Question

Give a simple explanation why the pressure changes by this factor.Word Bank:1. two2.greater3.smaller4.four5.eightDoubling the speed of the molecules means that they will hit the walls of the container___times as often.
Further, since the molecules bounce off the walls at twice the speed, their momentum change is___times as great.
This means that the average force imparted to the wall on each collision is___times .
Taken together, these two factors will lead to a factor of____in increase of the pressure.

Answer 1

Answer

speed of the molecules

s₁ = v t

when velocity is doubled

s₂ = (2 v)t

   = 2 s₁

they will hit the wall of container two times as often.

the momentum of molecule

p₁ = mvr

p₂ = m(2v)r = 2(mvr)

    = 2 p₁

the momentum change is two times as great.

force is change in momentum

Δp = F(Δt)

mv-(-mv) = 2 mv

$F = \dfrac{2 mv}{\Delta t}$

F α v

therefore average force impart to the wall on each collision is two times

$p = \dfrac{F_{total}}{A}$

$p = \dfrac{Nmv^2}{3LA}$

p α v²

here the velocity is doubled it means pressure becomes four times.