Question

The temperature at which the $RMS$ velocity of $C{O}_2$ is equal to the RMS velocity of $N_{2}O$ at ${27}^{o}C$ is:

• A. $0^{o}C$
• B. ${27}^{o}C$
• C. ${273}^{o}C$
• D. $-{273}^{o}C$

Answer 1

The correct option is B ${27}^{o}C$

At the same temperature, the molecules having the same molecular weight will have the same RMS velocity.

Here both $C{O}_2,N_{2}O$ have same molecular weight 44.

$r_1=r_2$

$\frac{r_1}{r_2}=\sqrt{\frac{T_1}{T_2}}$

$\Rightarrow T_1=T_2={27}^{0}C$

Hence option B is correct.