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Heat and Thermodynamics question

2023 · 25 Jan · Shift 2 · Q50
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Heat and Thermodynamics question

2023 · 25 Jan · Shift 2 · Q50

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1

Match List I with List II

List I List II
A. Isothermal Process I. Work done by the gas decreases internal energy
B. Adiabatic Process II. No change in internal energy
C. Isochoric Process III. The heat absorbed goes partly to increase internal energy and partly to do work
D. Isobaric Process IV. No work is done on or by the gas

Choose the correct answer from the options given below :

  1. A
    A-I, B-II, C-IV, D-III
  2. B
    A-II, B-I, C-III, D-IV
  3. C
    A-II, B-I, C-IV, D-III
  4. D
    A-I, B-II, C-III, D-IV
View written solutionFree

Correct answer: C

  1. Use the first law of thermodynamics

    ΔU=Q−W\Delta U = Q - WΔU=Q−W

    where:

    • ΔU\Delta UΔU = change in internal energy
    • QQQ = heat supplied to the gas
    • WWW = work done by the gas

  2. Match each process

    A. Isothermal process

    In an isothermal process, temperature remains constant.

    For an ideal gas, internal energy depends only on temperature, so ΔU=0\Delta U = 0ΔU=0

    Hence, this matches: II. No change in internal energy

    So, A→IIA \to IIA→II

    B. Adiabatic process

    In an adiabatic process, Q=0Q=0Q=0

    Therefore, ΔU=−W\Delta U = -WΔU=−W

    So if the gas does work, its internal energy decreases.

    Hence, this matches: I. Work done by the gas decreases internal energy

    So, B→IB \to IB→I

    C. Isochoric process

    In an isochoric process, volume remains constant, so W=PΔV=0W = P\Delta V = 0W=PΔV=0

    Hence, IV. No work is done on or by the gas

    So, C→IVC \to IVC→IV

    D. Isobaric process

    In an isobaric process, pressure remains constant.

    Heat supplied is used partly to increase internal energy and partly to do work: Q=ΔU+WQ = \Delta U + WQ=ΔU+W

    Hence, this matches: III. The heat absorbed goes partly to increase internal energy and partly to do work

    So, D→IIID \to IIID→III

  3. Final matching

    A\!-II,\; B\!-I,\; C\!-IV,\; D\!-III

  4. Compare with options

    This corresponds to Option C.

  5. Comparison with stored answer

    Stored correct answer = C

    Our derived answer = C

    So they agree.

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