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The r.m.s velocity of CO₂ at temperature T (in kelvin) is ${xCms}^{- 1}$ At what temperature (in kelvin) the r.m.s. velocity of nitrous oxide would be 4x cms-¹ ?

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16 T

2 T

4 T

32 T

answer is A.

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Detailed Solution

$\frac{U_{{CO}_{2}}}{U_{N_{2} O}} = \sqrt{\frac{T_{{CO}_{2}} \times M_{N_{2} O}}{M_{{CO}_{2}} \times T_{N_{2} O}}}$

$\Rightarrow \frac{x}{4 x} = \sqrt{\frac{T_{{C O}_{2}}}{44} \times \frac{44}{T_{N_{2} O}}} \Rightarrow T_{N_{2} O} = 16 T_{{C O}_{2}}$

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