# gsw_enthalpy_second_derivatives

    second derivatives of enthalpy

## Contents

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

## USAGE:

    [h_SA_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_2nd_derivatives(SA,CT,p)

## DESCRIPTION:

    Calculates the following three second-order derivatives of specific
    enthalpy (h),
     (1) h_SA_SA, second order derivative with respect to Absolute Salinity
         at constant CT & p.
     (2) h_SA_CT, second order derivative with respect to SA & CT at
         constant p.
     (3) h_CT_CT, second order derivative with respect to CT at constant
         SA & p.

    Click for a more detailed description of the second
    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_SA  =  The second derivative of specific enthalpy with respect to
                Absolute Salinity at constant CT & p.    [ J/(kg (g/kg)^2) ]
    h_SA_CT  =  The second derivative of specific enthalpy with respect to
                SA and CT at constant p.                  [ J/(kg K(g/kg)) ]
    h_CT_CT  =  The second derivative of specific enthalpy with respect to
                CT at constant SA and p.                      [ J/(kg K^2) ]

## EXAMPLE:

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

    [h_SA_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_second_derivatives(SA,CT,p)

    h_SA_SA =

      0.000082752219662
      0.000414449264358
      0.001089849221923
      0.002473058502734
      0.006107254340947
      0.010388021033928

     h_SA_CT =

      0.000130254397677
      0.000654928172110
      0.001880402010403
      0.005474186056408
      0.014339376841409
      0.025245467907619

     h_CT_CT =

      0.000714090119067
      0.003584609310758
      0.009736868475975
      0.024061418823850
      0.061537073639407
      0.107564288175526

## AUTHOR:

    Trevor McDougall and Paul Barker.  [ help_gsw@csiro.au ]

## VERSION NUMBER:

    2.0 (26th August, 2010)

## 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 Notes on the first and second order isobaric derivatives of
      specific enthalpy.

    McDougall T. J., D. R. Jackett, P. M. Barker, C. Roberts-Thomson, R.
     Feistel and R. W. Hallberg, 2010:  A computationally efficient 25-term
     expression for the density of seawater in terms of Conservative
     Temperature, and related properties of seawater.  To be submitted
     to Ocean Science Discussions.

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