A heat engine operates with the cold reservoir at temperature $324 K$. The minimum temperature of the hot reservoir, if the heat engine takes $300 \; J$ heat from the hot reservoir and delivers $180 \; J$ heat to the cold reservoir per cycle, is $\dots \; K .$
JEE MAIN 2022, Medium
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$T _{ c }=324 \; k$
$T _{ H }= ?$
$Q _{ H }=300 \; J$
$Q _{ L }=180 \; J$
$1-\frac{ Q _{ L }}{ Q _{ H }}=1-\frac{ T _{ L }}{ T _{ H }}$
$\frac{ Q _{ L }}{ Q _{ H }}=\frac{ T _{ L }}{ T _{ H }}$
$T _{ H }=\frac{ Q _{ H }}{ Q _{ L }} \times T _{ L }=\frac{300}{180} \times 324=540 K$
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