Question

A Carnot engine whose efficiency is 45% takes heat from a source maintained at a temperature of 327°C. To have an engine of efficiency of 60% what must be the intake temperature for the same exhaust (sink) temperature?

Answer 1

Efficiency of Carnot engine (η₁) = 45% = 0.45

Initial intake temperature (T₁) = 327°C = 600 K

New efficiency (η₂) = 60% = 0.6

Efficiency of Carnot engine is given by

η = `1 - "T"_2/"T"_1`

T₁ is the temperature of the source; T₂ is the temperature of the sink

1^st Case: T₂ = (1 − η)T₁ = (1 − 0.45) × 600

T₂ = 330 K

2^nd Case: `"T"_2/"T"_1 = 1 - η`

T₁ = `"T"_2/(1 - η)`

= `330/(1 - 0.6)`

= `330/0.4`

T₁ = 825 K

= 825 − 273

T₁ = 552°C