# Kinetic theory of gas. Pressure in a container derivation feels wrong

NOTE: Please Imagine A cube with 2 parllel faces I and II lying along the x axis.

In the derivation what we are thought

Change in the momentum of the molecule

= Final momentum - Initial momentum

= –mu1 – mu1 = –2mu1

During each successive collision on face I the molecule must travel a distance 2l from face I to face II and back to face I.

Time taken between two successive collisions is = 2l / u1

∴ Rate of change of momentum = Change in the momentum/Time taken

= – 2mu1/(2l/u1) = -2mu1^2/2l = – mu1^2/l

(i.e) Force exerted on the molecule = – mu1^2/l

Components of Velocity

∴ According to Newton’s third law of motion, the force exerted by the molecule,

= – (– mu1^22)/l = mu1^2/l

I think this is wrong my reason:

Assuming normal force equation F=ma, F=mdv/dt => F=dP/dt

in the derivation the total time taken between 2 successive collisions is given this is not the time taken to change the velocity of the particle it changes at the instant when the molecule hits the wall of the container and change in velocity with respect to time is acceleration so i think the above derivation feels wrong to me can any one help me out here am I missing something.

I have copied the derivation from somewhere else as I have very less time due to my exam :p.

• Please do not post formulae as plain text, but use MathJax instead. Feb 9 '19 at 10:49