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MHT CET 2026 (15 Apr, Shift 2) · Thermodynamic Processes

Thermodynamic Processes question from MHT CET 2026 (15 Apr, Shift 2)

Q34MHT CET 2026 · 15 APR · SHIFT 2Medium

Thermodynamic Processes

An ideal gas is expanded adiabatically. How many times has the gas to be expanded to reduce the r.m.s. speed of molecules 3 times? ( $\gamma = 1.5$ )

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Answer: (d)

$v_{rms} \propto \sqrt{T}$ : reducing it 3 times needs $T_2 = \frac{T_1}{9}$ .
Adiabatic: $TV^{1/2} =$ constant, so $\left(\frac{V_2}{V_1}\right)^{1/2} = 9$ .
$\frac{V_2}{V_1} = 81$
So the answer is (d) 81 times.

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