# gsw_gibbs

Gibbs energy and its derivatives

## Contents

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

## USAGE:

    gibbs = gsw_gibbs(ns,nt,np,SA,t,p)

## DESCRIPTION:

    Calculates specific Gibbs energy and its derivatives up to order 2 for
    seawater.  The Gibbs function for seawater is that of TEOS-10
    (IOC et al., 2010), being the sum of IAPWS-08 for the saline part and
    IAPWS-09 for the pure water part.  These International Association
    for the Properties of Water and Steam (IAPWS) releases are the
    officially blessed IAPWS descriptions of Feistel (2008) and the pure
    water part of Feistel (2003).  Absolute Salinity, SA, in all of the GSW
    routines is expressed on the Reference-Composition Salinity Scale of
    2008 (RCSS-08) of Millero et al. (2008).

    Click for a more detailed description of Gibbs energy.

## INPUT:

    ns  =  order of SA derivative                     [ integers 0, 1 or 2 ]
    nt  =  order of t derivative                      [ integers 0, 1 or 2 ]
    np  =  order of p derivative                      [ integers 0, 1 or 2 ]
    SA  =  Absolute Salinity                                        [ g/kg ]
    t   =  in-situ temperature (ITS-90)                            [ deg C ]
    p   =  sea pressure                                             [ dbar ]
           (ie. absolute pressure - 10.1325 dbar)

    SA, t and p need to have the same dimensions.

## OUTPUT:

    gibbs  =  Specific Gibbs energy or its derivatives.

              The Gibbs energy (when ns = nt = np = 0) has units of:
                                                                    [ J/kg ]
              The Absolute Salinity derivatives are output in units of:
                                                     [ (J/kg) (g/kg)^(-ns) ]
              The temperature derivatives are output in units of:
                                                        [ (J/kg) (K)^(-nt) ]
              The pressure derivatives are output in units of:
                                                       [ (J/kg) (Pa)^(-np) ]
              The mixed derivatives are output in units of:
                                [ (J/kg) (g/kg)^(-ns) (K)^(-nt) (Pa)^(-np) ]

    Note. The derivatives are taken with respect to pressure in Pa, not
      withstanding that the pressure input into this routine is in dbar.

## AUTHOR:

    David Jackett                     [ help_gsw@csiro.au ]

    MODIFIED:
    Trevor McDougall and Paul Barker

## VERSION NUMBER:

    2.0 (24th September, 2010)

## REFERENCES:

    Feistel, R., 2003: A new extended Gibbs thermodynamic potential of
     seawater,  Progr. Oceanogr., 58, 43-114.

    Feistel, R., 2008: A Gibbs function for seawater thermodynamics
     for -6 to 80°C and salinity up to 120 g kg–1, Deep-Sea Res. I,
     55, 1639-1671.

    IAPWS, 2008: Release on the IAPWS Formulation 2008 for the
     Thermodynamic Properties of Seawater. The International Association
     for the Properties of Water and Steam. Berlin, Germany, September
     2008, available from http://www.iapws.org.
      This Release is referred to as IAPWS-08.

    IAPWS, 2009: Supplementary Release on a Computationally Efficient
     Thermodynamic Formulation for Liquid Water for Oceanographic Use.
     The International Association for the Properties of Water and Steam.
     Doorwerth, The Netherlands, September 2009, available from
     http://www.iapws.org.
      This Release is referred to as IAPWS-09.

    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  http://www.TEOS-10.org
      See section 2.6 and appendices A.6,  G and H of this TEOS-10 Manual.

    Millero, F. J., R. Feistel, D. G. Wright, and T. J. McDougall, 2008:
     The composition of Standard Seawater and the definition of the
     Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72.

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