Question

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

Answer 1

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