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  4. 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 K.

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Q. 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____ $K$.

JEE MainJEE Main 2022Thermodynamics

Solution:

$T _{ c }=324 \,k$
$T _{ H }=?$
$Q _{ H }=300\, J$
$Q _{ L }=180 \,J$
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$1-\frac{ Q _{ L }}{ Q _{ H }}=1-\frac{ T _{ L }}{ T _{ H }}$
$\frac{ Q _{ L }}{ Q _{ H }}=\frac{ T _{ L }}{ T _{ H }}$
$T _{ H }=\frac{ Q _{ H }}{ Q _{ L }} \times T _{ L }=\frac{300}{180} \times 324=540\, K$