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Saturday, 31 October

JEE Main 2021 · PhysicsMultiple choiceDiagram basedHardMulti-step

JEE Main 24 February 2021, Shift 2, Physics Q5

Question 5 of 90 in this shift, Physics question 5 of 30, Section A.

If one mole of an ideal gas at (P1,V1)(P_1, V_1) is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value (B→CB \rightarrow C). Then it is restored to its initial state by a reversible adiabatic compression (C to A). The net workdone by the gas is equal to :

The figure, in words

P-V diagram: P on vertical axis with marks P_1, P_1/2, P_1/4 (dotted horizontal guide lines); V on horizontal axis with marks V_1 and 2V_1 (dotted vertical guide lines). Point A at (V_1, P_1), point B at (2V_1, P_1/2), point C at (2V_1, P_1/4). A curve from A to B with arrow pointing toward B (convex curve); a vertical straight line from B down to C with arrow pointing down; a steeper curve from C back to A with arrow pointing toward A.
  1. (1)RT(ln⁡2−12(γ−1))RT\left(\ln 2 - \frac{1}{2(\gamma - 1)}\right)Official answer
  2. (2)−RT2(γ−1)-\frac{RT}{2(\gamma - 1)}
  3. (3)RTln⁡2RT \ln 2
  4. (4)00

Official answer

Option 1

NTA final key.

Chapter
Thermodynamics
Topic
Thermodynamic Processes
Idea tested
Cyclic Process Work

Same idea in other shifts

Asked 7× in all
  1. 3 Apr 2025, Shift 2 · Q33An ideal gas exists in a state with pressure P0\mathrm{P_0}, volume V0\mathrm{V_0}. It is isothermally expanded to 4 times of its initial…MediumSingle correct
  2. 7 Apr 2025, Shift 1 · Q48An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is _______…MediumNumerical valueHas a figure
  3. 9 Apr 2024, Shift 2 · Q36A real gas within a closed chamber at 27∘C27^\circ C undergoes the cyclic process as shown in figure. The gas obeys PV3=RTPV^3=RT equation for…HardSingle correctHas a figure
  4. 15 Apr 2023, Shift 1 · Q33A thermodynamic system is taken through cyclic process. The total work done in the process is :EasyDiagram basedHas a figure
  5. 3 Aug 2021, Shift 1 · Q53An ideal monoatomic gas traverses the cycle ABCD as shown below in the figure. The work done during the cycle is xxPV. The value of xx…EasyNumerical valueHas a figure
  6. 24 Feb 2021, Shift 1 · Q9n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes. A → B : Isothermal expansion…MediumDiagram basedHas a figure

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.