# 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_second_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;]
    CT =  [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 =

       0.000082767011575
       0.000414469343141
       0.001089580017293
       0.002472193425999
       0.006103171596320
       0.010377465312462

     h_SA_CT =

       0.000130320164426
       0.000655016236924
       0.001879127443985
       0.005468695168037
       0.014315709000526
       0.025192691262061

     h_CT_CT =

       0.000714365642428
       0.003584965089168
       0.009733337653703
       0.024044402143825
       0.061449390733344
       0.107333638394904

## AUTHOR:

    Trevor McDougall and Paul Barker.          [ help@teos-10.org ]

## VERSION NUMBER:

    3.01 (16th May, 2011)

## 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., P.M. Barker, R. Feistel and D.R. Jackett, 2011:  A
     computationally efficient 48-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