From ce036db2131626b86b94ab87854c82a9bc6c3d0e Mon Sep 17 00:00:00 2001 From: Maxim Smolskiy Date: Sun, 29 Dec 2024 23:01:15 +0300 Subject: [PATCH] Fix sphinx/build_docs warnings for physics/speeds_of_gas_molecules (#12471) * Fix sphinx/build_docs warnings for physics/speeds_of_gas_molecules * Fix * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fix * Fix review issue * Fix * Fix * Fix --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> --- physics/speeds_of_gas_molecules.py | 36 ++++++++++++++++-------------- 1 file changed, 19 insertions(+), 17 deletions(-) diff --git a/physics/speeds_of_gas_molecules.py b/physics/speeds_of_gas_molecules.py index a50d1c0f6..42f90a9fd 100644 --- a/physics/speeds_of_gas_molecules.py +++ b/physics/speeds_of_gas_molecules.py @@ -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