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QJEEAdv23Ph821b: JEE Advanced 2023 Physics - Class 11 JEEAdv23Ph821b Solution: One mole of an ideal gas undergoes two different cyclic…

One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the P−VP-V diagrams below. In cycle I, processes a,b,ca, b, c and dd are isobaric, isothermal, isobaric and isochoric, respectively. In cycle II, processes a′,b′,c′a^{\prime}, b^{\prime}, c^{\prime} and d′d^{\prime} are isothermal, isochoric, isobaric and isochoric, respectively. The total work done during cycle I\mathrm{I} is WIW_I and that during cycle II is WIIW_{I I} . The ratio WI/WIIW_I / W_{I I} is ________.

JEE Advanced 2023 Paper 2 Online Physics - Heat and Thermodynamics Question 6 English

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JEE Advanced 2023 Paper 2 Online Physics - Heat and Thermodynamics Question 6 English Explanation 1
W1amp;=Wa+Wb+Wc+Wdamp;=4P0(2V0−V0)+nRTln⁡(4V02V0)+2P0(V0−4V0)+0amp;=4P0V0+nR(8P0V0nR)ln⁡2−6P0V0amp;=8P0V0ln⁡2−2P0V0\begin{aligned} W_1 & =W_a+W_b+W_c+W_d \\\\ & =4 P_0\left(2 V_0-V_0\right)+n R T \ln \left(\frac{4 V_0}{2 V_0}\right)+2 P_0\left(V_0-4 V_0\right)+0 \\\\ & =4 P_0 V_0+n R\left(\frac{8 P_0 V_0}{n R}\right) \ln 2-6 P_0 V_0 \\\\ & =8 P_0 V_0 \ln 2-2 P_0 V_0\end{aligned}

JEE Advanced 2023 Paper 2 Online Physics - Heat and Thermodynamics Question 6 English Explanation 2
WII amp;=Wa′+Wb′+Wc′+Wd′amp;=nRTln⁡(2V0V0)+0+P0(V0−2V0)+0amp;=nR(4P0V0nR)ln⁡2−P0V0amp;=4P0V0ln⁡2−P0V0\begin{aligned} W_{\text {II }} & =W_a^{\prime}+W_b^{\prime}+W_c^{\prime}+W_d^{\prime} \\\\ & =n R T \ln \left(\frac{2 V_0}{V_0}\right)+0+P_0\left(V_0-2 V_0\right)+0 \\\\ & =n R\left(\frac{4 P_0 V_0}{n R}\right) \ln 2-P_0 V_0 \\\\ & =4 P_0 V_0 \ln 2-P_0 V_0\end{aligned}

WIWII=8P0V0ln⁡2−2P0V04P0V0ln⁡2−P0V0=2\frac{W_I}{W_{I I}}=\frac{8 P_0 V_0 \ln 2-2 P_0 V_0}{4 P_0 V_0 \ln 2-P_0 V_0}=2

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