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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 20 / Problem 53P

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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Answer: A Carnot engine operates between two heat

Chapter 20, Problem 53P

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QUESTION:

Problem 53P

A Carnot engine operates between two heat reservoirs at temperatures TH and TC. An inventor proposes to increase the efficiency by running one engine between TH and an intermediate temperature T and a second engine between T and TC, using as input the heat expelled by the first engine. Compute the efficiency of this composite system, and compare it to that of the original engine.

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QUESTION:

Problem 53P

A Carnot engine operates between two heat reservoirs at temperatures TH and TC. An inventor proposes to increase the efficiency by running one engine between TH and an intermediate temperature T and a second engine between T and TC, using as input the heat expelled by the first engine. Compute the efficiency of this composite system, and compare it to that of the original engine.

ANSWER:

Solution 53P

Step 1 of 3:

The efficiency of the composite engine is ${e}_{12}=\frac{{W}_{1}+{W}_{2}}{{Q}_{H1}}$

Where ${Q}_{H1}$ is the heat input to the first engine and ${W}_{1}\ and\ \ {W}_{2\ \ }are\ the\ work\ outputs\ of\ two\ engines$

For any heat engine, $W={Q}_{C}+{Q}_{H}$

For any carnot engine, $\frac{{Q}_{low}}{{Q}_{High}}=-\frac{{T}_{low}}{{T}_{high}}$

Where ${Q}_{low}and\ {Q}_{high\ }are\ the\ heat\ flows\ at\ the\ two\ reservoirs\ that\ have\ temperatures\ \ {T}_{low}\ and\ \ {T}_{high}$

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