Question

At what temperature in ${}^{\circ }C$, the $U_{rms}$ of $S{O}_2$ is equal to the average velocity of $O_2$ at ${27}^{\circ }C$.

[ Give answer as $\frac{X}{59}$ is equal to]

Answer 1

Given,
$\sqrt{\frac{3RT}{64\times {10}^{-3}}}=\sqrt{\frac{8R\times 300}{\pi \times 32\times {10}^{-3}}}$

$T=\frac{8\times 300\times 64}{\pi \times 32\times {10}^{-3}}$

$T=\frac{8\times 300\times 64}{3\times 32\times \pi }=509.29K={236.29}^{\circ }C$

Answer is $236/59=4$.