Law: Gibbs energy change in dielectrics

symplyphysics/laws/thermodynamics/dielectrics/gibbs_energy_change_via_temperature_change_and_electic_displacement_change.py

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+"""
+Gibbs energy change via temperature change and electric displacement change
+===========================================================================
+
+The infinitesimal change in Gibbs energy of a system with a dielectric medium
+can be expressed using the change in temperature and the change in electric
+field strength.
+
+**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 31.8 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,
+)
+
+gibbs_energy_density_change = SymbolNew("dG", units.energy / units.volume)
+"""
+Infinitesimal change in :symbols:`gibbs_energy` of the system per unit :symbols:`volume`.
+"""
+
+entropy_density = SymbolNew("S", units.energy / units.temperature / units.volume)
+"""
+:symbols:`entropy` of the system per unit :symbols:`volume`.
+"""
+
+temperature_change = clone_as_symbol(
+    symbols.temperature,
+    display_symbol="dT",
+    display_latex="dT",
+)
+"""
+Infinitesimal change in :symbols:`temperature` of the system.
+"""
+
+electric_displacement = symbols.electric_displacement
+"""
+:symbols:`electric_displacement`.
+"""
+
+electric_field_change = clone_as_symbol(
+    symbols.electric_field_strength,
+    display_symbol="dE",
+    display_latex="dE",
+)
+"""
+Infinitesimal change in :symbols:`electric_field_strength`.
+"""
+
+law = Eq(
+    gibbs_energy_density_change,
+    -1 * entropy_density * temperature_change - electric_displacement * electric_field_change,
+)
+"""
+:laws:symbol::
+
+:laws:latex::
+"""
+
+# Derivation
+## Make use of the formula for Gibbs energy and that for free energy.
+
+
+@validate_input(
+    entropy_density_=entropy_density,
+    temperature_change_=temperature_change,
+    electric_displacement_=electric_displacement,
+    electric_field_change_=electric_field_change,
+)
+@validate_output(gibbs_energy_density_change)
+def calculate_gibbs_energy_density_change(
+    entropy_density_: Quantity,
+    temperature_change_: Quantity,
+    electric_displacement_: Quantity,
+    electric_field_change_: Quantity,
+) -> Quantity:
+    result = law.rhs.subs({
+        entropy_density: entropy_density_,
+        temperature_change: temperature_change_,
+        electric_displacement: electric_displacement_,
+        electric_field_change: electric_field_change_,
+    })
+    return Quantity(result)

test/thermodynamics/dielectrics/gibbs_energy_change_via_temperature_change_and_electic_displacement_change_test.py

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+from collections import namedtuple
+from pytest import fixture, raises
+from symplyphysics import (
+    assert_equal,
+    errors,
+    units,
+    Quantity,
+)
+from symplyphysics.laws.thermodynamics.dielectrics import (
+    gibbs_energy_change_via_temperature_change_and_electic_displacement_change as law,
+)
+
+Args = namedtuple("Args", "s dt d de")
+
+
+@fixture(name="test_args")
+def test_args_fixture() -> Args:
+    s = Quantity(10 * units.joule / units.kelvin / units.meter**3)
+    dt = Quantity(-1e-3 * units.kelvin)
+    d = Quantity(15 * units.coulomb / units.meter**2)
+    de = Quantity(3e-3 * units.volt / units.meter)
+    return Args(s=s, dt=dt, d=d, de=de)
+
+
+def test_law(test_args: Args) -> None:
+    result = law.calculate_gibbs_energy_density_change(test_args.s, test_args.dt, test_args.d, test_args.de)
+    assert_equal(result, -3.5e-2 * units.joule / units.meter**3)
+
+
+def test_bad_entropy_density(test_args: Args) -> None:
+    sb = Quantity(units.candela)
+    with raises(errors.UnitsError):
+        law.calculate_gibbs_energy_density_change(sb, test_args.dt, test_args.d, test_args.de)
+    with raises(TypeError):
+        law.calculate_gibbs_energy_density_change(100, test_args.dt, test_args.d, test_args.de)
+
+
+def test_bad_temperature(test_args: Args) -> None:
+    tb = Quantity(units.candela)
+    with raises(errors.UnitsError):
+        law.calculate_gibbs_energy_density_change(test_args.s, tb, test_args.d, test_args.de)
+    with raises(TypeError):
+        law.calculate_gibbs_energy_density_change(test_args.s, 100, test_args.d, test_args.de)
+
+
+def test_bad_electric_displacement(test_args: Args) -> None:
+    db = Quantity(units.candela)
+    with raises(errors.UnitsError):
+        law.calculate_gibbs_energy_density_change(test_args.s, test_args.dt, db, test_args.de)
+    with raises(TypeError):
+        law.calculate_gibbs_energy_density_change(test_args.s, test_args.dt, 100, test_args.de)
+
+
+def test_bad_electric_field_strength(test_args: Args) -> None:
+    eb = Quantity(units.candela)
+    with raises(errors.UnitsError):
+        law.calculate_gibbs_energy_density_change(test_args.s, test_args.dt, test_args.d, eb)
+    with raises(TypeError):
+        law.calculate_gibbs_energy_density_change(test_args.s, test_args.dt, test_args.d, 100)