particles and U is the total energy of the system. Find the conditions that and its derivatives ', d", and g(N) need to satisfy such that the entropy S, temperature T, energy U and specific heat CN = () of the system are thermodynamically correct. - N Hint: By "thermodynamically correct", think about whether variables are ex- tensive or intensive, always positive or always negative, etc.