Probl_3.5_sol - temperature, requiring less of temperature...

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Thermodynamics of Materials © John Kieffer, University of Michigan (2009) 1 P ROBLEM 3.5 S OLUTION One mole of copper at 0˚C is placed in thermal contact with a second mole of copper at 100˚C. Heat flows from hot to cold. What is the final uniform temperature of the joint configuration? What is the amount of entropy produced? Given c p = 22.64 + 6.28·10 3 T J/mol·K q = H = H hot + H cold = 0 . c p dT 273 T f + c p dT 373 T f = 0 22.64 T f 273 ( ) + 3.14·10 3 T f 2 273 2 ( ) + 22.64 T f 373 ( ) + 3.14·10 3 T f 2 373 2 ( ) = 0 , which yields T f = 323.32 K or 50.32˚C. The equilibrium temperature is not exactly half- way in between the two initial temperatures, because the heat capacity increases with
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Unformatted text preview: temperature, requiring less of temperature difference to store the same amount of heat at high temperature than at low temperature. ∆ S cold = c p T dT 273 T f ∫ = 22.64 ln T f 273 ( ) + 6.28·10 − 3 T f − 273 ( ) = 4.15 J/mol·K ∆ S hot = c p T dT 373 T f ∫ = 22.64 ln T f 373 ( ) + 6.28·10 − 3 T f − 373 ( ) = –3.55 J/mol·K ∆ S irr = 0.6 J/mol·K. The heat transferred from one block to the other is ∆ H = 22.64 323.32 − 273 ( ) + 3.14·10 − 3 323.32 2 − 273 2 ( ) = 1233 J/mol...
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This note was uploaded on 10/26/2009 for the course MSE 330 taught by Professor Kiffer during the Fall '09 term at University of Michigan-Dearborn.

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