
.. |dvdT_p| replace:: :math:`\left(\frac{\partial V}{\partial T}\right)_P`
.. |dT| replace:: :math:`\partial T`
.. |dv| replace:: :math:`\partial V`
.. |ds| replace:: :math:`\partial S`
.. |dvdT_p| replace:: :math:`\left(\frac{\partial V}{\partial T}\right)_P`
.. |dvdT_p| replace:: :math:`\left(\frac{\partial V}{\partial T}\right)_P`

.. |dvdT_p| replace:: :math:`\left(\frac{\partial V}{\partial T}\right)_P`

==================  ============= ====================================================================================
                    p             
------------------  ------------- ------------------------------------------------------------------------------------
|dT|                1
|dV|                |dVdT_p|
|ds|                :math:`c_p/T`
==================  ============= ====================================================================================

Building a table with the held-constant variable on the right side and 

.. math::

    (\partial T)_P=-(\partial P)_T=1

.. math::

    (\partial V)_P=-(\partial P)_V=\left(\frac{\partial V}{\partial T}\right)_P
    
.. math::

    (\partial S)_P=-(\partial P)_S=\frac{C_p}{T}

.. math::

    (\partial U)_P=-(\partial P)_U=C_P-P\left(\frac{\partial V}{\partial T}\right)_P

.. math::

    (\partial H)_P=-(\partial P)_H=C_P

.. math::

    (\partial G)_P=-(\partial P)_G=-S

.. math::

    (\partial A)_P=-(\partial P)_A=-S-P\left(\frac{\partial V}{\partial T}\right)_P

.. math::

    (\partial V)_T=-(\partial T)_V=-\left(\frac{\partial V}{\partial P}\right)_T
    
.. math::

    (\partial S)_T=-(\partial T)_S=\left(\frac{\partial V}{\partial T}\right)_P

.. math::

    (\partial U)_T=-(\partial T)_U=T\left(\frac{\partial V}{\partial T}\right)_P+P\left(\frac{\partial V}{\partial P}\right)_T

.. math::

    (\partial H)_T=-(\partial T)_H=-V+T\left(\frac{\partial V}{\partial T}\right)_P

.. math::

    (\partial G)_T=-(\partial T)_G=-V

.. math::

    (\partial A)_T=-(\partial T)_A=P\left(\frac{\partial V}{\partial P}\right)_T

.. math::

    (\partial S)_V=-(\partial V)_S=\frac{C_P}{T}\left(\frac{\partial V}{\partial P}\right)_T+\left(\frac{\partial V}{\partial T}\right)_P^2

.. math::

    (\partial U)_V=-(\partial V)_U=C_P\left(\frac{\partial V}{\partial P}\right)_T+T\left(\frac{\partial V}{\partial T}\right)_P^2

.. math::

    (\partial H)_V=-(\partial V)_H=C_P\left(\frac{\partial V}{\partial P}\right)_T+T\left(\frac{\partial V}{\partial T}\right)_P^2-V\left(\frac{\partial V}{\partial T}\right)_P

.. math::

    (\partial G)_V=-(\partial V)_G=-V\left(\frac{\partial V}{\partial T}\right)_P-S\left(\frac{\partial V}{\partial P}\right)_T

.. math::

    (\partial A)_V=-(\partial V)_A=-S\left(\frac{\partial V}{\partial P}\right)_T

.. math::

    (\partial U)_S=-(\partial S)_U=\frac{PC_P}{T}\left(\frac{\partial V}{\partial P}\right)_T+P\left(\frac{\partial V}{\partial T}\right)_P^2

.. math::

    (\partial H)_S=-(\partial S)_H=-\frac{VC_P}{T}

.. math::

    (\partial G)_S=-(\partial S)_G=-\frac{VC_P}{T}+S\left(\frac{\partial V}{\partial T}\right)_P

.. math::

    (\partial A)_S=-(\partial S)_A=\frac{PC_P}{T}\left(\frac{\partial V}{\partial P}\right)_T+P\left(\frac{\partial V}{\partial T}\right)_P^2+S\left(\frac{\partial V}{\partial T}\right)_P

.. math::

    (\partial H)_U=-(\partial U)_H=-VC_P+PV\left(\frac{\partial V}{\partial T}\right)_P-PC_P\left(\frac{\partial V}{\partial P}\right)_T-PT\left(\frac{\partial V}{\partial T}\right)_P^2

.. math::

    (\partial G)_U=-(\partial U)_G=-VC_P+PV\left(\frac{\partial V}{\partial T}\right)_P+ST\left(\frac{\partial V}{\partial T}\right)_P+SP\left(\frac{\partial V}{\partial P}\right)_T

.. math::

    (\partial A)_U=-(\partial U)_A=P(C_P+S)\left(\frac{\partial V}{\partial P}\right)_T+PT\left(\frac{\partial V}{\partial T}\right)_P^2+ST\left(\frac{\partial V}{\partial T}\right)_P

.. math::

    (\partial G)_H=-(\partial H)_G=-V(C_P+S)+TS\left(\frac{\partial V}{\partial T}\right)_P

.. math::

    (\partial A)_H=-(\partial H)_A=-\left[S+P\left(\frac{\partial V}{\partial T}\right)_P\right]\left[V-T\left(\frac{\partial V}{\partial T}\right)_P\right]+PC_P\left(\frac{\partial V}{\partial P}\right)_T

.. math::

    (\partial A)_G=-(\partial G)_A=-S\left[V+P\left(\frac{\partial V}{\partial P}\right)_T\right]-PV\left(\frac{\partial V}{\partial T}\right)_P