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Heat and Thermodynamics question

2023 · 10 Apr · Shift 2 · Q46
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Heat and Thermodynamics question

2023 · 10 Apr · Shift 2 · Q46

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
A gas is compressed adiabatically, which one of the following statement is NOT true.
  1. A
    There is no heat supplied to the system
  2. B
    The temperature of the gas increases.
  3. C
    There is no change in the internal energy
  4. D
    The change in the internal energy is equal to the work done on the gas.
View written solutionFree

Correct answer: C

  1. Use the first law of thermodynamics

    The first law is ΔQ=ΔU+ΔW\Delta Q = \Delta U + \Delta WΔQ=ΔU+ΔW where:

    • ΔQ\Delta QΔQ = heat supplied to the system,
    • ΔU\Delta UΔU = change in internal energy,
    • ΔW\Delta WΔW = work done by the system.

  2. For an adiabatic process

    In adiabatic compression, ΔQ=0\Delta Q = 0ΔQ=0 So, 0=ΔU+ΔW0 = \Delta U + \Delta W0=ΔU+ΔW ΔU=−ΔW\Delta U = -\Delta WΔU=−ΔW

    During compression, work is done on the gas, so work done by the gas is negative. Hence ΔU\Delta UΔU becomes positive.

    Therefore, the internal energy increases.

  3. Check each option

    A: There is no heat supplied to the system
    True, because adiabatic means ΔQ=0\Delta Q = 0ΔQ=0

    B: The temperature of the gas increases.
    True, because in compression the internal energy increases, and for a gas internal energy depends on temperature. So temperature rises.

    C: There is no change in the internal energy
    False, because in adiabatic compression, ΔU>0\Delta U > 0ΔU>0 So internal energy does change.

    D: The change in the internal energy is equal to the work done on the gas.
    True. Since no heat is exchanged, all the work done on the gas increases its internal energy: ΔU=Won\Delta U = W_{\text{on}}ΔU=Won​

  4. Conclusion

    The statement which is NOT true is: C\boxed{\text{C}}C​

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