Add Van der Waals equation of state

physics/vander_vaals_gas_law.py

@@ -0,0 +1,190 @@
+"""
+The van der Waals equation, named for its originator,
+the Dutch physicist Johannes Diderik van der Waals,
+is an equation of state that extends the ideal gas
+law to include the non-zero size
+of gas molecules and the interactions between them
+(both of which depend on the specific substance).
+
+As a result the equation is able to model the phase
+change from liquid to gas, and vice versa.
+It also produces simple analytic expressions for the
+properties of real substances that shed light on their
+behavior.
+
+( Description was taken from https://en.wikipedia.org/wiki/Van_der_Waals_equation )
+
+---------------------
+| (p+a/V^2)(V-bv)=vRT |
+---------------------
+! p - Pressure (Pa)
+! V - Volume (m^3)
+! v - Amount of gas (mol)
+! R - Universal gas constant
+! T Absolute temperature (K)
+! a, b - Parameters
+"""
+
+R = 8.314462618
+
+# Taken from https://ru.wikipedia.org/wiki/Уравнение_Ван-дер-Ваальса
+CONSTANTS = {
+    "nitrogen": {"a": 0.1370, "b": 38.7e-6},
+    "ammonia": {"a": 0.4225, "b": 37.1e-6},
+    "argon": {"a": 0.1355, "b": 32.0e-6},
+    "oxygen": {"a": 0.1382, "b": 31.9e-6},
+}
+
+
+def system_pressure(
+    quantity: float, temperature: float, volume: float, a: float, b: float
+) -> float:
+    """
+    Gets the system pressure from other 2 parameters
+    ---------------------
+    | p=(vRT)/(V-bv)-a/V^2 |
+    ---------------------
+
+    >>> system_pressure(1, 300, 1, 0.1382, 31.9e-6)
+    2494.2801573455995
+    >>> system_pressure(1, 100, 1, 0.1382, 31.9e-6)
+    831.3345857818664
+    >>> system_pressure(1, 300, -1, 0.1382, 31.9e-6)
+    Traceback (most recent call last):
+        ...
+    ValueError: Please provide the positive values
+    """
+
+    if temperature < 0 or volume < 0:
+        raise ValueError("Please provide the positive values")
+    return (quantity * R * temperature) / (volume - quantity * b) - a / (volume**2)
+
+
+def system_temperature(
+    quantity: float, pressure: float, volume: float, a: float, b: float
+) -> float:
+    """
+    Gets the system temperature from other 2 parameters
+    ---------------------
+    | T = 1/(vR)*(p+a/V^2)(V-bv) |
+    ---------------------
+
+    >>> system_temperature(1, 300, 1, 0.1382, 31.9e-6)
+    36.09717661628195
+    >>> system_temperature(1, 100, 1, 0.1382, 31.9e-6)
+    12.04347294491859
+    >>> system_temperature(1, 300, -1, 0.1382, 31.9e-6)
+    Traceback (most recent call last):
+        ...
+    ValueError: Please provide the positive values
+    """
+
+    if pressure < 0 or volume < 0:
+        raise ValueError("Please provide the positive values")
+    return 1 / (quantity * R) * (pressure + a / volume**2) * (volume - quantity * b)
+
+
+def critical_temperature(a: float, b: float) -> float:
+    """
+    Calculate the critical temperature from two parameters for each gas
+    ---------------------
+    | T_c=8a/(27bR) |
+    ---------------------
+
+    >>> critical_temperature(0.1382, 31.9e-6)
+    154.3865270378366
+    """
+
+    return 8 * a / (27 * b * R)
+
+
+def critical_volume(b: float) -> float:
+    """
+    Calculate the critical volume from one parameter for each gas
+    ---------------------
+    | V_c=3b |
+    ---------------------
+
+    >>> critical_volume(31.9e-6)
+    9.570000000000001e-05
+    """
+
+    return 3 * b
+
+
+def critical_pressure(a: float, b: float) -> float:
+    """
+    Calculate the critical pressure from two parameters for each gas
+    ---------------------
+    | p_c=a/(27b^2) |
+    ---------------------
+
+    >>> critical_pressure(0.1382, 31.9e-6)
+    5029941.253052267
+    """
+
+    return a / (27 * b**2)
+
+
+def critical_coefficient(a: float, b: float) -> float:
+    """
+    Calculate the critical coefficient from two parameters for each gas
+    ---------------------
+    | k_c=(R*T_c)/(p_c*V_c) |
+    ---------------------
+
+    >>> critical_coefficient(0.1382, 31.9e-6)
+    2.6666666666666665
+    """
+
+    return (
+        R * critical_temperature(a, b) / (critical_pressure(a, b) * critical_volume(b))
+    )
+
+
+def given_volume(volume: float, b: float) -> float:
+    """
+    Calculate the given volume from one parameter for each gas and volume
+    ---------------------
+    | φ = V / V_c |
+    ---------------------
+
+    >>> given_volume(1, 31.9e-6)
+    10449.32079414838
+    """
+
+    return volume / critical_volume(b)
+
+
+def given_pressure(pressure: float, a: float, b: float) -> float:
+    """
+    Calculate the given pressure from two parameters for each gas and pressure
+    ---------------------
+    | π = p / p_c |
+    ---------------------
+
+    >>> given_pressure(1, 0.1382, 31.9e-6)
+    1.9880947901591899e-07
+    """
+
+    return pressure / critical_pressure(a, b)
+
+
+def given_temperature(temperature: float, a: float, b: float) -> float:
+    """
+    Calculate the given temperature from two parameters for each gas and temperature
+    ---------------------
+    | τ = T / T_c |
+    ---------------------
+
+    >>> given_temperature(1, 0.1382, 31.9e-6)
+    0.006477249143346057
+    """
+
+    return temperature / critical_temperature(a, b)
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()