Isochoric and isobaric heat capacities of homogeneous substance
===============================================================

The **Mayer's relation** is the relation between heat capacity at constant pressure and heat
capacity at constant volume. In the current form it is applicable to any homogeneous substance,
not just ideal gases.

**Links:**

#. `Wikipedia, second formula <https://en.wikipedia.org/wiki/Mayer%27s_relation>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.isochoric_and_isobaric_heat_capacities_of_homogeneous_substance

.. py:data:: isobaric_heat_capacity

    :attr:`~symplyphysics.symbols.thermodynamics.heat_capacity` at constant :attr:`~symplyphysics.symbols.classical_mechanics.pressure`.

Symbol:
    :code:`C_p`

Latex:
    :math:`C_{p}`

Dimension:
    :code:`energy/temperature`


.. py:data:: isochoric_heat_capacity

    :attr:`~symplyphysics.symbols.thermodynamics.heat_capacity` at constant :attr:`~symplyphysics.symbols.classical_mechanics.volume`.

Symbol:
    :code:`C_V`

Latex:
    :math:`C_{V}`

Dimension:
    :code:`energy/temperature`


.. py:data:: volume

    :attr:`~symplyphysics.symbols.classical_mechanics.volume` of the substance.

Symbol:
    :code:`V`

Latex:
    :math:`V`

Dimension:
    :code:`volume`


.. py:data:: temperature

    :attr:`~symplyphysics.symbols.thermodynamics.temperature` of the substance.

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: thermal_expansion_coefficient

    :attr:`~symplyphysics.symbols.thermodynamics.thermal_expansion_coefficient` of the substance. Also see :doc:`Thermal volumetric expansion
    coefficient <definitions.volumetric_coefficient_of_thermal_expansion>`.

Symbol:
    :code:`alpha_V`

Latex:
    :math:`\alpha_{V}`

Dimension:
    :code:`1/temperature`


.. py:data:: isothermal_compressibility

    :attr:`~symplyphysics.symbols.thermodynamics.thermodynamic_compressibility` of the substance. Also see :doc:`Isothermal compressibility
    <definitions.thermodynamic_compressibility>`.

Symbol:
    :code:`beta_T`

Latex:
    :math:`\beta_{T}`

Dimension:
    :code:`1/pressure`


.. py:data:: law

    :code:`C_p - C_V = V * T * alpha_V^2 / beta_T`


    Latex:
        .. math::
            C_{p} - C_{V} = \frac{V T \alpha_{V}^{2}}{\beta_{T}}