   Chapter 12.4, Problem 12.3QQ

Chapter
Section
Textbook Problem

Three engines operate between reservoirs separated in temperature by 300 K. The reservoir temperatures are as follows:Engine A: Th = 1000 K, Tc = 700 K Engine B: Th = 800 K, Tc = 500 K Engine C: Th = 600 K, Tc = 300 KRank the engines in order of their theoretically possible efficiency, from highest to lowest (a) A, B, C (b) B, C, A (c) C, B, A (d) C, A, B

To determine
The order of the engine’s theoretically possible efficiency from the highest to the lowest.

Explanation

Section1:

To determine: To determine the efficiency of engine A.

Answer: The theoretical efficiency of engine A is 0.300.

Explanation:

Given Info:

The cold reservoir temperature (Tc)=700K .

The hot reservoir temperature (Th)=1000K .

The highest theoretically possible efficiency of an engine is The Carnot efficiency.

Formula to calculate the Carnot efficiency of the engine is

ec=1TcTh

• Tc is the temperature of cold reservoir
• Th is the temperature of hot reservoir

Substitute 700 K for Tc and 1000 K for Th ,

ec=1700K1000K=0.300

Thus, the theoretical efficiency of engine A is 0.300.

Section2:

To determine: To determine the efficiency of engine B.

Answer: The theoretical efficiency of engine B is 0.375.

Explanation:

Given Info:

The cold reservoir temperature (Tc)=500K .

The hot reservoir temperature (Th)=800K .

The highest theoretically possible efficiency of an engine is the Carnot efficiency

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