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 II . The ratio W I / W II is \ \ \ \ .

Physics · Thermodynamics

JEE Advanced 2023 — Paper 2 — Question 26

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 $\mathrm{a}^{\prime}$ , $\mathrm{b}^{\prime}$ , $\mathrm{c}^{\prime}$ and $\mathrm{d}^{\prime}$ are isothermal, isochoric, isobaric and isochoric, respectively. The total work done during cycle I is $\mathrm{W}_{\mathrm{I}}$ and that during cycle II is $\mathrm{W}_{\text {II }}$ . The ratio $\mathrm{W}_{\mathrm{I}}$ / $\mathrm{W}_{\text {II }}$ is $\_\_\_\_$ .

Answer: 2

Numerical answer — enter this value.

Step-by-step solution

Work done in cycle I is $\mathrm{W}_{\mathrm{I}}=4 \mathrm{P}_{0} \mathrm{~V}_{0}+8 \mathrm{P}_{0} \mathrm{~V}_{0} \ln 2-6 \mathrm{P}_{0} \mathrm{~V}_{0}$ $\mathrm{W}_{\mathrm{II}}=4 \mathrm{P}_{0} \mathrm{~V}_{0} \ln 2-\mathrm{P}_{0} \mathrm{~V}_{0}$ $\frac{\mathrm{W}_{\mathrm{I}}}{\mathrm{W}_{\mathrm{II}}}=2$ .

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2023
Paper: Paper 2
Subject: Physics
Chapter: Thermodynamics
Topic: Calculation of Work, Heat and Internal Energy