Physics - Heat & Thermo Question with Solution | TestHub

At $200 \mathrm{K}$, the rms speed is given by

$v_0=\sqrt{\frac{3R\times 200}{M}} ...\left(1\right)$

At $800 \mathrm{K}$, the rms speed is given by

$v\text{'}=\sqrt{\frac{3R\times 800}{M}} ...\left(2\right)$

Divide equation (2) by equation (1) and solve to calculate the required speed.

$\begin{array}{rcl}\frac{v\text{'}}{v_0}& =& \frac{\sqrt{\frac{3R\times 800}{M}}}{\sqrt{\frac{3R\times 200}{M}}}\\ & =& \sqrt{\frac{800}{200}}\\ & =& 2\\ & \Rightarrow & v\text{'}=2v_0\end{array}$