An ideal Carnot engine operates between a high temperature reservoir at $492 \mathrm {~K}$ and a river with water at $290 \mathrm {~K}$. If it absorbs $4000 \mathrm {~J}$ of heat each cycle, how much work per cycle does it perform?
A) $2358 \mathrm {~J}$
B) $1483 \mathrm {~J}$
C) $1642 \mathrm {~J}$
D) $2517 \mathrm {~J}$

Question

Quizplus · Accepted Answer

The efficiency of a Carnot engine is given by $ \eta = 1 - \frac{T_c}{T_h} $. Substituting $ T_h = 492 \mathrm{~K} $ and $ T_c = 290 \mathrm{~K} $, we find $ \eta = 1 - \frac{290}{492} \approx 0.41 $. The work done per cycle is $ W = \eta \times Q_h = 0.41 \times 4000 \mathrm{~J} \approx 1642 \mathrm{~J} $.

An Ideal Carnot Engine Operates Between a High Temperature Reservoir 492 K492 \mathrm {~K}492 K

An Ideal Carnot Engine Operates Between a High Temperature Reservoir $492 \mathrm {~K}$