PS6_08-Solution

PS6_08-Solution - Chem 444B Homework Set #6 - Solutions...

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Problem Set #6 -1- Chem 444B Homework Set #6 - Solutions DUE: Friday, March 7, 2008 1) Beginning with dU TdS PdV =− and HUP V = + a) Derive the expression dH TdS VdP = + () There is more than one correct way to approach this problem. Here is one option: dU TdS PdV dU d PV TdS PdV d PV dU PV T d S P dV += + PdV + VdP V dH TdS VdP + =+ b) Derive the Maxwell relation SP TV PS ∂∂ ⎛⎞⎛⎞ = ⎜⎟⎜⎟ ⎝⎠⎝⎠ The total derivative of H(S,P) is given by. .. Compare this to the result of part a. .. and We learned in Math Chapter H that the 2nd cross-d HH dH dS dP ⎛⎞ ⎜⎟ ⎝⎠ == erivatives must be equal, so S P ⎡⎤ = ⎢⎥ ⎣⎦ = =
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Problem Set #6 -2- 2) In lecture 18 we derived the relationship () ,' id V id V V P STV S dV T ⎛⎞ −= ⎜⎟ ⎝⎠ . Evaluate this expression using the Bertheot equation of state: 2 R Ta P Vb TV =− and compare your results to the results we obtained from the van der Waals equation of state and for an ideal gas. 2 2 2 2 2 2 2 1 ' 11 ,l n V The 1st term resembles the result from an ideal gas Rln or a vdW ga V id id VV id V id id id RT a P PR a TVb a b Vb a R VbT V V =+ ∂− = + ∫∫ s ln but the 2nd term is completely new. id R 3) We also looked at the dependence of U with volume for an ideal gas and a van der Waals gas. Evaluate T U V for a Bertheot gas and compare with the results from Lecture 18. Does your answer surprise you at all?
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PS6_08-Solution - Chem 444B Homework Set #6 - Solutions...

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