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PS2F07 - Chemistry 391 Problem Set 2(Due Monday September...

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Chemistry 391 Fall 2007 Problem Set 2 (Due, Monday September 10) 1. Starting with the van der Waals equation of state, find an expression for the total differential dP in terms of dV and dT . Calculate the appropriate mixed partial derivatives and decide if dP is an exact differential. 2. A differential ( ) ( ) ,, dz f x y dx g x y dy =+ is exact if the integral () f x y dx g x y dy + ∫∫ is independent of the path. Demonstrate that the differential 2 2 dz xydx x dy is exact by integrating dz along the paths: a) (1,1) (5,1) (5,5), and b) (1,1) (3,1) (3,3) (5,3) (5,5). (The first/second number in each set of parentheses is the x / y coordinate.) 3. Derive the following expression for calculating the isothermal change in the constant volume heat capacity: 2 2 . V T V CP T VT ⎛⎞ ∂∂ = ⎜⎟ ⎝⎠ You will need the thermodynamic identity (we will derive it later) TV UP TP =− . Hint: consider the definition of V C . 4. A bottle at 21.0ºC contains an ideal gas at a pressure of 126.4 x 10 3 Pa. The rubber
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