One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the $P-V$ diagrams below. In cycle I, processes $a, b, c$ and $d$ are isobaric, isothermal, isobaric and isochoric, respectively. In cycle II, processes $a^{\prime}, b^{\prime}, c^{\prime}$ and $d^{\prime}$ are isothermal, isochoric, isobaric and isochoric, respectively. The total work done during cycle I is $W_I$ and that during cycle II is $W_{I I}$. The ratio $W_I / W_{I I}$ is . . . .
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IIT 2023, Advanced
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$\frac{\mathrm{W}_{\mathrm{I}}}{\mathrm{W}_{\mathrm{II}}}=\frac{4 \mathrm{P}_0 \mathrm{~V}_0+8 \mathrm{P}_0 \mathrm{~V}_0 \ell \mathrm{n} 2-6 \mathrm{P}_0 \mathrm{~V}_0-0}{4 \mathrm{P}_0 \mathrm{~V}_0 \ln 2-0-\mathrm{P}_0 \mathrm{~V}_0+0}$
$=\frac{8 \ell \mathrm{n} 2-2}{4 \ell \mathrm{n} 2-1}=2$
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