Question

The r.m.s. speed of the molecules of a gas at $100^{\circ}\,C$ is $ν$. The temperature at which the r.m.s. speed will be $\sqrt{3}v$ is

• A. 546$^{\circ}$C
• B. 646$^{\circ}$C
• C. 746$^{\circ}$C
• D. 846$^{\circ}$C

Answer 1

Answer: (D)

$v_{ ms }=\sqrt{\frac{3 R T}{M}}$
Given, $T=100^{\circ} C =373\, K$
$\therefore v=\sqrt{\frac{3 \,R \times 373}{M}}$
For $\sqrt{3} v=\sqrt{\frac{3\, R T}{M}}$
$\therefore \frac{\sqrt{3} V }{ V }=\frac{\sqrt{3 R T / M}}{\sqrt{3\, R \times 373 / M}}$
$\Rightarrow \sqrt{3}=\sqrt{\frac{T}{373}}$
$\Rightarrow 3=\frac{T}{373}$
$\Rightarrow T=1119 \,K$
or $T=846^{\circ} C$