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

i) $Q_1 = 5000 \;J$

$Q_2 = 4500 \;J$

$η = 1 - \frac{Q_2}{Q_1} = 1 - \frac{4500}{5000} = 0.1$

ii) $Q_1 = 25000 \;J$

$W = 2000 \;J$

$W = Q_1 – Q_2$

$Q_2 = 25000 – 2000 = 23000 \;J$

$η = 1 - \frac{Q_2}{Q_1} = 1 - \frac{23000}{25000} = 0.08$

iii) $W = 400 \;J$

$Q_2 = 2800 \;J$

$W = Q_1 – Q_2$

$Q_1 = W + Q_2 = 400 + 2800 = 3200 \;J$

$η = 1 - \frac{Q_2}{Q_1} = 1 - \frac{2800}{3200} = 0.125$

Engine (iii) has the highest thermal efficiency 1.25.

Engine (ii) has the lowest thermal efficiency 0.08.