A Car not engine whose low temperate reservoir is at $7\,^oC$ has an efficiency of $50\%$ . It is desired to increase the efficiency to $70\%$ . By how many degrees should the temperature of the high temperature reservoir be increased .... $K$
Diffcult
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Initially $\eta=\frac{\mathrm{T}_{1}-\mathrm{T}_{2}}{\mathrm{T}_{1}} \Rightarrow 0.5=\frac{\mathrm{T}_{1}-(273+7)}{\mathrm{T}_{1}}$
$\Rightarrow \frac{1}{2}=\frac{\mathrm{T}_{1}-280}{\mathrm{T}_{1}} \Rightarrow \mathrm{T}_{1}=560 \mathrm{K}$
Finally $\eta_{1}^{\prime}=\frac{T_{1}^{\prime}-T_{2}}{T_{1}^{\prime}} \Rightarrow 0.7=\frac{T_{1}^{\prime}-(273+7)}{T_{1}^{\prime}}$
$\Rightarrow \mathrm{T}_{1}^{\prime}=933 \mathrm{K}$
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