Question

The rms velocities of $C{O}_2$ at a temperature $T$ (in Kelvin) is $xcm/sec$. At what temperature (in Kelvin) the rms velocity of nitrous oxide would be $4xcm/sec$ :

• A. $16T$
• B. $2T$
• C. $4T$
• D. $32T$

Answer 1

Answer: (A)

$16T$

The molar masses of carbon dioxide and nitrous oxide are the same.

Hence, there rms velocities will be directly proportional to the square root of temperature.

$\frac{rm{s}_{N_{2}O}}{rm{s}_{C{O}_2}}=\sqrt{\frac{T_{N_{2}O}}{T_{C{O}_2}}}$

$\frac{4x}{x}=\sqrt{\frac{T_{N_{2}O}}{T}}$

$T_{N_{2}O}=16T$

So, the correct option is $A$