Root mean-square speed (rms) of oxygen molecules (O₂) at a certain absolute temperature is u

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12.Kinetic Theory of Gases

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The root mean-square speed $(rms)$ of oxygen molecules $(O_2)$ at a certain absolute temperature is $\upsilon $ . If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the $rms$ speed would be

A

$\upsilon $

B

$\sqrt 2\upsilon $

C

$2\upsilon $

D

$2\sqrt 2\upsilon $

Solution

The rms speed is given by

$v_{r m s}=\sqrt{\frac{3 R T}{M}}$

$\left(v_{r m s}\right)_{O_{2}}=\sqrt{\frac{3 R T}{M}}=\sqrt{\frac{3 R T}{M}}=v$

$\left(v_{r m s}\right)_{O}=\sqrt{\frac{3 R(2 T)}{M / 2}}=2 \sqrt{\frac{3 R T}{M}}=2 v$

Standard 11

Physics

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