# T6 - Phy sics 7B WS T6 rev 3.0 Page 1 T-6 Entropy and the...

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Physics 7B WS T6 (rev. 3.0) Page 1 T-6. Entropy and the Second Law Questions for discussion 1. Shown below are schematic figures for the energy and entropy of a heat engine. a) What is the relation between Δ S in and Δ S out ? Why is it not possible to develop a cyclic engine that converts heat entirely into work? Why must some heat (Q out ) be ejected from the system? b) In a Carnot engine, Q in enters the system only along the isotherm T H , and Q out leaves the system only along the isotherm T L . Use your result of (a) to find Q out /Q in in terms of T H and T L . c) An efficient engine converts as much heat as possible into work, ejecting as little as possible. Can you explain why a Carnot gives the greatest possible efficiency? [Hint: Q in enters the system only at the highest temperature of the cycle. Q out leaves the system only at the lowest temperature of the cycle.] More challenging questions or problems will be marked with a *. Your GSI will guide you as to whether you need to to complete them.

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Physics 7B WS T6 (rev. 3.0) Page 2 2 . A cyclic heat engine uses an ideal gas as its working substance. Which of the following are true? _____ For a complete cycle, the change in entropy of the gas is zero ( Δ S gas = 0). _____ For a complete cycle, the change in entropy of the gas is zero ( Δ S gas = 0), but only if the engine operates reversibly. If the engine operates irreversibly , then Δ S gas > 0. _____ For a complete cycle, the change in entropy of the universe is zero ( Δ S universe = Δ S gas + Δ S environment = 0). _____ For a complete cycle, the change in entropy of the universe is zero ( Δ S universe = Δ S gas + Δ S environment = 0), but only if the engine operates reversibly. If the engine operates irreversibly , then Δ S universe > 0. 3 . A box with total volume V o is divided in half by a partition. On the left-hand side of the partition, there is a sample of ideal gas with initial pressure P o and initial temperature T o . On the right-hand side of the partition, the box is empty. The partition is then suddenly removed, and the gas expands freely to fill the entire box. Soon the gas is in thermal equilibrium again. a) Intuitively, what do you think happens to the entropy of the gas when it expands freely? Does the entropy increase, decrease, or stay the same? Justify your answer. b)
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## This note was uploaded on 11/19/2010 for the course LECTURE 1 taught by Professor Yildiz during the Fall '10 term at Berkeley.

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T6 - Phy sics 7B WS T6 rev 3.0 Page 1 T-6 Entropy and the...

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