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What are (a) the thermal efficiency and (b) the heat extracted from the hot reservoir for the heat engine shown in FIGUREEX21.15?

Short Answer

Expert verified

a.Thermal efficiency heat engine is13%.

b.The heat extracted from the hot reservoir for the heat engine is320J.

Step by step solution

01

Calculation for efficiency of heat engine (part a)

a.

To calculate the efficiency we can use the following formula,

η=WoutQ=WoutWout+Qc

where Qcis the heat that was given to the cold reservoir.

On the other hand, the work done by the gas in one cycle will be equal to the region encircled by the graph.

Work is ,

localid="1648643811450" role="math" Wout=12·(300-100)·103·(600-200)·10-6=40J

On the other hand, the total amount of heat lost is equal to the sum of the two losses.

localid="1648643864648" role="math" Qc=100+180=280J

The efficiency ,

localid="1648643885687" η=4040+280≈13%

02

Calculation for the heat extracted from the hot reservoir for the heat engine (part b)

b.

The heat extracted from the hot reservoir will be as follows:

From solution a,

Wout=40J

Qc=280

Substitute above value,

we get,

Qc=Wout+Qc=40+280=320J

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