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"""

The root-mean-square speed is essential in measuring the average speed of particles

contained in a gas, defined as,

-----------------

| Vrms = √3RT/M |

-----------------

In Kinetic Molecular Theory, gasified particles are in a condition of constant random

motion; each particle moves at a completely different pace, perpetually clashing and

changing directions consistently velocity is used to describe the movement of gas

particles, thereby taking into account both speed and direction. Although the velocity

of gaseous particles is constantly changing, the distribution of velocities does not

change.

We cannot gauge the velocity of every individual particle, thus we frequently reason

in terms of the particles average behavior. Particles moving in opposite directions

have velocities of opposite signs. Since gas particles are in random motion, it's

plausible that there'll be about as several moving in one direction as within the other

way, which means that the average velocity for a collection of gas particles equals

zero; as this value is unhelpful, the average of velocities can be determined using an

alternative method.

"""

UNIVERSAL_GAS_CONSTANT = 8.3144598

def rms_speed_of_molecule(temperature: float, molar_mass: float) -> float:

"""

>>> rms_speed_of_molecule(100, 2)

35.315279554323226

>>> rms_speed_of_molecule(273, 12)

23.821458421977443

"""

if temperature < 0:

raise Exception("Temperature cannot be less than 0 K")

if molar_mass <= 0:

raise Exception("Molar mass cannot be less than or equal to 0 kg/mol")

else:

return (3 * UNIVERSAL_GAS_CONSTANT * temperature / molar_mass) ** 0.5

if __name__ == "__main__":

import doctest

# run doctest

doctest.testmod()

# example

temperature = 300

molar_mass = 28

vrms = rms_speed_of_molecule(temperature, molar_mass)

print(f"Vrms of Nitrogen gas at 300 K is {vrms} m/s")

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