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# A Carnot heat engine uses a hot reservoir consisting of a ISBN: 9780321675460 31

## Solution for problem 20E Chapter 20

University Physics | 13th Edition

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Problem 20E

A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In 5 minutes of operation, the heat rejected by the engine melts 0.0400 kg of ice. During this time, how much work W is performed by the engine?

Step-by-Step Solution:

Solution 20E Step 1: Latent heat of fusion of ice, H (ice)f 333.55 kJ/kg Equation for latent heat of fusion, H = Q/m f Where, Q - Amount of heat m - Mass of the substance Efficiency of a heat engine can be given by, = 1 - (T c )H Where, T - Cmperature of the cold reservoir TH temperature of the hot reservoir Step 2: In this problem, they have provided, the hot reservoir is having boiling water. Therefore, T = 100 = 100 + 273 = 373 K H Cold reservoir is having a large tub of ice, then T = 0 = 0 + 273 K = 273 K C Therefore, the maximum possible efficiency of the heat engine, = 1 - (273 K /373 K) = 1 - 0.732 = 0.268 Or, = 26.8%

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##### ISBN: 9780321675460

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