Two flasks `X` and `Y` have capacity `1` L and `2` L respectively and each of them contains `1` mole of a gas. The temperature of the flasks are so adjusted that average speed of molecules in `X` is twice as those in `Y`. The pressure in flask `X` would be

Options

A. same as that in `Y`
B. half of that in `Y`
C. twice of that in `Y`
D. 8 times of that in `Y`

Answer

D

Explanation

According to kinetic gas equation
`PV = (1)/(3) mN u^(2)`
`PV prop u^(2)` for a particular gas
In flask `X : P_(x) (1) prop u_(x)^(2)`
In flask `Y : P_(y) (2) prop u_(y)^(2)`
Now `u_(x) = 2u_(y)`
`:. (P_(x))/(2P_(y)) = (u_(x)^(2))/(u_(y)^(2)) = (4u_(y)^(2))/(u_(y)^(2)) " or " P_(x) = 8P_(y)`