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# sol8 - MasteringPhysics 3:06 PM Assignment Display Mode...

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1/7/09 3:06 PM MasteringPhysics Page 1 of 21 http://session.masteringphysics.com/myct Assignment Display Mode: View Printable Answers Physics 5D Fall 2008 Assignment 8 Due at 4:00pm on Thursday, December 11, 2008 View Grading Details Carnot Cycle: Just How Ideal Is It? Description: A mix of conceptual and quantitative questions about ideal heat engines. Learning Goal: To understand the quantitative relationships related to ideal (Carnot) engines and the limitations of such devices imposed by the second law of thermodynamics. In 1824, Sadi Carnot, a French engineer, introduced a theoretical engine that has been since then called a Carnot engine , the most efficient engine possible. The following statement is known as Carnot's theorem : No engine operating between a hot and a cold reservoir can be more efficient than the Carnot engine that operates between the same two reservoirs. The Carnot engine operates cyclically, just like any real engine.The Carnot cycle includes four reversible steps: two isothermal processes and two adiabatic ones. In this problem, you will be asked several questions about Carnot engines. We will use the following symbols: : the absolute value (magnitude) of the heat absorbed from the hot reservoir during one cycle or during some time specified in the problem; : the absolute value (magnitude) of the heat delivered to the cold reservoir during one cycle or during some time specified in the problem; : the amount of work done by the engine during one cycle or during some time specified in the problem; : the absolute temperature of the hot reservoir; and : the absolute temperature of the cold reservoir. Part A In general terms, the efficiency of a system can be thought of as the output per unit input. Which of the expressions is a good mathematical representation of efficiency of any heat engine? ANSWER: Part B During the Carnot cycle, the overall entropy ________. Hint B.1 Some useful equations Recall that in a Carnot cycle, , where we have taken all heat exchanged to be positive. Also, the definition of the entropy change when heat is transferred at a temperature is . ANSWER: [ Print ]

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1/7/09 3:06 PM MasteringPhysics Page 2 of 21 http://session.masteringphysics.com/myct ANSWER: increases decreases remains constant Part C Which of the following gives the efficiency of the Carnot engine? Hint C.1 Some useful equations Recall that in a Carnot cycle, , where we have taken all heat exchanged to be positive. Substitute for and in the earlier expression for the efficiency. Also recall that . ANSWER: Part D Consider a Carnot engine operating between the melting point of lead ( ) and the melting point of ice ( ). What is the efficiency of such an engine? ANSWER: 0 0.455 0.545 1 infinity Part E We have stressed that the Carnot engine does not exist in real life: It is a purely theoretical device, useful for understanding the limitations of heat engines. Real engines never operate on the Carnot cycle; their efficiency is hence lower than that of the Carnot engine. However, no attempts to build a Carnot engine are being made. Why is that?
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