A heat engine


A heat engine has an efficiency of $\frac{1}{6}$. When the temperature of $\operatorname{sink}$ is reduced by $62^{\circ} \mathrm{C}$, its efficiency get doubled. The temperature of the source is :

  1. $124^{\circ} \mathrm{C}$

  2. $37^{\circ} \mathrm{C}$

  3. $62^{\circ} \mathrm{C}$

  4. $99^{\circ} \mathrm{C}$

Correct Option: , 4


$\eta=1-\frac{\mathrm{T}_{\mathrm{L}}}{\mathrm{T}_{\mathrm{H}}} \ldots$ (i)

$2 \eta=1-\frac{\left(\mathrm{T}_{\mathrm{L}}-62\right)}{\mathrm{T}_{\mathrm{H}}}=1-\frac{\mathrm{T}_{\mathrm{L}}}{\mathrm{T}_{\mathrm{H}}}+\frac{62}{\mathrm{~T}_{\mathrm{H}}}$

$\Rightarrow \eta=\frac{62}{\mathrm{~T}_{\mathrm{H}}} \Rightarrow \frac{1}{6}=\frac{62}{\mathrm{~T}_{\mathrm{H}}} \Rightarrow \mathrm{T}_{\mathrm{H}}=6 \times 62=372 \mathrm{~K}$

In ${ }^{\circ} \mathrm{C} \Rightarrow 372-273=99^{\circ} \mathrm{C}$

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