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Chapter 20: Q26P (page 605)

In a hypothetical nuclear fusion reactor, the fuel is deuterium gas at a 7×100°Ctemperature of . If this gas could be used to operate a Carnot engine with TL=100°C, what would be the engine’s efficiency? Take both temperatures to be exact and report your answer to seven significant figures.

Short Answer

Expert verified

The efficiency of the engine is 99.99995%

Step by step solution

01

The given data

The temperature of the high-temperature reservoir,TH=7×108K

The temperature of the low-temperature reservoir,TL=100°C=373K

02

Understanding the concept of the efficiency of the engine

We use the formula of efficiency of Carnot's heat engine to calculate the efficiency of the engine

Formula:

The efficiency of the Carnot’s engine,

ε=1-TLTH (2)

03

Calculation of the engine’s efficiency

The efficiency of Carnot’s engine using equation (1) can be given as:

ε=1-373K7×108K×100%=1-2.3285×10-7×100%=0.9999995×100%=99.99995%

Hence, the value of the engine’s efficiency is 99.99995%

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