   Chapter 12, Problem 62AP

Chapter
Section
Textbook Problem

A Carnot engine operates between the temperatures Th = 1.00 × 102°C and Tc = 20.0°C. By what factor does the theoretical efficiency increase if the temperature of the hot reservoir is increased to 5.50 × 102°C?

To determine
The factor at which the theoretical efficiency increases.

Explanation

Section1:

To determine: the Carnot efficiency of the engine.

Answer: the efficiency of the Carnot engine is 0.214 .

Explanation:

Given Info:

Temperature of the hot reservoir is 1.00×102°C .

Temperature of the cold reservoir is 20.0°C .

Formula to calculate the Carnot efficiency is,

ec=1TcTh

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

Substitute 20.0°C for Tc and 1.00×102°C for Th to find the efficiency,

ec=1(100+273)K(20+273)K=0.214

Thus, the efficiency of the Carnot engine is 0.214 .

Section2:

To determine: the Carnot efficiency of the engine after increasing the temperature of hot reservoir.

Answer: the Carnot efficiency of the engine after increasing the temperature of hot reservoir is 0.644 .

Explanation:

Given Info:

Temperature of the hot reservoir is 5.50×102°C

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