1. In this problem, you’re going to define 4 new thermodynamic variables: W, X, Y, and Z (instead of P, V, T and S). And, you’re going to have new thermodynamic potentials: K, L, M and N (instead of U, H, F and G).
   You will start with a new definition of the 1^st Law: dK(X,Z)=WdX+YdZ, with K being a function of X and Z, K=K(X,Z).
   a. Show the Legendre transform equivalent/analogous to equation (5.2) that takes you from K(X,Z)->L(X,Y). Then construct the differential dL(X,Y)=... (find the right hand side of this).
   b. Show the Legendre transform that takes you from L(X,Y)->M(W,Y), and find the differential dM(W,Y).
   c. Show the Legendre transform that takes you from M(W,Y)->N(W,Z), and find the differential dN(W,Z).
2. problem 5.2
3. problem 5.5. In part (a) you must explicitly calculate ΔG just like we've done in class, with ΔG=ΔH-TΔS. I need to see all the steps. When you see "waste heat" think "-TΔS." On the right hand side the H₂O is liquid water, not water vapor.
4. problem 5.10. In class, I showed the full equation, dG=-SdT+VdP=(∂G/∂T)_PdT+(∂G/∂P)_TdP. I used (∂G/∂P)_T=V to get G(P₂)=G(P₁)+∫VdP (<--that's an integral if your computer doesn't show it). Here, you're looking at the Gibbs free energy changing with temperature, so you're doing G(T₂)=G(T₁)-∫SdT. This problem and the next assume that the entropy S for these species don't change over this small temperature range, so the integral becomes trivial.
5. problem 5.11

That's all for homework #4.

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