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Graham's Law (#8162)
* grahams law * doctest and type hints * doctest formatting * peer review updates
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Blake Reimer
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physics/grahams_law.py
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208
physics/grahams_law.py
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"""
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Title: Graham's Law of Effusion
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Description: Graham's law of effusion states that the rate of effusion of a gas is
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inversely proportional to the square root of the molar mass of its particles:
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r1/r2 = sqrt(m2/m1)
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r1 = Rate of effusion for the first gas.
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r2 = Rate of effusion for the second gas.
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m1 = Molar mass of the first gas.
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m2 = Molar mass of the second gas.
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(Description adapted from https://en.wikipedia.org/wiki/Graham%27s_law)
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"""
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from math import pow, sqrt
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def validate(*values: float) -> bool:
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"""
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Input Parameters:
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-----------------
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effusion_rate_1: Effustion rate of first gas (m^2/s, mm^2/s, etc.)
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effusion_rate_2: Effustion rate of second gas (m^2/s, mm^2/s, etc.)
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molar_mass_1: Molar mass of the first gas (g/mol, kg/kmol, etc.)
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molar_mass_2: Molar mass of the second gas (g/mol, kg/kmol, etc.)
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Returns:
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--------
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>>> validate(2.016, 4.002)
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True
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>>> validate(-2.016, 4.002)
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False
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>>> validate()
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False
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"""
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result = len(values) > 0 and all(value > 0.0 for value in values)
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return result
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def effusion_ratio(molar_mass_1: float, molar_mass_2: float) -> float | ValueError:
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"""
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Input Parameters:
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-----------------
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molar_mass_1: Molar mass of the first gas (g/mol, kg/kmol, etc.)
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molar_mass_2: Molar mass of the second gas (g/mol, kg/kmol, etc.)
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Returns:
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--------
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>>> effusion_ratio(2.016, 4.002)
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1.408943
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>>> effusion_ratio(-2.016, 4.002)
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ValueError('Input Error: Molar mass values must greater than 0.')
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>>> effusion_ratio(2.016)
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Traceback (most recent call last):
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...
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TypeError: effusion_ratio() missing 1 required positional argument: 'molar_mass_2'
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"""
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return (
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round(sqrt(molar_mass_2 / molar_mass_1), 6)
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if validate(molar_mass_1, molar_mass_2)
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else ValueError("Input Error: Molar mass values must greater than 0.")
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)
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def first_effusion_rate(
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effusion_rate: float, molar_mass_1: float, molar_mass_2: float
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) -> float | ValueError:
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"""
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Input Parameters:
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-----------------
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effusion_rate: Effustion rate of second gas (m^2/s, mm^2/s, etc.)
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molar_mass_1: Molar mass of the first gas (g/mol, kg/kmol, etc.)
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molar_mass_2: Molar mass of the second gas (g/mol, kg/kmol, etc.)
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Returns:
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--------
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>>> first_effusion_rate(1, 2.016, 4.002)
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1.408943
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>>> first_effusion_rate(-1, 2.016, 4.002)
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ValueError('Input Error: Molar mass and effusion rate values must greater than 0.')
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>>> first_effusion_rate(1)
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Traceback (most recent call last):
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...
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TypeError: first_effusion_rate() missing 2 required positional arguments: \
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'molar_mass_1' and 'molar_mass_2'
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>>> first_effusion_rate(1, 2.016)
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Traceback (most recent call last):
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...
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TypeError: first_effusion_rate() missing 1 required positional argument: \
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'molar_mass_2'
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"""
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return (
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round(effusion_rate * sqrt(molar_mass_2 / molar_mass_1), 6)
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if validate(effusion_rate, molar_mass_1, molar_mass_2)
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else ValueError(
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"Input Error: Molar mass and effusion rate values must greater than 0."
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)
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)
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def second_effusion_rate(
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effusion_rate: float, molar_mass_1: float, molar_mass_2: float
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) -> float | ValueError:
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"""
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Input Parameters:
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-----------------
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effusion_rate: Effustion rate of second gas (m^2/s, mm^2/s, etc.)
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molar_mass_1: Molar mass of the first gas (g/mol, kg/kmol, etc.)
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molar_mass_2: Molar mass of the second gas (g/mol, kg/kmol, etc.)
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Returns:
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--------
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>>> second_effusion_rate(1, 2.016, 4.002)
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0.709752
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>>> second_effusion_rate(-1, 2.016, 4.002)
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ValueError('Input Error: Molar mass and effusion rate values must greater than 0.')
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>>> second_effusion_rate(1)
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Traceback (most recent call last):
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...
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TypeError: second_effusion_rate() missing 2 required positional arguments: \
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'molar_mass_1' and 'molar_mass_2'
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>>> second_effusion_rate(1, 2.016)
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Traceback (most recent call last):
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...
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TypeError: second_effusion_rate() missing 1 required positional argument: \
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'molar_mass_2'
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"""
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return (
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round(effusion_rate / sqrt(molar_mass_2 / molar_mass_1), 6)
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if validate(effusion_rate, molar_mass_1, molar_mass_2)
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else ValueError(
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"Input Error: Molar mass and effusion rate values must greater than 0."
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)
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)
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def first_molar_mass(
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molar_mass: float, effusion_rate_1: float, effusion_rate_2: float
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) -> float | ValueError:
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"""
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Input Parameters:
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-----------------
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molar_mass: Molar mass of the first gas (g/mol, kg/kmol, etc.)
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effusion_rate_1: Effustion rate of first gas (m^2/s, mm^2/s, etc.)
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effusion_rate_2: Effustion rate of second gas (m^2/s, mm^2/s, etc.)
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Returns:
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--------
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>>> first_molar_mass(2, 1.408943, 0.709752)
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0.507524
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>>> first_molar_mass(-1, 2.016, 4.002)
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ValueError('Input Error: Molar mass and effusion rate values must greater than 0.')
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>>> first_molar_mass(1)
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Traceback (most recent call last):
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...
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TypeError: first_molar_mass() missing 2 required positional arguments: \
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'effusion_rate_1' and 'effusion_rate_2'
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>>> first_molar_mass(1, 2.016)
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Traceback (most recent call last):
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...
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TypeError: first_molar_mass() missing 1 required positional argument: \
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'effusion_rate_2'
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"""
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return (
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round(molar_mass / pow(effusion_rate_1 / effusion_rate_2, 2), 6)
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if validate(molar_mass, effusion_rate_1, effusion_rate_2)
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else ValueError(
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"Input Error: Molar mass and effusion rate values must greater than 0."
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)
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)
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def second_molar_mass(
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molar_mass: float, effusion_rate_1: float, effusion_rate_2: float
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) -> float | ValueError:
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"""
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Input Parameters:
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-----------------
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molar_mass: Molar mass of the first gas (g/mol, kg/kmol, etc.)
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effusion_rate_1: Effustion rate of first gas (m^2/s, mm^2/s, etc.)
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effusion_rate_2: Effustion rate of second gas (m^2/s, mm^2/s, etc.)
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Returns:
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--------
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>>> second_molar_mass(2, 1.408943, 0.709752)
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1.970351
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>>> second_molar_mass(-2, 1.408943, 0.709752)
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ValueError('Input Error: Molar mass and effusion rate values must greater than 0.')
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>>> second_molar_mass(1)
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Traceback (most recent call last):
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...
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TypeError: second_molar_mass() missing 2 required positional arguments: \
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'effusion_rate_1' and 'effusion_rate_2'
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>>> second_molar_mass(1, 2.016)
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Traceback (most recent call last):
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...
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TypeError: second_molar_mass() missing 1 required positional argument: \
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'effusion_rate_2'
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"""
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return (
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round(pow(effusion_rate_1 / effusion_rate_2, 2) / molar_mass, 6)
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if validate(molar_mass, effusion_rate_1, effusion_rate_2)
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else ValueError(
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"Input Error: Molar mass and effusion rate values must greater than 0."
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)
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)
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