Probability of finding ideal gas molecules in volume

For ideal gas molecules, we can calculate the probability of N molecules occupying a certain region in space, say, a container with gas particles.

Conditions:

1. The gas is ideal.

2. \(V \le V_0\)

3. There are no external fields acting on the particles.

Links:

1. Formula 80.1 on p. 292 of “General Course of Physics” (Obschiy kurs fiziki), vol. 1 by Sivukhin D.V. (1979).

probability

probability of finding particle_count gas particles in partial_volume.

Symbol:

P

Latex:

\(P\)

Dimension:

dimensionless

total_volume

Total volume of the region.

Symbol:

V_0

Latex:

\(V_{0}\)

Dimension:

volume

partial_volume

volume of part of the container where we are looking for the particles.

Symbol:

V

Latex:

\(V\)

Dimension:

volume

particle_count

particle_count in partial_volume.

Symbol:

N

Latex:

\(N\)

Dimension:

dimensionless

law

P = (V / V_0)^N

Latex:

\[P = \left(\frac{V}{V_{0}}\right)^{N}\]