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Thermodynamics question

2024 · 30 Jan · Shift 1 · Q27
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Thermodynamics question

2024 · 30 Jan · Shift 1 · Q27

JEE MainChemistryThermodynamicsNumerical+4 / −1
JEE Main 2024 (Online) 30th January Morning Shift Chemistry - Thermodynamics Question 44 English An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path A→B→C→A\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C} \rightarrow \mathrm{A}A→B→C→A as shown in the diagram above. The total work done in the process is ‾\underline{\hspace{2cm}}​ J.
Numerical answer
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Correct answer: 200

  1. Work done in a cyclic process

    For a cyclic transformation on a PPP–VVV diagram, the net work done is equal to the area enclosed by the cycle.

  2. Shape of the path A→B→C→AA \to B \to C \to AA→B→C→A

    From the diagram, the cycle forms a triangle in the PPP–VVV plane.

    Hence, W=Area of triangle=12×(ΔV)×(ΔP)W = \text{Area of triangle} = \frac{1}{2} \times (\Delta V) \times (\Delta P)W=Area of triangle=21​×(ΔV)×(ΔP)

  3. Reading values from the graph

    From the given figure:

    • Change in volume, ΔV=2 m3\Delta V = 2\,\text{m}^3ΔV=2m3
    • Change in pressure, ΔP=200 Pa\Delta P = 200\,\text{Pa}ΔP=200Pa
  4. Calculate the enclosed area

    W=12×2×200=200 JW = \frac{1}{2} \times 2 \times 200 = 200\,\text{J}W=21​×2×200=200J

  5. Direction of the cycle

    Since the path A→B→C→AA \to B \to C \to AA→B→C→A is clockwise, the work done by the gas is positive.

Therefore, the total work done in the cyclic process is 200 J\boxed{200\,\text{J}}200J​

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