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s_chapter_19 - Chapter 19 The Second Law of Thermodynamics...

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1779 Chapter 19 The Second Law of Thermodynamics Conceptual Problems 1 Modern automobile gasoline engines have efficiencies of about 25%. About what percentage of the heat of combustion is not used for work but released as heat? ( a ) 25%, ( b ) 50%, ( c ) 75%, ( d ) 100%, ( e ) You cannot tell from the data given. Determine the Concept The efficiency of a heat engine is the ratio of the work done per cycle W to the heat absorbed from the high-temperature reservoir Q h . The percentage of the heat of combustion (heat absorbed from the high- temperature reservoir) is the ratio of Q c to Q h . We can use the relationship between W, Q h , and Q c ( c h Q Q W = ) to find Q c / Q h . Use the definition of efficiency and the relationship between W, Q h , and Q c to obtain: h c h c h h 1 Q Q Q Q Q Q W = = = ε Solving for Q c / Q h yields: ε = 1 h c Q Q Substitute for ε to obtain: 75 . 0 25 . 0 1 h c = = Q Q and ( ) c is correct. 2 If a heat engine does 100 kJ of work per cycle while releasing 400 kJ of heat, what is its efficiency? ( a ) 20%, ( b ) 25%, ( c ) 80%, ( d ) 400%, ( e ) You cannot tell from the data given. Determine the Concept The efficiency of a heat engine is the ratio of the work done per cycle W to the heat absorbed from the high-temperature reservoir Q h . We can use the relationship between W, Q h , and Q c ( c h Q Q W = ) to express the efficiency of the heat engine in terms of Q c and W . Use the definition of efficiency and the relationship between W, Q h , and Q c to obtain: W Q Q W W Q W c c h 1 1 + = + = = ε
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