Derivation of the kinetic theory of gases equation
- The equation for the kinetic theory of ideal gases contains the mean square speed of the particles:
- Where
- c = average speed of the gas particles
- <c2> has the units m2 s-2
- Since particles travel in all directions in 3D space and velocity is a vector, some particles will have a negative direction and others a positive direction
- When there are a large number of particles, the total positive and negative velocity values will cancel out, giving a net zero value overall
- To calculate the average speed of the particles in a gas, take the square root of the mean square speed:
- cr.m.s is known as the root-mean-square speed and still has the units of m s-1
- The mean square speed is not the same as the mean speed