A one litre vessel at a pressure `P_1` and a two litre vessel at pressure `P_(2)` contain one mole each of oxygen gas. If the temperature is so adjusted such that the velocities of `O_(2)` molecules in 1 lit. vessel are 4 times that of 2 lit. vessel, then at what ratio `P_(1)` and `P_(2)` will be

Options

A. `4 : 1`
B. `8 : 1`
C. `16 : 1`
D. `32: 1`

Answer

D

Explanation

`(4)/(1) = (sqrt((3RT_(1))/(mn)))/(sqrt((3RT_(2))/(mn))) therefore (T_(1))/(T_(2)) = (16)/(1) , (P_(1))/(P_(2)) = (RT_(1)//1)/(RT_(2)//2) = (32)/(1)`