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Unformatted text preview: Chem 444 B Exam 1 Answer Key February 20, 2008 1) a) (8 pts) At the point where a gas condenses to form a liquid (T<T c ), T P V ∂ ⎛ ⎞ = ⎜ ⎟ ∂ ⎝ ⎠ , since the fluid will change volume with no change in pressure. This is always true until T=T c . At this point, the range of volumes over which the gas and liquid shrinks to a(n inflection) point. So both C T P V ∂ ⎛ ⎞ = ⎜ ⎟ ∂ ⎝ ⎠ and 2 2 C T P V ⎛ ⎞ ∂ = ⎜ ⎟ ∂ ⎝ ⎠ 1) b) (12 pts) Starting from the van der Waals equation 2 R T a P V b V = − − ( ) 2 3 2 C C T C C RT P a V V V b ∂ ⎛ ⎞ = − + = ⎜ ⎟ ∂ ⎝ ⎠ − and ( ) 2 3 2 4 2 6 C C C T C RT P a V V V b ⎛ ⎞ ∂ = − = ⎜ ⎟ ∂ − ⎝ ⎠ These yield the following two relationships: ( ) 2 3 2 C C C V RT a V b = − and ( ) 3 4 2 6 C C C V RT a V b = − Taking the ratio of the two equations, we get ( ) 1 1 2 3 C C V V b = − or ( ) 2 3 C C V V b = − , which yields 3 C V b = Substituting into the first of the two equations above, we get ( ) 3 2 27 2 4 C b RT a b = , which yields 8 27 C a T Rb = Returning to the first van der Waals equation: 2 2 2 2 8 4 27 2 9 2 7 9 2 7 C C a R a a a a Rb P P b b b b b ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ = − = − = = Problem 2 a) 2 (2 pts)....
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This test prep was uploaded on 04/13/2008 for the course CHEM 444 taught by Professor Jameslis during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 JamesLis

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