Question

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

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

Answer 1

The correct option is D ${846}^{o}C$

$v_{rms}=\sqrt{\frac{3RT}{M}}$
Given $T={100}^{o}C=373K$
$\therefore$ $v=\sqrt{\frac{3R\times 373}{M}}$
Let the r.m.s. speed be $\sqrt{3}v$ at the temperature of $TK$

So, $\sqrt{3}v=\sqrt{\frac{3RT}{M}}$
$\therefore \frac{\sqrt{3}v}{v}=\frac{\sqrt{3RT/M}}{\sqrt{3R\times 373/M}}$
$\Rightarrow \sqrt{3}=\sqrt{\frac{T}{373}}$
$\Rightarrow 3=\frac{T}{373}$
$\Rightarrow T=1119K$
or $T={846}^{o}C$