If the rms speeds of helium and oxygen are eq | vedclass

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(A) The $rms$ speed of a gas is given by the formula $V_{rms} = \sqrt{\frac{3RT}{M}}$.Given that the $rms$ speeds of helium $(He)$ and oxygen $(O_2)$

Vedclass · Accepted Answer

$1: 8$

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(A) The $rms$ speed of a gas is given by the formula $V_{rms} = \sqrt{\frac{3RT}{M}}$.Given that the $rms$ speeds of helium $(He)$ and oxygen $(O_2)$ are equal,we have $V_{rms, He} = V_{rms, O_2}$.Substituting the formula: $\sqrt{\frac{3RT_{He}}{M_{He}}} = \sqrt{\frac{3RT_{O_2}}{M_{O_2}}}$.Squaring both sides and canceling common terms $(3R)$: $\frac{T_{He}}{M_{He}} = \frac{T_{O_2}}{M_{O_2}}$.Rearranging for the ratio of temperatures: $\frac{T_{He}}{T_{O_2}} = \frac{M_{He}}{M_{O_2}}$.The molar mass of helium $(M_{He})$ is $4 \ g/mol$ and the molar mass of oxygen $(M_{O_2})$ is $32 \ g/mol$.Therefore,$\frac{T_{He}}{T_{O_2}} = \frac{4}{32} = \frac{1}{8}$.

If the $rms$ speeds of helium and oxygen are equal,then the ratio of the temperatures of helium and oxygen is

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