Two flasks A and B having capacity 1L and 2L respecitvely contain one mole of a gas each. If the temperatrue of the flasks are so adjusted that the average velocity of molecules in A is twice that of molecules in B, the pressure of A is `:`

Options

A. half that in B
B. same as that in B
C. four times that in B
D. eight times that in B.

Answer

D

Explanation

According to kinetic gas equation.
`pV = 1//3 m mu^(2)`
For gas in flask A,
`P_(A) = ( 1)/( 3). ( m_(A) mu_(A)^(2))/(V_(A))`
For gas in flask B,
`p_(A) = ( 1)/( 3) . ( m_(B) mu _(B)^(2))/( V_(B))`
For one mole of each gas `m_(A) = m_(B)`
`:. ( p_(A))/( p_(B)) = ( mu_(A^(2)))/(mu_(B^(2)) )xx( V_(B))/(V_(A))`
`= ( (2)^(2)xx2)/(1 xx (1)^(2)) = 8 ` or `p_(A) = 8 p_(B)`