Question

Each molecule of mass $m$ of a monoatomic gas has got three degrees of freedom. The r.m.s. velocity of these molecules is $v$ at temperature $T$. For a diatomic molecule of mass $m$ and temperature $T$ which has got five degrees of freedom, r.m.s. velocity of molecule is

• A. $\sqrt{\frac{5}{3}}v$
• B. $\sqrt{\frac{3}{5}}v$
• C. $v$
• D. None of these

Answer 1

The correct option is C $v$

We know that,
$P=\frac{1}{3}\frac{M}{V}{v}_{rms}^2$ ....(1)
(Here $M$ is the total mass of the gas)
and $PV=nRT$....(2)
From (1) and (2)
$v_{rms}^2=\frac{3nRT}{M}$
$\therefore v_{\text{rms}}$ depends on molar mass and temperature. It does not depends on degree of freedom.
$\therefore v_{\text{rms}}$ of both gas will be same as both have same molar mass and temperature.