physics.speeds_of_gas_molecules

The root-mean-square, average and most probable speeds of gas molecules are 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:

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

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:

vavg = √(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:

vmp = √(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:

vrms = √(3RT/M) |

Here we have defined functions to calculate the average and most probable speeds of molecules in a gas given the temperature and molar mass of the gas.

Functions

avg_speed_of_molecule(→ float)	Takes the temperature (in K) and molar mass (in kg/mol) of a gas
mps_speed_of_molecule(→ float)	Takes the temperature (in K) and molar mass (in kg/mol) of a gas

Module Contents

physics.speeds_of_gas_molecules.avg_speed_of_molecule(temperature: float, molar_mass: float) → float

Takes the temperature (in K) and molar mass (in kg/mol) of a gas 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 445.52572733919885 >>> avg_speed_of_molecule(-273, 0.028) # invalid temperature Traceback (most recent call last):

…

Exception: Absolute temperature cannot be less than 0 K >>> avg_speed_of_molecule(273, 0) # invalid molar mass Traceback (most recent call last):

…

Exception: Molar mass should be greater than 0 kg/mol

physics.speeds_of_gas_molecules.mps_speed_of_molecule(temperature: float, molar_mass: float) → float

Takes the temperature (in K) and molar mass (in kg/mol) of a gas 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 394.836895549922 >>> mps_speed_of_molecule(-273, 0.028) # invalid temperature Traceback (most recent call last):

…

Exception: Absolute temperature cannot be less than 0 K >>> mps_speed_of_molecule(273, 0) # invalid molar mass Traceback (most recent call last):

…

Exception: Molar mass should be greater than 0 kg/mol