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Heat and Thermodynamics question

2025 · 24 Jan · Shift 2 · Q61
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Heat and Thermodynamics question

2025 · 24 Jan · Shift 2 · Q61

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases. Reason (R) : Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statements, choose the correct answer from the options given below :
  1. A
    Both (A)(\mathbf{A})(A) and (R)(\mathbf{R})(R) are true and (R)(\mathbf{R})(R) is the correct explanation of (A)(\mathbf{A})(A)
  2. B
    Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
  3. C
    (A) is false but (R) is true
  4. D
    (A) is true but (R)(\mathbf{R})(R) is false
View written solutionFree

Correct answer: C

  1. Analyze Assertion (A)

    The gas is in an insulated container, so no heat is exchanged: Q=0Q=0Q=0 Hence the process is adiabatic.

    The gas is said to be shrunk to half of its initial volume, i.e. it is compressed.

    From the first law of thermodynamics, ΔU=Q−W\Delta U = Q - WΔU=Q−W where WWW is work done by the gas.

    In compression, work is done on the gas, so work done by the gas is negative: W<0W<0W<0 Thus, ΔU=0−W>0\Delta U = 0 - W >0ΔU=0−W>0

    For an ideal gas, internal energy depends only on temperature, so ΔU>0⇒ΔT>0\Delta U >0 \Rightarrow \Delta T>0ΔU>0⇒ΔT>0

    Therefore, during adiabatic compression, the temperature increases, not decreases.

    So Assertion (A) is false.

  2. Analyze Reason (R)

    Free expansion of an ideal gas means expansion into vacuum.

    • No external pressure opposes expansion, so no work is done: W=0W=0W=0
    • If the container is insulated, no heat exchange occurs: Q=0Q=0Q=0

    Hence free expansion is an adiabatic process.

    Also, free expansion cannot be reversed by an infinitesimal change; it is a classic irreversible process.

    Therefore, Reason (R) is true.

  3. Choose the correct option

    • Assertion (A): False
    • Reason (R): True

    Hence the correct option is: C\boxed{\text{C}}C​

  4. Comparison with stored answer

    Stored correct answer: C

    My derived answer: C

    So they agree.

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