Work done by a Carnot engine operating between temperatures $127^{\circ}\,C$ and $27^{\circ}\,C$ is $2\,kJ$. The amount of heat transferred to the engine by the reservoir is $........\,kJ$
JEE MAIN 2023, Medium
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$\eta=1-\frac{ T _2}{ T _1}=\frac{ W }{ Q _1}$
$\Rightarrow \frac{ W }{ Q _1}=1-\frac{300}{400}=\frac{1}{4}$
$\Rightarrow \frac{2 kJ }{ Q _1}=\frac{1}{4}$
$\Rightarrow Q _1=8\,kJ$
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