# Derivation for Kinetic Theory of Gases

by platina
Tags: derivation, gases, kinetic, theory
 Mentor P: 41,303 Derivation for Kinetic Theory of Gases Now that I've read the rest of your quoted proof more carefully, I'd say that assuming 1/3 of particles hit during that time is a bit lame. I prefer thinking in terms of one dimension at a time, thus considering the x-component of the velocity ($v_x$) for calculating the change in momentum and the travel time for all particles along the x-axis. Thus your force term will equal $m v_x^2/L$. Since, by symmetry, there's nothing special about the x-direction, you can write the average force in terms of the average value of $(1/3) m v^2/L$. (The average values of $v_x^2$, $v_y^2$, and $v_z^2$ are all equal and add up to $v^2$.) This gets you to the same place, with a bit less handwaving.
 Mentor P: 41,303 Imagine a cube aligned with the axes. Every particle has some component of velocity along the x-axis, $v_x$. Thus its travel time (between the walls perpendicular to the x-axis) must be $2L/v_x$. (The actual value will be different for each particle--that's why we end up taking the average value.)