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(D) The root mean square (r.m.s.) velocity '$v$' of a gas molecule is given by the formula: $v = \sqrt{\frac{3RT}{M}}$ where '$R$' is the universal ga

Vedclass · Accepted Answer

$\frac{v^2}{T} = 	ext{constant}$

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(D) The root mean square (r.m.s.) velocity '$v$' of a gas molecule is given by the formula: $v = \sqrt{\frac{3RT}{M}}$ where '$R$' is the universal gas constant,'$T$' is the absolute temperature, and '$M$' is the molar mass of the gas. Squaring both sides of the equation, we get: $v^2 = \frac{3RT}{M}$ Since '$3$','$R$',and '$M$' are constants for a given gas, we can write: $v^2 \propto T$ This implies that: $\frac{v^2}{T} = 	ext{constant}$ Therefore, the correct relation is $\frac{v^2}{T} = 	ext{constant}$.

When the r.m.s. velocity of a gas is denoted by '$v$' at temperature '$T$',which of the following relations is true?

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