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Unformatted text preview: ME320 Thermodynamics Homework set #5 Due: Wednesday 10/08/03 at the start of class 1. The Dieterici equation of state is given by P = RT - b exp parenleftbigg- a RT parenrightbigg , with a and b material constants. Using the conditions parenleftbigg P parenrightbigg T = T cr =constant = 0 and parenleftbigg 2 P 2 parenrightbigg T = T cr =constant = 0 , show that a = 2 RT cr cr and b = cr 2 . Solution: Direct calculations show that parenleftbigg P parenrightbigg T = P parenleftbigg- 1 - b + a RT 2 parenrightbigg and parenleftbigg 2 P 2 parenrightbigg T = P parenleftbigg- 1 - b + a RT 2 parenrightbigg 2 + P parenleftbigg 1 ( - b ) 2- 2 a RT 3 parenrightbigg Thus, the critical conditions reduce to the system 2 - b = a RT , 3 ( - b ) 2 = 2 a RT , which is solved easily to yield a = 2 RT cr cr and b = cr / 2. 2. Introducing P prime = P P cr , prime = cr , and T prime = T T cr , show that the Dieterici equation of state can be expressed in the form P prime = exp(2) T prime 2 prime- 1 exp parenleftbigg- 2 T prime prime parenrightbigg and interpret this result in terms of the law of corresponding states.and interpret this result in terms of the law of corresponding states....
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This note was uploaded on 04/11/2008 for the course MASE 320 taught by Professor Shen during the Spring '08 term at Washington University in St. Louis.
- Spring '08