solutions 8

# solutions 8 - PHYS 253 Assignment 8 Solutions Total Marks...

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PHYS 253 Assignment 8 Solutions November 24 2010 Total Marks: 12 marks 1) 6 marks a) A critical point occurs on a P-V plot when the slope and the second derivative vanish (inflection point): P v Tc = 0 2 P v 2 Tc = 0 Given the van der Waals equation, we can re-arrange it for P and then solve for these points: P a v 2 v b = RT P = RT v b a v 2 P v Tc = RT c v b 2 2a v 3 RT c v c b 2 = 2a v c 3 2 P v 2 Tc = 2 RT c v b 3 6a v 4 2 RT c v c b 3 = 6a v c 4 Dividing the first derivative term by the second derivative term: v c 3 = v c b 2 v c = 3b Then solving for T c using either the first or second derivative equation: RT c 3 b b 2 = 2a 3b 3 T c = 8 a 27 bR We can then solve for P c using the initial van der Waals equation: P c = RT c v c b a v 2 = R 8 a 27 bR 3 b b a

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solutions 8 - PHYS 253 Assignment 8 Solutions Total Marks...

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