Question

At what temperature the RMS velocity of oxygen will be same as that of methane at ${27}^{o}C$?

• A. ${54}^{o}C$
• B. $327K$
• C. $600K$
• D. $573K$

Answer 1

Answer: (C)

$600K$

At a temperature of $600K$, the RMS velocity of oxygen will be the same as that of methane at ${27}^{o}C$.

The root mean square velocity $u=\sqrt{\frac{3RT}{M}}$
$\frac{u_o}{u_m}=\sqrt{\frac{T_o\times M_m}{T_m\times M_o}}$

The subscripts o and m refers to oxygen and methane respectively.

But $u_o=u_m$

Hence, $\frac{u_o}{u_m}=1$

$T_m=27{}^{o}C=(273+27)K$

$1=\sqrt{\frac{T_o\times 16}{(273+27)\times 32}}$

Square both sides of the equation

$1=\frac{T_o\times 16}{300\times 32}$

$T_o=600K$

Hence, the correct option is $\text{C}$