A certain engine which operates in a Carnot cycle absorbe `3.0 kJ` at `400^(@)C` in a cycle. If it rejects heat at `100^(@)C`, how much work is done on the engine per cycle and how much heat is evolved at `100^(@)C` in each cycle?

Explanation

Given,
Heat absorbs `(q_(2)) = 3.0 kJ`
`T_(2) = 400 + 273.15 K = 673.15 K`
`T_(1) = 100 +273.15 K = 373.15 K`
Efficiency of the Carnot cycle is given by
`eta = (T_(2)-T_(1))/(T_(2)) = (q_(2)+q_(1))/(q_(2))`
Thus, `(-T_(1))/(T_(2)) = (q_(1))/(q_(2))`
Hence, `q_(1) = ((-T_(1))/(T_(2))) (q_(2))`
Thus, heat evolved
`q_(1) =- ((373.15K)/(673.15K)) (3.0kJ) =- 1.662 kJ`
The work done on the engine is
`w =- (q_(2)+q_(1)) = - (3.0 +1.662) kJ =- 4.662kJ`