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Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford
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Solved: A TS-Diagram. (a) Graph a Carnot cycle, plotting

Chapter 20, Problem 60P

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QUESTION:

Problem 60P

A TS-Diagram. (a) Graph a Carnot cycle, plotting Kelvin temperature vertically and entropy horizontally. This is called a temperature-entropy diagram, or T.S-diagram. (b) Show that the area under any curve representing a reversible path in a temperature-entropy diagram represents the heal absorbed by the system. (c) Derive from your diagram the expression for the thermal efficiency of a Carnot cycle. (d) Draw a temperature-entropy diagram for the Stirling cycle described. Use this diagram to relate the efficiencies of the Carnot and Stirling cycles.

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QUESTION:

Problem 60P

A TS-Diagram. (a) Graph a Carnot cycle, plotting Kelvin temperature vertically and entropy horizontally. This is called a temperature-entropy diagram, or T.S-diagram. (b) Show that the area under any curve representing a reversible path in a temperature-entropy diagram represents the heal absorbed by the system. (c) Derive from your diagram the expression for the thermal efficiency of a Carnot cycle. (d) Draw a temperature-entropy diagram for the Stirling cycle described. Use this diagram to relate the efficiencies of the Carnot and Stirling cycles.

ANSWER:

Solution 60P

a)

The temperature vs entropy diagram is given below.

     

b)

We know that,

           ------------------------(1)

This is the universal definition of temperature.

As this is an exact differential we can write it as,

           -----------------(2)

This is the heat added to the system or the differential heat element.

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