Question

If pressure of a fixed quantity of a gas increased $4$ times keeping the temperature constant, the $r.m.s$ velocity will be

• A. $4times$
• B. $2times$
• C. Same
• D. $\frac{1}{2}times$

Answer 1

The correct option is B $2times$

$C_{rms}=\sqrt{\frac{3p}{d}}$

If pressure increased $4$ times

$C_{rms}=\sqrt{\frac{3\times 4p}{d}}=\sqrt{\frac{3\times 2^2\times p}{d}}=2\sqrt{\frac{3p}{d}}$

Therefore, If pressure increased $4$ times $r.m.s$ velocity

will increase $2$ times.