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Fix sphinx/build_docs warnings for physics/speeds_of_gas_molecules (#12471)

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physics/speeds_of_gas_molecules.py
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@ -4,43 +4,43 @@ derived from the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann
distribution is a probability distribution that describes the distribution of
speeds of particles in an ideal gas.
The distribution is given by the following equation:
The distribution is given by the following equation::
-------------------------------------------------
| f(v) = (M/2πRT)^(3/2) * 4πv^2 * e^(-Mv^2/2RT) |
-------------------------------------------------
where:
f(v) is the fraction of molecules with a speed v
M is the molar mass of the gas in kg/mol
R is the gas constant
T is the absolute temperature
* ``f(v)`` is the fraction of molecules with a speed ``v``
* ``M`` is the molar mass of the gas in kg/mol
* ``R`` is the gas constant
* ``T`` is the absolute temperature
More information about the Maxwell-Boltzmann distribution can be found here:
https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution
The average speed can be calculated by integrating the Maxwell-Boltzmann distribution
from 0 to infinity and dividing by the total number of molecules. The result is:
from 0 to infinity and dividing by the total number of molecules. The result is::
---------------------
| vavg = √(8RT/πM) |
---------------------
----------------------
| v_avg = √(8RT/πM) |
----------------------
The most probable speed is the speed at which the Maxwell-Boltzmann distribution
is at its maximum. This can be found by differentiating the Maxwell-Boltzmann
distribution with respect to v and setting the result equal to zero. The result is:
distribution with respect to ``v`` and setting the result equal to zero. The result is::
---------------------
| vmp = √(2RT/M) |
---------------------
----------------------
| v_mp = √(2RT/M) |
----------------------
The root-mean-square speed is another measure of the average speed
of the molecules in a gas. It is calculated by taking the square root
of the average of the squares of the speeds of the molecules. The result is:
of the average of the squares of the speeds of the molecules. The result is::
---------------------
| vrms = √(3RT/M) |
---------------------
----------------------
| v_rms = √(3RT/M) |
----------------------
Here we have defined functions to calculate the average and
most probable speeds of molecules in a gas given the
@ -57,6 +57,7 @@ def avg_speed_of_molecule(temperature: float, molar_mass: float) -> float:
and returns the average speed of a molecule in the gas (in m/s).
Examples:
>>> avg_speed_of_molecule(273, 0.028) # nitrogen at 273 K
454.3488755020387
>>> avg_speed_of_molecule(300, 0.032) # oxygen at 300 K
@ -84,6 +85,7 @@ def mps_speed_of_molecule(temperature: float, molar_mass: float) -> float:
and returns the most probable speed of a molecule in the gas (in m/s).
Examples:
>>> mps_speed_of_molecule(273, 0.028) # nitrogen at 273 K
402.65620701908966
>>> mps_speed_of_molecule(300, 0.032) # oxygen at 300 K