The molecular velocities of two gases at same temperature are `u_(1)` and `u_(2)`, their masses are `m_(1)` and `m_(2)` respectively, which of the following expression is correct ?

Options

A. `(m_(1))/(u_(1)^(2)) = (m_(2))/(u_(2)^(2))`
B. `m_(1) u_(1) = m_(2) u_(2)`
C. `(m_(1))/(u_(1)) = (m_(2))/(u_(2))`
D. `m_(1) u_(1)^(2) = m_(2) u_(2)^(2)`

Answer

D

Explanation

`C prop (T)/(sqrtM) rArr u_(1) prop (T)/(sqrt(m_(1))) and u_(2) prop (T)/(sqrt(m_(2))) rArr u_(1) sqrt(m_(1)) = u_(2) sqrt(m_(2)) rArr m_(1) u_(1)^(2) = m_(2) u_(2)^(2)`