Question 18: An inventor claims to have developed a heat engine, working between 27^{°} and 227° having an efficiency of 45%. Is the claim valid? Why?

ANSWER

The efficiency of a heat engine is given by the equation,

η = 1 – T_{2}/T_{1}

In the given case;

Temperature of the hot reservoir = T_{1} = 227°C = 227 + 273 = 500k

Temperature of the cold reservoir = T_{2} = 27°C = 27 + 273 = 300k

Putting these values, the efficiency of the engine is given by;

η = 1 – 300/500 = 1 – 3/5 = (5-3)/5 = 2/5

And percent efficiency = η*100 = 2/5 x 100 = 200/5 = 40

Hence, the maximum efficiency of the engine working between these two temperatures would be 40%.

The inventor’s claim doesn’t seem to be valid, therefore.

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