Which of the following expressions is equivalent to (?V/?T)P for the van der Waals equation of state?
A.-RT/b ln??V-2a/?V
B.R(1/P+?V^2/a-?V^3/2ab)
C.R/(P- a/?V^2 + 2ab/?V^3 )
D.Taking this derivative is not possible.
E.None of these are equivalent.
A. Incorrect. You are mixing up the operations of integration and differentiation, and losing track of which variable you are differentiating and which you are holding constant.
B. Incorrect. It appears you evaluated (?T/?V)P correctly, but erred in taking the reciprocal to get (?V/?T)P.
C. Correct.
D. Incorrect. Try transforming the van der Waals equation to be explicit in T, and then manipulate the partial differential to match.
E. Incorrect. One of these is the correct equivalent.
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