# gsw_enthalpy_first_derivatives_CT_exact

    first derivatives of enthalpy

## Contents

- USAGE:
- DESCRIPTION:
- INPUT:
- OUTPUT:
- EXAMPLE:
- AUTHOR:
- VERSION NUMBER:
- REFERENCES:

## USAGE:

    [h_SA, h_CT, h_P] = gsw_enthalpy_first_derivatives(SA,CT,p)

## DESCRIPTION:

    Calculates the following three derivatives of specific enthalpy (h)
     (1) h_SA, the derivative with respect to Absolute Salinity at
         constant CT and p, and
     (2) h_CT, derivative with respect to CT at constant SA and p.
     (3) h_P, derivative with respect to pressure (in Pa) at constant
         SA and CT.

    Note that this function uses the full Gibbs function.  There is an
    alternative to calling this function, namely
    gsw_enthalpy_first_derivatives(SA,CT,p),which uses the computationally
    efficient 75-term expression for specific volume in terms of SA, CT and
    p (Roquet et al., 2015).

    Click for a more detailed description of the first
    derivatives of specific enthalpy.

## INPUT:

    SA  =   Absolute Salinity                                       [ g/kg ]
    CT  =   Conservative Temperature                               [ deg C ]
    p   =   sea pressure                                            [ dbar ]
            (i.e. absolute pressure - 10.1325 dbar)

    SA & CT need to have the same dimensions.
    p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT are MxN.

## OUTPUT:

    h_SA   =  The first derivative of specific enthalpy with respect to
              Absolute Salinity at constant CT and p.
                                              [ J/(kg (g/kg))]  i.e. [ J/g ]
    h_CT   =  The first derivative of specific enthalpy with respect to
              CT at constant SA and p.                          [ J/(kg K) ]
    h_P    =  The first partial derivative of specific enthalpy with
              respect to pressure (in Pa) at fixed SA and CT.  Note that
              h_P is specific volume (1/rho).                     [ m^3/kg ]

## EXAMPLE:

    SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
    CT = [28.7856; 28.4329; 22.8103; 10.2600;  6.8863;  4.4036;]
    p =  [     10;      50;     125;     250;     600;    1000;]

    [h_SA, h_CT] = gsw_enthalpy_first_derivatives_CT_exact(SA,CT,p)

    h_SA =

      -0.070224183838619
      -0.351159869043798
      -0.887036550157504
      -1.829626251448858
      -4.423522691827955
      -7.405211691293971

    h_CT =

    1.0e+003 *

       3.991899712269790
       3.992025674159605
       3.992210402650973
       3.992283991748418
       3.992685275917238
       3.993014370250710

## AUTHOR:

    Trevor McDougall.                      [ help@teos-10.org ]

## VERSION NUMBER:

    3.05 (16th February, 2015)

## REFERENCES:

    IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
     seawater - 2010: Calculation and use of thermodynamic properties.
     Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
     UNESCO (English), 196 pp.  Available from the TEOS-10 web site.
      See Eqns. (A.11.18), (A.11.15) and (A.11.12) of this TEOS-10 Manual.

    Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate
     polynomial expressions for the density and specifc volume of seawater
     using the TEOS-10 standard. Ocean Modelling.

    This software is available from http://www.TEOS-10.org