Add links ­— thermodynamics (1) (#935)

* Add links

* Update symplyphysics/laws/thermodynamics/canonical_partition_function_of_classical_discrete_system.py

---------

Co-authored-by: blackyblack <[email protected]>

symplyphysics/laws/thermodynamics/average_kinetic_energy_of_ideal_gas_from_temperature.py

@@ -13,6 +13,10 @@
 **Conditions:**
 
 #. The gas is ideal.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Kinetic_theory_of_gases#Temperature_and_kinetic_energy>`__.
 """
 
 from sympy import Eq, solve, Rational, stats, Interval, S

symplyphysics/laws/thermodynamics/average_speed_in_maxwell_boltzmann_statistics.py

@@ -12,6 +12,10 @@
 
 #. The gas is in thermal equilibrium with the environment.
 #. The gas particles are distributed according to Maxwell—Boltzmann statistics.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution#Typical_speeds>`__.
 """
 
 from sympy import Eq, sqrt, pi, S, stats, Interval

symplyphysics/laws/thermodynamics/average_square_speed_in_maxwell_boltzmann_statistics.py

@@ -13,6 +13,10 @@
 
 #. The gas is in thermal equilibrium with the environment.
 #. The gas particles are distributed according to Maxwell—Boltzmann statistics.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution#Typical_speeds>`__.
 """
 
 from sympy import (Eq, solve, S, stats, Interval)

symplyphysics/laws/thermodynamics/bose_einstein_statistics/single_particle_state_distribution.py

@@ -9,6 +9,10 @@
 **Conditions:**
 
 #. :math:`E_i > \mu`.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics#Bose%E2%80%93Einstein_distribution>`__.
 """
 
 from sympy import Eq, exp

symplyphysics/laws/thermodynamics/canonical_partition_function_of_classical_discrete_system.py

@@ -6,6 +6,13 @@
 with the environment, with a temperature T and whose volume and number of constituent particles remain
 constant. For a classical discrete system the partition function is the sum of the Boltzmann factors
 of all the possible energy states:
+
+**Links:**
+
+#. `Wikipedia, derivable from here <https://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics)#Classical_discrete_system>`__.
+
+..
+    NOTE replace `boltzmann_factor` with actual exponent?
 """
 
 from typing import Sequence

symplyphysics/laws/thermodynamics/change_in_entropy_of_ideal_gas_from_volume_and_temperature.py

@@ -16,8 +16,13 @@
 
 #. The gas is ideal.
 
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Entropy#Entropy_change_formulas_for_simple_processes>`__.
+
 ..
     TODO refactor `mass / molar_mass` into `amount_of_substance`
+    TODO find other link
 """
 
 from sympy import Eq, solve, log

symplyphysics/laws/thermodynamics/chemical_potential_is_gibbs_energy_per_particle.py

@@ -5,6 +5,10 @@
 Chemical potential of a thermodynamic system can be expressed as the Gibbs energy of the system
 per particle. Therefore, chemical potential is an intensive physical quantity, whereas Gibbs energy
 and particle count are extensive.
+
+**Links:**
+
+#. `Wikipedia, last formula in paragraph <https://en.wikipedia.org/wiki/Gibbs_free_energy#Definitions>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/thermodynamics/chemical_potential_is_particle_count_derivative_of_enthalpy.py

@@ -5,6 +5,10 @@
 The chemical potential of the system is the amount of energy the system absorbs or releases
 due to the introduction of a particle into the system, i.e. when the particle count increases
 by one.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Chemical_potential#Thermodynamic_definition>`__.
 """
 
 from sympy import Eq, Derivative, Point2D

symplyphysics/laws/thermodynamics/chemical_potential_is_particle_count_derivative_of_free_energy.py

@@ -5,6 +5,10 @@
 The chemical potential of the system is the amount of energy the system absorbs or releases
 due to the introduction of a particle into the system, i.e. when the particle count increases
 by one.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Chemical_potential#Thermodynamic_definition>`__.
 """
 
 from sympy import Eq, Derivative, Point2D

symplyphysics/laws/thermodynamics/chemical_potential_is_particle_count_derivative_of_gibbs_energy.py

@@ -5,6 +5,10 @@
 The chemical potential of the system is the amount of energy the system absorbs or releases
 due to the introduction of a particle into the system, i.e. when the particle count increases
 by one.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Chemical_potential#Thermodynamic_definition>`__.
 """
 
 from sympy import Eq, Derivative, Point2D

symplyphysics/laws/thermodynamics/chemical_potential_is_particle_count_derivative_of_internal_energy.py

@@ -5,6 +5,10 @@
 The chemical potential of a system is the amount of energy the system absorbs or releases
 due to the introduction of a particle into the system, i.e. when the particle count increases
 by one.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Chemical_potential#Thermodynamic_definition>`__.
 """
 
 from sympy import Eq, Derivative, Point2D

symplyphysics/laws/thermodynamics/chemical_potential_of_ideal_gas.py

@@ -12,6 +12,10 @@
 **Conditions:**
 
 #. The gas is ideal.
+
+**Links:**
+
+#. Formula on p. 394 of "Statistical Mechanics" by Terrent L. Hill (1987)
 """
 
 from sympy import Eq, log

symplyphysics/laws/thermodynamics/classical_isochoric_molar_heat_capacity_of_solids.py

@@ -12,6 +12,10 @@
 **Conditions:**
 
 #. The temperature of the system is big enough to disregard quantum effects.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Dulong%E2%80%93Petit_law>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/thermodynamics/compressibility_factor_via_intermolecular_force_potential.py

@@ -16,6 +16,10 @@
 
 #. The virial expansion is done up to the second virial coefficient inclusively.
 
+**Links:**
+
+#. `Wikipedia, second formula <https://en.wikipedia.org/wiki/Compressibility_factor#Theoretical_models>`__.
+
 ..
     TODO Simplify this law by reducing it to the formula of the second virial coefficient
 """

symplyphysics/laws/thermodynamics/diffusion_coefficient_of_spherical_brownian_particles_from_temperature_and_dynamic_viscosity.py

@@ -22,6 +22,10 @@
 #. The inertia of a Brownian particle can be neglected compared to the influence of friction forces.
 #. Particles are spherical.
 #. Low Reynolds number, i.e. non-turbulent flow.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Einstein_relation_(kinetic_theory)>`__.
 """
 
 from sympy import Eq, solve, pi

symplyphysics/laws/thermodynamics/diffusion_flux_from_diffusion_coefficient_and_concentration_gradient.py

@@ -14,6 +14,10 @@
 **Conditions:**
 
 #. The mixture is ideal.
+
+**Links:**
+
+#. `Wikipedia, first formula <https://en.wikipedia.org/wiki/Fick%27s_laws_of_diffusion#Fick's_first_law>`__.
 """
 
 from sympy import Eq, Derivative

symplyphysics/laws/thermodynamics/efficiency_of_heat_engine.py

@@ -4,6 +4,10 @@
 
 Efficiency of a heat engine is the ratio of the useful energy to the total energy received
 by the system.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Heat_engine#Efficiency>`__.
 """
 
 from sympy import Eq, solve

symplyphysics/laws/thermodynamics/enthalpy_derivative_via_volume_derivative.py

@@ -8,6 +8,10 @@
 **Conditions:**
 
 #. Works for an infinitesimal quasi-static isothermal process.
+
+**Links:**
+
+#. `Wikipedia, see third table <https://en.wikipedia.org/wiki/Table_of_thermodynamic_equations#Maxwell's_relations>`__.
 """
 
 from sympy import Eq, Derivative

symplyphysics/laws/thermodynamics/enthalpy_differential.py

@@ -20,6 +20,10 @@
 
 #. The system is in thermal equilibrium with its surroundings.
 #. The system is composed of only one type of particles, i.e. the system is a pure substance.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Fundamental_thermodynamic_relation>`__.
 """
 
 from sympy import Eq, Function as SymFunction, Symbol as SymSymbol, symbols as sympy_symbols

symplyphysics/laws/thermodynamics/enthalpy_is_internal_energy_plus_pressure_energy.py

@@ -5,6 +5,10 @@
 Enthalpy :math:`H` of a thermodynamic system is defined as the sum of its internal energy
 :math:`U` and the product of its pressure :math:`p` and volume :math:`V`, which is sometimes
 referred to as the pressure energy.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Enthalpy#Definition>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/thermodynamics/enthalpy_via_gibbs_energy.py

@@ -9,6 +9,10 @@
 
 #. Particle count must be constant.
 #. Pressure in the system must be constant.
+
+**Links:**
+
+#. `Wikipedia, equivalent concise form of this law <https://en.wikipedia.org/wiki/Gibbs%E2%80%93Helmholtz_equation>`__.
 """
 
 from sympy import Eq, Derivative, Point2D, solve

symplyphysics/laws/thermodynamics/equations_of_state/dieterici_equation.py

@@ -20,6 +20,10 @@
 
 #. Only applicable in the limits :math:`b \ll V_m` and :math:`a \ll p V_m^2`.
 #. Inapplicable for high pressures.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Real_gas#Dieterici_model>`__.
 """
 
 from sympy import Eq, solve, exp

symplyphysics/laws/thermodynamics/equations_of_state/ideal_gas_equation.py

@@ -8,6 +8,10 @@
 **Notation:**
 
 #. :quantity_notation:`molar_gas_constant`.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Ideal_gas_law>`__.
 """
 
 from sympy import (Eq, solve)

symplyphysics/laws/thermodynamics/equations_of_state/van_der_waals/critical_molar_volume.py

@@ -4,6 +4,10 @@
 
 Critical molar volume of a van der Waals fluid is proportional to the excluded volume
 parameter :math:`b` of the van der Waals equation. See :ref:`vdw_critical_parameters_def`.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Van_der_Waals_equation#Critical_point_and_corresponding_states>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/thermodynamics/equations_of_state/van_der_waals/critical_pressure.py

@@ -4,6 +4,10 @@
 
 Critical pressure in a van der Waals fluid depends on the parameters :math:`a` and
 :math:`b` of the van der Waals equation. See :ref:`vdw_critical_parameters_def`.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Van_der_Waals_equation#Critical_point_and_corresponding_states>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/thermodynamics/equations_of_state/van_der_waals/critical_temperature.py

@@ -8,6 +8,10 @@
 **Notation:**
 
 #. :quantity_notation:`molar_gas_constant`.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Van_der_Waals_equation#Critical_point_and_corresponding_states>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/thermodynamics/equations_of_state/van_der_waals/dimensionless_equation.py

@@ -6,6 +6,10 @@
 <vdw_reduced_units_def>`. One notable property of the dimensionless equation of state is that it
 contains no substance-specific quantities, i.e. all van der Waals fluids will plot on the same
 reduced pressure-volume curve at the same reduced temperature.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Van_der_Waals_equation#Critical_point_and_corresponding_states>`__.
 """
 
 from sympy import Eq, Rational, solve

symplyphysics/laws/thermodynamics/equations_of_state/van_der_waals/equation.py

@@ -13,6 +13,10 @@
 **Notation:**
 
 #. :quantity_notation:`molar_gas_constant`.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Van_der_Waals_equation#>`__.
 """
 
 from sympy import (Eq, solve)

symplyphysics/laws/thermodynamics/equations_of_state/van_der_waals/molar_internal_energy.py

@@ -8,6 +8,10 @@
 **Conditions:**
 
 #. The fluid is homogeneous and in a single phase state.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Van_der_Waals_equation#Internal_energy_and_specific_heat_at_constant_volume>`__.
 """
 
 from sympy import Eq, Integral

symplyphysics/laws/thermodynamics/equations_of_state/van_der_waals/reduced_pressure.py

@@ -3,6 +3,10 @@
 ================
 
 See :ref:`vdw_reduced_units_def`.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Van_der_Waals_equation#Critical_point_and_corresponding_states>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/thermodynamics/equations_of_state/van_der_waals/reduced_temperature.py

@@ -3,6 +3,10 @@
 ===================
 
 See :ref:`vdw_reduced_units_def`.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Van_der_Waals_equation#Critical_point_and_corresponding_states>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/thermodynamics/equations_of_state/van_der_waals/reduced_volume.py

@@ -7,6 +7,10 @@
 **Note:**
 
 #. Specific or molar volumes can be used in the right-hand side of the law.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Van_der_Waals_equation#Critical_point_and_corresponding_states>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/thermodynamics/equations_of_state/van_der_waals/second_virial_coefficient.py

@@ -15,6 +15,10 @@
 **Conditions:**
 
 #. The gas density is small enough within the context of perturbation theory.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Van_der_Waals_equation#Virial_expansion>`__.
 """
 
 from sympy import Eq, solve, Symbol as SymSymbol

symplyphysics/laws/thermodynamics/equations_of_state/virial_equation.py

@@ -20,6 +20,10 @@
    the second and third virial coefficients. Moreover, the latter have been extensively studied and tabulated
    for many fluids.
 #. In this law the limit :math:`\rho \to 0` is assumed.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Virial_expansion>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/thermodynamics/euler_relations/enthalpy_formula.py

@@ -9,6 +9,10 @@
 
 #. This formula works for a single-component system. For a multi-component system replace the
    product of chemical potential and particle count with a sum over each type of components.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Thermodynamic_potential#Euler_relations>`__.
 """
 
 from sympy import Eq