Question

If the mass of all molecules of a gas is halved and their speeds doubled, then the ratio of initial and final pressures is ________. 

Options

• 2 : 1

• 1 : 2

• 4 : 1

• 1 : 4

Answer 1

If the mass of all molecules of a gas is halved and their speeds doubled, then the ratio of initial and final pressures is 1 : 2.

Explanation:

P = `1/3 "Nm"/"V" "c"^2`

∴ P ∝ mc²

∴ `"P"/"P'" = ("mc"^2)/("m'" ("c'")^2)`

= `("mc"^2)/(("m"/2) (2"c")^2)`

= `1/2`