Question 11: 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 – T₂/T₁
In the given case;
Temperature of the hot reservoir = T₁ = 227°C = 227 + 273 = 500k
Temperature of the cold reservoir = T₂ = 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.