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Homework #6: Do not turn these in since there is a test next week. I will post my solutions so you can check your work.
That's all for homework #6.
- 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 1st Law: dK(X,Z)=(-)WdX+YdZ, with K being a function of X and Z, which means 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).
- problem 5.5. Seriously, can you tell that ΔG is the bottom line for the real world reactions? 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 numbers. When you see "waste heat" think "-TΔS." On the right hand side the H2O is liquid water, not water vapor.
- Looking back at your numbers from problem 5.5, determine (a) the change in the internal energy ΔU and (b) the amount of energy required to make room for reaction in problem 5.5. (c) Comment on the sign of the eneregy required to make room for this system--what does it tell you?
- problem 5.10
- problem 5.11
- As usual, these are representative of the things that we've covered. Which means that you should be able to take these and generalize them to similar situations. For example, in class I let the pressure change, but problems 5.10 and 5.11 let the temperature change. But both are dealing with the identity dG=(-)SdT+VdP, and they are both looking at those partials that I showed you in class.