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  4. At what temperature, pressure remaining constant, will the r.m.s. velocity of a gas be half of its value at 0°C?

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Q. At what temperature, pressure remaining constant, will the r.m.s. velocity of a gas be half of its value at $0^{\circ}C$?

Kinetic Theory

Solution:

$\nu_{rms } \propto \sqrt{T} $
At $0^{\circ}C , \nu_{rms} \propto\sqrt{273}$
At temp. $ T, \frac{\nu_{rms }}{2} \propto \sqrt{T} $
$\therefore \frac{1}{2} = \frac{\sqrt{T}}{\sqrt{273}} $ or $ T = \frac{273}{4} = 68.2 K \approx 69 K$
$ T = 69 - 273 = - 204^{\circ} C$