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MHT CET 2021 (24 Sep, Shift 1) · Pressure & Kinetic Energy of a Gas

Pressure & Kinetic Energy of a Gas question from MHT CET 2021 (24 Sep, Shift 1)

Q32MHT CET 2021 · 24 SEP · SHIFT 1Medium

Pressure & Kinetic Energy of a Gas

At what temperature does the average translational kinetic energy of a molecule in a gas becomes equal to kinetic energy of an electron accelerated from rest through potential difference of 'V' volt? ( $N =$ number of molecules, $R =$ gas constant, $c =$ electronic charge)

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Answer: (a)

KE of the electron $= eV$ ; average KE of a molecule $= \frac{3}{2}k_BT$ with $k_B = \frac{R}{N}$ .
$\frac{3}{2}\frac{R}{N}T = eV$
$T = \frac{2eVN}{3R}$
So the answer is (a) $\frac{2eVN}{3R}$ .

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