A carnot engine with its cold body at $17\,^oC$ has $50\%$ effficiency. If the temperature of its hot body is now increased by $145\,^oC$, the efficiency becomes...... $\%$
Medium
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$\eta=\frac{T_{1}-T_{2}}{T_{1}}$
$\left.\mathrm{T}_{1}=\text { temperature of source (in } \mathrm{K}\right)$
$\mathrm{T}_{2}=$ temperature of $\operatorname{sink}(\mathrm{in} \mathrm{K})$
$\frac{1}{2}=\frac{\mathrm{T}_{1}-290}{\mathrm{T}_{1}}$
$\mathrm{T}_{1}=580 \mathrm{K}$
If $\mathrm{T}_{1}$ is increased by $145^{\circ} \mathrm{C}$
$\mathrm{T}_{1}^{\prime}=580+145=725 \mathrm{K}$
$\eta^{\prime}=\frac{725-290}{725}=0.6$
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