The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is
AIIMS 2008, Diffcult
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$\mathrm{Q}_{1}=\mathrm{T}_{0} \mathrm{S}_{0}+\frac{1}{2} \mathrm{T}_{0} \mathrm{S}_{0}=\frac{3}{2} \mathrm{T}_{0} \mathrm{S}_{0}$
${\mathrm{Q}_{2}=\mathrm{T}_{0}\left(2 \mathrm{S}_{0}-\mathrm{S}_{0}\right)=\mathrm{T}_{0} \mathrm{S}_{0} \text { and } \mathrm{Q}_{3}=0}$
${\eta=\frac{\mathrm{W}}{\mathrm{Q}_{1}}=\frac{\mathrm{Q}_{1}-\mathrm{Q}_{2}}{\mathrm{Q}_{1}}} $
${=1-\frac{\mathrm{Q}_{2}}{\mathrm{Q}_{1}}=1-\frac{\mathrm{T}_{0} \mathrm{S}_{0}}{\frac{3}{2} \mathrm{T}_{0} \mathrm{S}_{0}}=\frac{1}{3}}$
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