# gsw_enthalpy_first_derivatives

    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.

    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).

## 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, h_CT, h_P] = gsw_enthalpy_first_derivatives(SA,CT,p)

    h_SA =

    -0.070221017857321
    -0.351155742717708
    -0.887081852469166
    -1.829811186103484
    -4.424369449732652
    -7.407229217110896

    h_CT =

    1.0e+003 *

     3.991899729625529
     3.992025696743769
     3.992210168035032
     3.992283178760239
     3.992681641668387
     3.993005774345293

    h_P =

    1.0e-003 *

     0.978626618725186
     0.978222134953103
     0.976154774939840
     0.972961213383549
     0.971026778012244
     0.968989993773259

## AUTHOR:

    Trevor McDougall.  [ help_gsw@csiro.au ]

## VERSION NUMBER:

    2.0 (17th 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 Eqns. (A.11.18), (A.11.15) and (A.11.12) of this TEOS-10 Manual.

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