Merge branch 'master' into condition-dielectric-equation-of-state

symplyphysics/laws/thermodynamics/dielectrics/__init__.py

@@ -0,0 +1,6 @@
+"""
+**Dielectric Thermodynamics**
+=============================
+
+This module describes the laws concerning the thermodynamics of dielectric media.
+"""

symplyphysics/laws/thermodynamics/dielectrics/internal_energy_change_via_heat_and_electric_displacement_change.py

@@ -0,0 +1,88 @@
+"""
+Internal energy change via heat and electric displacement change
+================================================================
+
+Internal energy change of the system with a dielectric medium can be
+expressed using the infinitesimal heat flowing in or out of the system
+and the change in electric displacement.
+
+**Conditions:**
+
+#. The dielectric is isotropic whether or not the electric field is present.
+#. The medium is homogeneous.
+#. The volume change of the medium is insignificant.
+
+**Links:**
+
+#. Formula 31.2 on p. 122 of "General Course of Physics" (Obschiy kurs fiziki), vol. 3 by Sivukhin D.V. (1979).
+"""
+
+from sympy import Eq
+from symplyphysics import (
+    symbols,
+    units,
+    Quantity,
+    SymbolNew,
+    clone_as_symbol,
+    validate_input,
+    validate_output,
+)
+
+internal_energy_density_change = SymbolNew("dU", units.energy / units.volume)
+"""
+Infinitesimal change in :symbols:`internal_energy` per unit :symbols:`volume`.
+"""
+
+heat_density = SymbolNew("delta(Q)", units.energy / units.volume, display_latex="\\delta Q")
+"""
+Small amount of :symbols:`heat` added to or taken from the system per unit :symbols:`volume`.
+"""
+
+electric_field_strength = symbols.electric_field_strength
+"""
+:symbols:`electric_field_strength` in the medium.
+"""
+
+electric_displacement_change = clone_as_symbol(
+    symbols.electric_displacement,
+    display_symbol="dD",
+    display_latex="dD",
+)
+"""
+Infinitesimal change in :symbols:`electric_displacement`.
+"""
+
+law = Eq(
+    internal_energy_density_change,
+    heat_density + electric_field_strength * electric_displacement_change
+)
+"""
+:laws:symbol::
+
+:laws:latex::
+"""
+
+# Derivation
+# 1. First law of thermodynamics: `delta(Q) = dU + delta(A)`
+# 2. Work done by the dielectric is composed of two parts: `delta(A) = p*dV - V*dot(E, dD)`
+#    We omit the former term and focus on the latter one (TODO add this law).
+# 3. Divide both parts of the (1) by `V`.
+
+
+@validate_input(
+    heat_density_=heat_density,
+    electric_field_strength_=electric_field_strength,
+    electric_displacement_change_=electric_displacement_change,
+)
+@validate_output(internal_energy_density_change)
+def calculate_internal_energy_density_change(
+    heat_density_: Quantity,
+    electric_field_strength_: Quantity,
+    electric_displacement_change_: Quantity,
+) -> Quantity:
+    result = law.rhs.subs({
+        heat_density: heat_density_,
+        electric_field_strength: electric_field_strength_,
+        electric_displacement_change: electric_displacement_change_,
+    })
+    return Quantity(result)

symplyphysics/symbols/__init__.py

@@ -140,6 +140,7 @@
     "emissivity",
     "magnetic_moment",
     "absolute_permeability",
+    "electric_displacement",
     # optics
     "relative_refractive_index",
     "radiant_exitance",

symplyphysics/symbols/electrodynamics.py

@@ -176,5 +176,16 @@
 
 **Links:**
 
-#. `Magnetic moment <https://en.wikipedia.org/wiki/Magnetic_moment>`__.
+#. `Wikipedia <https://en.wikipedia.org/wiki/Magnetic_moment>`__.
+"""
+
+electric_displacement = SymbolNew("D", units.charge / units.area)
+"""
+**Electric displacement field**, also called **electric flux density** or **electric induction**,
+is a vector field, which accounts for the electromagnetic effects of polarization and that of an
+electric field, combining the two in an auxiliary field.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Electric_displacement_field>`__.
 """

test/thermodynamics/dielectrics/internal_energy_change_via_heat_and_electric_displacement_change_test.py

@@ -0,0 +1,50 @@
+from collections import namedtuple
+from pytest import fixture, raises
+from symplyphysics import (
+    assert_equal,
+    errors,
+    units,
+    Quantity,
+)
+from symplyphysics.laws.thermodynamics.dielectrics import (
+    internal_energy_change_via_heat_and_electric_displacement_change as law,
+)
+
+Args = namedtuple("Args", "dq e dd")
+
+
+@fixture(name="test_args")
+def test_args_fixture() -> Args:
+    dq = Quantity(1e-3 * units.joule / units.meter**3)
+    e = Quantity(10 * units.volt / units.meter)
+    dd = Quantity(4e-3 * units.coulomb / units.meter**2)
+    return Args(dq=dq, e=e, dd=dd)
+
+
+def test_law(test_args: Args) -> None:
+    result = law.calculate_internal_energy_density_change(test_args.dq, test_args.e, test_args.dd)
+    assert_equal(result, 4.1e-2 * units.joule / units.meter**3, tolerance=5e-3)
+
+
+def test_bad_heat(test_args: Args) -> None:
+    qb = Quantity(units.second)
+    with raises(errors.UnitsError):
+        law.calculate_internal_energy_density_change(qb, test_args.e, test_args.dd)
+    with raises(TypeError):
+        law.calculate_internal_energy_density_change(100, test_args.e, test_args.dd)
+
+
+def test_bad_electric_field(test_args: Args) -> None:
+    eb = Quantity(units.second)
+    with raises(errors.UnitsError):
+        law.calculate_internal_energy_density_change(test_args.dq, eb, test_args.dd)
+    with raises(TypeError):
+        law.calculate_internal_energy_density_change(test_args.dq, 100, test_args.dd)
+
+
+def test_bad_electric_displacement(test_args: Args) -> None:
+    db = Quantity(units.second)
+    with raises(errors.UnitsError):
+        law.calculate_internal_energy_density_change(test_args.dq, test_args.e, db)
+    with raises(TypeError):
+        law.calculate_internal_energy_density_change(test_args.dq, test_args.e, 100)