Question

The rms velocity of $CO_{2}$ at a temperature T (in kelvin) is x cm$s^{- 1}$. At what temperature (in kelvin) the rms velocity of nitrous oxide would be 4x cm$s^{- 1}$

• A. 16 T
• B. 2 T
• C. 4 T
• D. 32 T

Answer 1

Answer: (A)

16 T

Answer 2

$u = \sqrt{\frac{3RT}{M}}$

∴ $\frac{u_{CO_{2}}}{u_{N_{2}O}} = \sqrt{\frac{T_{CO_{2}}}{M_{CO_{2}}} \times \frac{M_{N_{2}O}}{T_{N_{2}O}}}$

i.e., $\frac{x}{4x} = \sqrt{\frac{T}{44} \times \frac{44}{T_{N_{2}O}}}$ or $\frac{1}{4} = \sqrt{\frac{T}{T_{N_{2}O}}}$ or

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