Isobaric molar heat capacity of ideal gas via adiabatic index
=============================================================

For ideal gases the isobaric and isochoric heat capacities can be calculated via the molar gas
constant and the adiabatic index of the gas.

**Notation:**

#. :math:`R` (:code:`R`) is :attr:`~symplyphysics.quantities.molar_gas_constant`.

**Conditions:**

#. The gas is ideal.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Heat_capacity_ratio#Ideal-gas_relations>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.isobaric_molar_heat_capacity_of_ideal_gas_via_adiabatic_index

.. py:data:: isobaric_molar_heat_capacity

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

Symbol:
    :code:`c_pm`

Latex:
    :math:`c_{p, \text{m}}`

Dimension:
    :code:`energy/(amount_of_substance*temperature)`


.. py:data:: adiabatic_index

    :attr:`~symplyphysics.symbols.thermodynamics.adiabatic_index`, or :doc:`heat capacity ratio <definitions.heat_capacity_ratio>`
    of the gas.

Symbol:
    :code:`gamma`

Latex:
    :math:`\gamma`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`c_pm = R * gamma / (gamma - 1)`


    Latex:
        .. math::
            c_{p, \text{m}} = \frac{R \gamma}{\gamma - 1}