Question

The root mean square speed of $8g$ of $He$ is $300{\text{ms}}^{-1}$. Total kinetic energy of $He$ gas is:

• A. $120J$
• B. $240J$
• C. $360J$
• D. None of these

Answer 1

The correct option is C $360J$

We know,
$\text{root mean square velocity}=\sqrt{\frac{3RT}{M}}$
Where,
$M=\text{molar mass in kg}$
$T=\text{temperature}$
$R=\text{gas constant}$

$\therefore 300=\sqrt{\frac{3RT}{4\times {10}^{-3}}}$
$\Rightarrow RT=120$
Again, we know, total K.E. of $He$ gas =$\frac{3}{2}nRT$
Here number of moles of $He$ = $\frac{8}{4}$
$\therefore \text{K.E of He gas}=\frac{3}{2}\times \frac{8}{4}\times 120J$
$=360J$