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MHT CET 2026 (19 Apr, Shift 2) · Thermodynamic Processes

Thermodynamic Processes question from MHT CET 2026 (19 Apr, Shift 2)

Q31MHT CET 2026 · 19 APR · SHIFT 2Medium

Thermodynamic Processes

An ideal gas (γ=1.5\gamma = 1.5) is expanded adiabatically. To reduce the root mean square velocity of molecules two times, the gas should be expanded

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Answer: (b)

  1. vrms∝Tv_{rms} \propto \sqrt{T}: halving it needs T2=T14T_2 = \frac{T_1}{4}.
  2. Adiabatic: TVγ−1=TV1/2=TV^{\gamma - 1} = TV^{1/2} = constant, so (V2V1)1/2=T1T2=4\left(\frac{V_2}{V_1}\right)^{1/2} = \frac{T_1}{T_2} = 4.
  3. V2V1=16\frac{V_2}{V_1} = 16
  4. So the answer is (b) 16 times.
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