CHEM163B_HW5_solutions_2011

CHEM163B_HW5_solutions_2011 - Winter 2011 Chemistry 163B...

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Winter 2011 Chemistry 163B 1 Homework #5 Problems (#23-#29) 23. The diagram below, where Carnot engine X and Carnot heat pump C are coupled, is similar to that used in lecture to illustrate that the efficiency of any Carnot engine, ! x , has to be the same as that of an ideal gas Carnot engine, ! c , when the engines operate between the same two temperatures. The diagram below differs in that now 33% (-20 J) of the total work done by engine X is done on the surroundings, while 67% (-40 J) is input into the Carnot refrigerator C. Assume that as indicated ! x = 0.6 and ! c =0.5 . For (q U ) x = 100J, (w surr ) x ="20 J, (w i ) x =-"40 J, (w t ) c =+40J, and (q U ) c = ± 80J Calculate: a. (q L ) x b. (q L ) c c. (q U ) total = (q U ) x + (q U ) C d. (q L ) total = (q L ) x + (q L ) C e. w total = (w surr ) x + (w i ) x + (w t ) c f. Considering the [correct] results for parts c, d, and e, how does the process with coupled Carnot engines X and C having ² x = 0.6 and ² c =0.5 violate one of the ‘phenomenological’ statements of the Second Law of Thermodynamics.
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This note was uploaded on 03/16/2011 for the course CHEM 163B taught by Professor Geneswitkes during the Spring '11 term at UCSC.

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CHEM163B_HW5_solutions_2011 - Winter 2011 Chemistry 163B...

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