To find, At what temperature root mean square velocity of gaseaus hydrogen is equal to that of oxygen molecule at \(47^{\circ} C\)
we know, Root mean square velocity
\(V=\sqrt{\frac{3 R T}{m}}\)
So, Let at temperature T, RMS velocity of hydrogen is equal to oxygen at \(47^{\circ} C\).
\(\therefore \sqrt{\frac{3 R T}{2}}=\sqrt{\frac{3 R \times(273+47)}{32}}\)
\(\Rightarrow T=20 \; K\)
($N _{2}$ વાયુનું મોલર દળ $28\, g$)