PS2KEYF07 - Chemistry 391 PS2 KEY 1. Since P = f (V , T ) ,...

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1 Chemistry 391 Fall 2007 PS2 KEY 1. Since () , PfV T = , VT PP dP dT dV TV ∂∂ ⎛⎞ =+ ⎜⎟ ⎝⎠ . Then the appropriate mixed partial derivatives are: V and T The van der Waals equation of state in the appropriate form for the desired derivatives is: 2 22 mm nRT n a RT a P Vn bV V bV =− = −− where for convenience the molar volume / m VV n = has been used. The first derivatives are: 2 23 2 2 m m T m V RT a a RT VV b V V Vb RT a R TV b V V b ⎡⎤ −= ⎢⎥ ∂− ⎣⎦ Therefore, 2 3 2 m aR T R dP dV dT b + . The mixed partials are 3 V V 2 2 = T m V m T m T Pa R T R T V PR R V == and are equal. Therefore, dP is an exact differential.
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2 2. Demonstrate that the differential 2 2 dz xydx x dy =+ is exact by integrating dz along the paths (1,1) (5,1) (5,5) and (1,1) (3,1) (3,3) (5,3) (5,5). [] () ( ) [] [] ( ) 2 55 5 5 2 1 1 11 33 5 5 35 22 13 3 3 2 Path 1 2 25 25 25 1 25 5 1 124 Path 2 29 62 5 9 3 2 5 9 1 9 3 1 3 25 9 25 5 3 124 dz xydx x dy dz xdx dy x y dz xdx dy xdx dy x y x y ⎡⎤ =+= + = + = ⎣⎦ ++= + + + =
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This note was uploaded on 07/25/2008 for the course CEM 391 taught by Professor Cuckier during the Fall '08 term at Michigan State University.

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PS2KEYF07 - Chemistry 391 PS2 KEY 1. Since P = f (V , T ) ,...

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