Entropy derivative via volume derivative
========================================

Maxwell relations are a set of equations that unite the most common thermodynamic quantities between
one another. They are derived from the fundamental themodynamic relations featuring differentials
of thermodynamic potentials, and this method of derivation is called the method of thermodynamic
potentials.

**Conditions:**

#. Particle count must be constant.

**Links:**

#. `Wikipedia, first table <https://en.wikipedia.org/wiki/Table_of_thermodynamic_equations#Maxwell's_relations>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.entropy_derivative_via_volume_derivative

.. py:data:: temperature

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

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: pressure

    :attr:`~symplyphysics.symbols.classical_mechanics.pressure` inside the system.

Symbol:
    :code:`p`

Latex:
    :math:`p`

Dimension:
    :code:`pressure`


.. py:data:: entropy

    :attr:`~symplyphysics.symbols.thermodynamics.entropy` of the system as a function of temperature and pressure.

Symbol:
    :code:`S(T, p)`

Latex:
    :math:`S{\left(T,p \right)}`

Dimension:
    :code:`energy/temperature`


.. py:data:: volume

    :attr:`~symplyphysics.symbols.classical_mechanics.volume` of the system as a function of temperature and pressure.

Symbol:
    :code:`V(T, p)`

Latex:
    :math:`V{\left(T,p \right)}`

Dimension:
    :code:`volume`


.. py:data:: law

    :code:`Derivative(S(T, p), p) = -Derivative(V(T, p), T)`


    Latex:
        .. math::
            \frac{\partial}{\partial p} S{\left(T,p \right)} = - \frac{\partial}{\partial T} V{\left(T,p \right)}