Question

A heat engine with a thermal efficiency of $40{\mathrm{\%}}_{}$does $100J$of work per cycle. How much heat is (a) extracted from the hot reservoir and (b) exhausted to the cold reservoir per cycle?

Short answer

(a) The heat extracted from the hot reservoir is $250J$.

(b) The heat exhausted to the cold reservoir is $150J$.

Step-by-step solution

Step :1  Hot reservoir (part a)

(a) The work done per cycle equals $W$and the received heat i.e. the heat extracted from the hot reservoir $Q_1$,efficiency of the engine can be expressed as follows.

$\eta =\frac{W}{Q_1}$

This yields

$Q_1=\frac{W}{\eta }$

Substitute 100 W for W and .4 for $\eta$in the equation above$(\eta =40\mathrm{\%}=0.4)$

$Q_1=\frac{100W}{0.4}=250W.$

Step :2 Difference between heat extracted and work done   (part b)

(b) The difference in heat extracted from the hot reservoir and heat exhausted to the cold reservoir.$Q_2$per cycle is equal to the total work done per cycle. Therefore

$W=Q_1-Q_2$

localid="1648496332888">Q2=Q1−W=250W-100W=150J