final_2005_solutions - MS&E 303 Fall 2005 Final Exam...

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Unformatted text preview: MS&E 303 Fall 2005 Final Exam (2.5 hours) Solutions 1. Short, quick answers. (a) What are the four laws of thermodynamics. Provide a one-line verbal answer (on all) and a one line mathematical answer (for all but the 0 th Law). (b) Define (text and math) the activity as it relates to the chemical potential. (c) How is the activity of an arbitrary material related to the vapor pressure (text and math)? 2. Calculate the temperature change resulting from adiabatic, reversible compression (sound waves) of water from 1 atm to 100 atm at 27 o C. Show all derivations, explain non-obvious steps, and give the answer in K. You may assume that the temperature change will be small. Physical constants for water (independent of T and P) at 25 o C are approximately: = 250 10- 6 K- 1 , v = 20 cm 3 /mole, T = 5 10- 10 Pa- 1 , and c P = 75 J/K-mole. Water is being compressed from approximately 1 10 5 Pa to 200 10 5 Pa, or more precisely a P of 201 . 63 10 5 Pa. The volume and temperature changes are just integrals of dV and dT respectively, where S is held constant. We can then write the net changes as (and using the approximation of small changes) T = Z dT = Z P f P i T P s dP =- Z P f P i s P T s T P dP = Z P f P i v T P c P /T dP = Z P f P i vT c P dP vT c P P Our assumption of small changes in T and v must ultimately be justified by the answers. But we proceed assuming this is valid. For T , its a straight plug and grind T = V T C P P = (257 10- 6 )(18 . 07 10- 6 )(298) 75 . 44 (201 . 63 10 5 ) = 0 . 3699 K Clearly the assumption of a small T is justified. Over 0.4 K, neither T nor change enough to concern us. [As a side note I get away with ignoring units since I took everything into the MKS space. If not, you have to fight the units cancellation.] 3. Liquid Pb at T m is used to run a perfect thermodynamic engine producing work, using the environment as an infinite thermal reservoir at 25 o C. Calculate the total heat energy (enthalpy) and the total work that can be extracted per mole of liquid lead. Use symbols for values and taken them as independent of temperature: c liq P , c sol P , T m , and H m . Explain your steps. Hint: Dont think much about the mechanism for converting from heat to work. Work on a higher level. This problem requires understanding how to keep reversibility in the face of various heat flow conditions. Before beginning, I want to digress momentarily to address a subtlety that is usually ignored. Specifically, we look at the enthalpy in this type of problem as equivalent to the energy for balancing heat flow and work. It is strictly correct, and requires tracking carefully the different types of work through the Legendre transforms....
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This note was uploaded on 09/21/2008 for the course MSE 303 taught by Professor Thompson during the Fall '04 term at Cornell University (Engineering School).

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final_2005_solutions - MS&E 303 Fall 2005 Final Exam...

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