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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 distribution is a probability distribution that describes the distribution of
speeds of particles in an ideal gas. 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) | | f(v) = (M/2πRT)^(3/2) * 4πv^2 * e^(-Mv^2/2RT) |
------------------------------------------------- -------------------------------------------------
where: where:
f(v) is the fraction of molecules with a speed v * ``f(v)`` is the fraction of molecules with a speed ``v``
M is the molar mass of the gas in kg/mol * ``M`` is the molar mass of the gas in kg/mol
R is the gas constant * ``R`` is the gas constant
T is the absolute temperature * ``T`` is the absolute temperature
More information about the Maxwell-Boltzmann distribution can be found here: More information about the Maxwell-Boltzmann distribution can be found here:
https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution
The average speed can be calculated by integrating the Maxwell-Boltzmann 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 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 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 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 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 Here we have defined functions to calculate the average and
most probable speeds of molecules in a gas given the 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). and returns the average speed of a molecule in the gas (in m/s).
Examples: Examples:
>>> avg_speed_of_molecule(273, 0.028) # nitrogen at 273 K >>> avg_speed_of_molecule(273, 0.028) # nitrogen at 273 K
454.3488755020387 454.3488755020387
>>> avg_speed_of_molecule(300, 0.032) # oxygen at 300 K >>> 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). and returns the most probable speed of a molecule in the gas (in m/s).
Examples: Examples:
>>> mps_speed_of_molecule(273, 0.028) # nitrogen at 273 K >>> mps_speed_of_molecule(273, 0.028) # nitrogen at 273 K
402.65620701908966 402.65620701908966
>>> mps_speed_of_molecule(300, 0.032) # oxygen at 300 K >>> mps_speed_of_molecule(300, 0.032) # oxygen at 300 K