4. In cases I and II above, you used trial and error to find two different sets of thermodynamic parameters that gave exactly the same populations of A and B. However, there is a simple way to calculate the value of WA directly, rather than resorting to guessing. What is it? That is, explain how to calculate the correct WA in case II from thermodynamics principles, and show that your calculated WA is close to your guessed WA. Hint: The Gibbs free energy combines the effects of both U and W for a system at a specified temperature, and the free energy difference between any two macrostates determines their relative probabilities; that is, if a pair of macrostates {A1, B1} has the probabilities as a different pair of macro states {A2, B2}, the free energy difference between A1 and B1 must be exactly the same as the free energy difference between A2 and B2.