Temperature is derivative of internal energy
============================================

Temperature of a thermodynamic system can be found when internal energy is known as a function of entropy.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Internal_energy#Internal_energy_of_multi-component_systems>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.temperature_is_derivative_of_internal_energy

.. py:data:: temperature

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

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: entropy

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

Symbol:
    :code:`S`

Latex:
    :math:`S`

Dimension:
    :code:`energy/temperature`


.. py:data:: volume

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

Symbol:
    :code:`V`

Latex:
    :math:`V`

Dimension:
    :code:`volume`


.. py:data:: particle_count

    :attr:`~symplyphysics.symbols.basic.particle_count` of the system.

Symbol:
    :code:`N`

Latex:
    :math:`N`

Dimension:
    :code:`dimensionless`


.. py:data:: internal_energy

    :attr:`~symplyphysics.symbols.thermodynamics.internal_energy` of the system as a function of its natural variables.

Symbol:
    :code:`U(S, V, N)`

Latex:
    :math:`U{\left(S,V,N \right)}`

Dimension:
    :code:`energy`


.. py:data:: law

    :code:`T = Derivative(U(S, V, N), S)`


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