Question

If the rms velocity of a gas is $v$, then

• A. $v^{2}T=\text{constant}$
• B. $\frac{v^2}{T}=\text{constant}$
• C. $v{T}^2=\text{constant}$
• D. $v$ is independent of $T$

Answer 1

The correct option is B $\frac{v^2}{T}=\text{constant}$

RMS velocity is given by:
$v=\sqrt{\frac{3RT}{M}}{v}^2=\frac{3RT}{M}$
For a gas, $R$ and $M$ are constants
$\therefore \frac{v^2}{T}=\text{constant}$
Hence, the correct answer is option (b).