Average speed in Maxwell—Boltzmann statistics

The average, or mean, speed is the expected value of the speed distribution of gas particles.

Notation:

1. \(k_\text{B}\) (k_B) is boltzmann_constant.

Conditions:

1. The gas is in thermal equilibrium with the environment.

2. The gas particles are distributed according to Maxwell—Boltzmann statistics.

Links:

1. Wikipedia.

average_speed

Average molecular speed.

Symbol:

avg(v)

Latex:

\(\langle v \rangle\)

Dimension:

velocity

equilibrium_temperature

Equilibrium temperature of the gas.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

molecular_mass

mass of a gas molecule.

Symbol:

m

Latex:

\(m\)

Dimension:

mass

law

avg(v) = sqrt(8 * k_B * T / (pi * m))

Latex:

\[\langle v \rangle = \sqrt{\frac{8 k_\text{B} T}{\pi m}}\]