Question

A Carnot engine operates between two reservoirs of temperatures $900K$ and $300K$. The engine performs $1200J$ of work per cycle. The heat energy (in $J$) delivered by the engine to the low temperature reservoir, in a cycle, is __________.

Answer 1

Answer: 600.00

We have to find $Q_2$
from first law of thermal dynamic for a cyclic process of heat engine $\oint Q=\oint W$
$<br/>Q_1-Q_2=W<br/>$
$<br/>\Rightarrow Q_2=Q_1-W<br/>$
Now from efficiency of cannot cycle.
$<br/>\begin{array}{l}<br/>\eta =\frac{W}{Q_1}=1-\frac{T_2}{T_1}\left(\begin{array}{c}<br/>T_2=300k\\ <br/>T_1=900k<br/>\end{array}\right)\\ <br/>=1-\frac{300}{900}<br/>\end{array}<br/>$
$<br/>=\frac{600}{900}=\frac{2}{3}<br/>$
$<br/>\Rightarrow \frac{W}{Q_1}=\frac{2}{3}\Rightarrow Q_1=\frac{3\times W}{2}=\frac{3\times 1200}{2}=1800J/\text{ cycle }<br/>$
$\therefore$ Heat transferred to low temperature reservoir
$<br/>\Rightarrow Q_2=Q_1-W=1800-1200<br/>$