Maxwell's Distribution
The distribution of speeds in an ideal gas is an interesting function of temperature. This is called Maxwell's distribution, or the Maxwell-Boltzmann distribution. James Clerk Maxwell showed that the probability of finding a molecule of a particular speed v is given by:
| P(v) |
= 4π |
( |
| M
|  |
| 2πRT
|
|
) |
3/2 |
v2 e-Mv2/2RT
|
M is the molar mass (mass of 1 mole) of the gas.
The distribution is characterized by three speeds. These are:
| The root-mean-square speed: vrms |
= |
( |
| 3RT
| |
| M
|
|
) |
½ |
| The average speed: vav |
= |
( |
| 8RT
| |
| πM
|
|
) |
½ |
| The most probable speed: vprob |
= |
( |
| 2RT
| |
| M
|
|
) |
½ |