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Quiz3-Sol-SSI09

Quiz3-Sol-SSI09 - Physics 2C Summer Session I Quiz#3...

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Physics 2C Summer Session I Quiz #3 Multiple Choice. Choose the answer that best completes the statement or answers the question. 1 . An ideal Carnot engine operates between 52 ° C and 269 ° C with a heat input of 250 J per cycle. Assuming that the acceleration due to gravity is g = 10 m=s 2 ; how many cycles are required to lift a 400 g rock 50 m ? A) 1 B) 2 C) 4 D) 5 E) 8 The e¢ ciency of this engine is given by e = 1 ° T c T h = 1 ° 52 + 273 269 + 273 = : 4 : Hence the work output per cycle is 100 J: The work required to lift a 400 g rock 50 m is 200 J . Hence 2 cycles are required to lift the rock. ! B 2 . Given that the gas in problem 1 expands by a factor of 5 : 1 during the isothermal expansion process at T = 269 ° C; how many moles of an inert gas are required in the Carnot cycle of problem 1 to produce the 250 J per cycle? A) : 086 moles B) : 098 moles C) : 112 moles D) : 136 moles E) : 156 moles The net work by the gas in a Carnot cycle is given by W = nRT h ln V B =V A ° nRT c ln V C =V D ; where V B =V A is the expansion ratio during the isothermal expansion process at T = T h . The expansion ratio V C =V D for the expansion ratio at T = T c is found from T h V ° ± 1 B = T c V ° ± 1 C T h V ° ± 1 A = T c V ° ± 1 D V B =V A = V C =V D : Hence the expansion ratios are equal and W = nR ( T h ° T c ) ln V B =V A ! 250 = n (8 : 314) (217) ln 5 n = 250 = ((8 : 314) (217) ln 5) = : 086 moles !

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