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52 lines
1.9 KiB
Python
52 lines
1.9 KiB
Python
"""
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The root-mean-square speed is essential in measuring the average speed of particles
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contained in a gas, defined as,
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-----------------
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| Vrms = √3RT/M |
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-----------------
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In Kinetic Molecular Theory, gasified particles are in a condition of constant random
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motion; each particle moves at a completely different pace, perpetually clashing and
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changing directions consistently velocity is used to describe the movement of gas
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particles, thereby taking into account both speed and direction. Although the velocity
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of gaseous particles is constantly changing, the distribution of velocities does not
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change.
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We cannot gauge the velocity of every individual particle, thus we frequently reason
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in terms of the particles average behavior. Particles moving in opposite directions
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have velocities of opposite signs. Since gas particles are in random motion, it's
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plausible that there'll be about as several moving in one direction as within the other
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way, which means that the average velocity for a collection of gas particles equals
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zero; as this value is unhelpful, the average of velocities can be determined using an
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alternative method.
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"""
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UNIVERSAL_GAS_CONSTANT = 8.3144598
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def rms_speed_of_molecule(temperature: float, molar_mass: float) -> float:
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"""
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>>> rms_speed_of_molecule(100, 2)
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35.315279554323226
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>>> rms_speed_of_molecule(273, 12)
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23.821458421977443
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"""
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if temperature < 0:
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raise Exception("Temperature cannot be less than 0 K")
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if molar_mass <= 0:
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raise Exception("Molar mass cannot be less than or equal to 0 kg/mol")
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else:
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return (3 * UNIVERSAL_GAS_CONSTANT * temperature / molar_mass) ** 0.5
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if __name__ == "__main__":
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import doctest
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# run doctest
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doctest.testmod()
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# example
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temperature = 300
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molar_mass = 28
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vrms = rms_speed_of_molecule(temperature, molar_mass)
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print(f"Vrms of Nitrogen gas at 300 K is {vrms} m/s")
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