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Chapter 20: Q26P (page 605)

In a hypothetical nuclear fusion reactor, the fuel is deuterium gas at a 7脳100掳Ctemperature of . If this gas could be used to operate a Carnot engine with TL=100掳C, what would be the engine鈥檚 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脳108K

The temperature of the low-temperature reservoir,TL=100掳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鈥檚 engine,

蔚=1-TLTH (2)

03

Calculation of the engine’s efficiency

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

蔚=1-373K7脳108K脳100%=1-2.3285脳10-7脳100%=0.9999995脳100%=99.99995%

Hence, the value of the engine鈥檚 efficiency is 99.99995%

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