# PS6 - CBE 102B Problem Set 6 [ABET] Due: Wednesday, May 19,...

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CBE 102B Problem Set 6 [ABET] Due: Wednesday, May 19, 2010 For a fluid that obeys the van der Waals equation of state 2 1 , mm RT pa Vb V =− we found the following expressions for the functions , , , , and m U m H m S m A m G µ = () ( ) ) () () (o) (o) 1 ,( 1 ,2 ,, l n 1 1 l n 1 1 l n 1 2 m m m m m m m UVT U T a V RTb 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) T H T a Vb V b SVT S VT R V b T A VT R T a VV bR T b VT VT R T a bV µµ =+ ⎛⎞ ⎜⎟ ⎝⎠ + HV AV where superscript (o) signifies ideal-gas property at and T . Also, recall the critical parameters m V 2 83 3, , , 27 27 8 cm c mc c c c c pV aa R T p Z bbR T == = = = and the reduced form of the van der Waals equation 2 (6) , 31 r r mr mr T p where / rc p pp = , , and / TT T = / mr m mc V = . 1. (10 pts.) Suppose that the ideal-gas contribution to is . Also, suppose that we set the ideal-gas functions and Vm C (o) 3/ 2 Vm CR = (o) 0 m S = (o) 0 m H = at the critical point. Using the critical point as a reference point, derive explicit expressions for the reduced ideal-gas functions (o) (o) (o) (o) (o) (o) (o) (o) , , m mr mr mr mr r cc c c UH A UHSA (o) (o) m S R TR TRR T ===== in terms of V and T .

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PS6 - CBE 102B Problem Set 6 [ABET] Due: Wednesday, May 19,...

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