Question

Which of the following heat engines has the highest thermal efficiency? The lowest?
i) An engine that in one cycle absorbs 5000 J of heat and rejects 4500 J of heat; ii) An engine that in one cycle absorbs 25000 J of heat and does 2000 J of work; iii) An engine that in one cycle does 400 J of work and rejects 2800 J of heat

Answer 1

$\textsf{Thermal Efficiency }(\eta) = \dfrac{W}{Q_H}$

(i) W = 5000J - 4500J = 500J

$Q_H$ = 5000J

$\eta = \dfrac{500J}{5000J} = 0.1$

(ii) W = 2000J

$Q_H$ = 25000J

$\eta = \dfrac{2000J}{25000J} = 0.08$

(iii) W = 400J

$Q_H$ = 400J + 2800J = 3200J

$\eta = \dfrac{400J}{3200J} = 0.125$

$\therefore$ Engine number (iii) with 0.125 thermal efficiency has the highest efficiency, and Engine number (ii) with 0.08 thermal efficiency has the lowest efficiency.