One mole of an ideal gas is taken from a to $b$ along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is $\mathrm{w}_{\mathrm{s}}$ and that along the dotted line path is $w_d$, then the integer closest to the ratio $w_d / w_5$ is
IIT 2010, Advanced
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$w_d=4 \times 1.5+1 \times 1+2.5 \times 2 / 3=8.65$
Process is isothermal
$ \mathrm{w}_{\mathrm{s}}=2 \times 2.303 \log \frac{5.5}{0.5}=2 \times 2.303 \times \log 11=2 \times 2.303 \times 1.0414=4.79 $
$ \frac{\mathrm{w}_{\mathrm{d}}}{\mathrm{w}_{\mathrm{s}}}=\frac{8.65}{4.79}=1.80=2$
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