1. Write down the zeroth, first, second, and third laws of thermodynamics, putting each in any form you wish as long as it is correct.
2. Consider a system A, having Nl particles at chemical potential pl, and a system A2 having N2 particles at chemical potential µ2, with µl > µ2. If these two systems are briefly brought into diffusive contact, a small number of particles, AN, goes from one to the other.
(a) Which system acquires these particles and why?
(b) In terms of Nl, N2, µ, and µ2, what is the Gibbs free energy of the two systems before the interaction? (c) For small AN the change in Gibbs free energy is roughly (µ2 - µl) A N. But for larger AN, some second-order terms might become important. What are these second-order terms?