Class Note - WHY THE EFFICIENCY OF A CARNOT ENGINE IS...

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WHY THE EFFICIENCY OF A CARNOT ENGINE IS INDE- PENDENT OF THE KIND OF WORKING MATERIAL CHEMISTRY 213B Here are two proofs that the efficiency of a rev ersible Carnot engine depends only on the temperatures of the heat baths. 1. Method I using Thompson’s Principle W Q H Q H Q ’ Q ’ L L T H T L R E W’ where W = the work produced by the engine, Q H = the heat absorbed by the engine from the hot reservoir, Q L = the heat given off by the engine to the cooler reservoir, W = the work used to run the Carnot refrigerator, Q H = the heat given off by the refrigerator to the hot reservoir, Q L = the heat absorbed by the refrigerator from the cooler reservoir. The sizes of the engine and refrigerator are adjusted such that no net heat is taken from the cool reservoir in one cycle (i.e., Q L = Q L ). According to Thompson’s principle, no net positive work can be realized in the surroundings from any device which takes heat from a single heat source. Thus, W ′ - W 0. (1) However, from the First Law, the net work produced must equal the net heat absorbed by the sys- tem; i.e., Winter Term 2001-2002
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