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 dPin terms of dVand dT. Calculate the appropriate mixed partial derivatives and decide if dPis an exact differential. 2. A differential ( ) ( ),,dzf x y dxg x y dy=+is exact if the integral ()fx y dxg x y dy+∫∫is independent of the path. Demonstrate that the differential 22dzxydxx dyis exact by integrating dzalong 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/ycoordinate.) 3. Derive the following expression for calculating the isothermal change in the constant volume heat capacity: 22.VTVCPTVT⎛⎞∂∂=⎜⎟⎝⎠You will need the thermodynamic identity (we will derive it later) TVUPTP=−. Hint: consider the definition of VC. 4. A bottle at 21.0ºC contains an ideal gas at a pressure of 126.4 x 103Pa. The rubber
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