## Kinetic Theory of Gases

Pressure is caused by the constant bombardment of the many individual molecules of a gas.

The ideal gas law can be explained by the constant bombardment of the many individual molecules of a gas.

Pressure is caused by the collisions of gas molecules with the walls of the container holding the gas.

Assume one-third of the molecules move along the x-axis at constant speed v.

This is the average force exerted by

eachsingle molecule. But we have N/3 molecules hitting this wall. Therefore, thetotalforce on the wall isNow, to get the

pressure. Remember, in our simplified model, we are looking at acubewith edge length L,P V = (

^{1}/_{3}) N m v^{2}The

kinetic energyof each molecule is KE = (^{1}/_{2}) m v^{2}so we can rewrite this asP V = ( ^{2}/_{3}) N (^{1}/_{2}) m v^{2}We already know that

P V = N k T so this means

( ^{2}/_{3}) N (^{1}/_{2}) m v^{2 }= N k Tor

( ^{1}/_{2}) m v^{2 }= (^{3}/_{2}) k TLet us replace our

constantspeed v with anaveragespeed <v>,( ^{1}/_{2}) m <v>^{2 }= (^{3}/_{2}) k T(

^{1}/_{2}) m <v>^{2 }= E_{int}E

_{int, tot}= N (^{3}/_{2}) k TE

_{int, tot}= (^{3}/_{2}) N k T = (^{3}/_{2}) n R T(c) 2005, Doug Davis; all rights reserved

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