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Exam 2 - 1st Version - Solution

# Exam 2 - 1st Version - Solution - Name_Solution EMA 4314...

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Name__Solution________________ EMA 4314 Fall 2010 Exam #2 (100 points) There are four questions, each worth 33 points (you get 1 point for writing your name above). You will receive credit for 3 questions only; if you attempt all 4, you will get credit for the best 3. Question 1 [Energy and its analysis] a. The Helmholtz free energy, A, is a measure of the capacity of a system for what? Contrast this with G, U and H (10 points) A is the capacity of the system to do mechanical (P-V) work G is the capacity of the system to do non-mechanical work The heat added to a system at constant volume is the change in U of the system The heat added to a system at constant pressure is the change in H of the system b. Beginning from the equation for the combined First and Second Laws of thermodynamics, and the definitions of A and G, determine dA and dG. Show your work. (8 points) A = U-TS dA = dU – TdS -SdT But dU= TdS - PdV So dA = -SdT - PdV Likewise G = U + PV –TS dG = dU + PdV +VdP –TdS – SdT = TdS – PdV + PdV +VdP –TdS – SdT dG = -SdT + VdP c. From the result of (b) show that . Show your work. (5 points) dG = VdP - SdT d. From the result of (b) show that . Show your work. (10 points) Euler Equation (where k and a are the isothermal compressibility and isobaric thermal expansion) Question 2 [Phase transitions]

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a. On the axes below sketch the temperature dependence of the chemical potential for the solid, liquid and vapor phases. Show the transition temperatures and
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