A heat engine operates between a cold reservoir at temperature ${T}_{2}=400\, {K}$ and a hot reservoir at temperature ${T}_{1} .$ It takes $300 \,{J}$ of heat from the hot reservoir and delivers $240\, {J}$ of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be $....{K}$
JEE MAIN 2021, Medium
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${Q}_{\text {in }}=300\, {J} ; Q_{\text { out }}=240\, {J}$
Work done $=Q_{\text {in }}-Q_{\text {out }}=300-240=60 {J}$
Efficiency $=\frac{W}{{Q}_{\text {in }}}=\frac{60}{300}=\frac{1}{5}$
efficiency $=1-\frac{{T}_{2}}{{T}_{1}}$
$\frac{1}{5}=1-\frac{400}{{T}_{1}} \Rightarrow \frac{400}{{T}_{1}}=\frac{4}{5}$
${T}_{1}=500\, {k}$
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