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E115_Problem_Set_16

E115_Problem_Set_16 - (15 points P cr = a 27 b 2 V cr = 3 b...

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e 115 Engineering Thermodynamics Fall 2009 University of California Problem set 16 Due: Monday, October 19 th , in lecture 1) (20 points) In lecture, we discussed the van der Waals equation for 1 mole of gas. As part of this description, equations were given describing the critical pressure, temperature, and volume of a substance in terms of the two van der Waals parameters a and b . In general, curves of P versus T for a van der Waals gas at values of T below the critical temperature exhibit a maximum and minimum at the two points where P V ( ) T = 0 . The inflection point between the maximum and minimum occurs at that point where 2 P V 2 ( ) T = 0 . At the critical pressure, temperature, and volume, these three points (maximum, minimum, and inflection) coalesce into a single point, i.e. , at P crit , V crit , T crit ( ) both P V ( ) T and 2 P V 2 ( ) T are equal to zero. a) Using the expression for 1 mole of a van der Waals gas and taking the proper derivatives, derive the equations for P crit , V crit
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Unformatted text preview: (15 points) P cr = a 27 b 2 ; V cr = 3 b ; T cr = 8 a 27 b R b) Using the definition of a reduced pressure, reduced volume, and reduced temperature, show that the van der Waals equation of state can be rewritten in the form: (5 points) P r + 3 V r 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ V r − 1 3 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 8 3 T r Extra Credit ( 15 points ) Consider a gas following the Clausius equation of state, P V − b ' ( ) = RT where b ' is a constant that does not depend on pressure, volume, or temperature. Calculate expressions for dU , dH and dS that may be used to evaluate the changes in internal energy, enthalpy, and entropy for processes in which T and P are changed. How do these expressions compare to those calculated for an ideal gas? In particular, does the enthalpy and internal energy of the system still depend only on the temperature of the gas?...
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