Temperature derivative via volume derivative
============================================

The **Joule—Thompson effect** describes the change in temperature that accompanies the expansion of
a gas without production of work or transfer of heat, which is in effect an isenthalpic process.

**Notes:**

#. The left-hand side of the equation is also called the **Joule—Thompson coefficient**.

**Conditions:**

#. Particle count is assumed to be constant.
#. Heat capacity is assumed to be independent of temperature.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Joule%E2%80%93Thomson_effect#The_Joule%E2%80%93Thomson_(Kelvin)_coefficient>`__.

#. `Chemistry LibreTexts <https://chem.libretexts.org/Courses/Millersville_University/CHEM_341-_Physical_Chemistry_I/04%3A_Putting_the_First_Law_to_Work/4.05%3A_The_Joule-Thomson_Effect>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.temperature_derivative_via_volume_derivative

.. py:data:: pressure

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

Symbol:
    :code:`p`

Latex:
    :math:`p`

Dimension:
    :code:`pressure`


.. py:data:: enthalpy

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

Symbol:
    :code:`H`

Latex:
    :math:`H`

Dimension:
    :code:`energy`


.. py:data:: temperature

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

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

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

Dimension:
    :code:`temperature`


.. py:data:: volume

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

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

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

Dimension:
    :code:`volume`


.. py:data:: isobaric_heat_capacity

    :attr:`~symplyphysics.symbols.thermodynamics.heat_capacity` of the system at constant pressure.

Symbol:
    :code:`C_p`

Latex:
    :math:`C_{p}`

Dimension:
    :code:`energy/temperature`


.. py:data:: law

    :code:`Derivative(T(p, H), p) = (T(p, H) * Derivative(V(T(p, H), p), T(p, H)) - V(T(p, H), p)) / C_p`


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