# gsw_entropy_second_derivatives

    second derivatives of entropy

## Contents

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

## USAGE:

    [eta_SA_SA, eta_SA_CT, eta_CT_CT] = gsw_entropy_second_derivatives(SA,CT)

## DESCRIPTION:

    Calculates the following three second-order partial derivatives of
    specific entropy (eta)
     (1) eta_SA_SA, the second derivative with respect to Absolute
         Salinity at constant Conservative Temperature, and
     (2) eta_SA_CT, the derivative with respect to Absolute Salinity and
         Conservative Temperature.
     (3) eta_CT_CT, the second derivative with respect to Conservative
         Temperature at constant Absolute Salinity.

    Click for a more detailed description of the second
    derivatives of entropy.

## INPUT:

    SA   =   Absolute Salinity                                      [ g/kg ]
    CT   =   Conservative Temperature                              [ deg C ]

    SA & CT need to have the same dimensions.

## OUTPUT:

    eta_SA_SA =  The second derivative of specific entropy with respect
                 to Absolute Salinity (in units of g/kg) at constant
                 Conservative Temperature.  eta_SA_SA has units of:
                                                         [ J/(kg K(g/kg)^2)]
    eta_SA_CT =  The second derivative of specific entropy with respect
                 to Conservative Temperature at constant Absolute
                 Salinity. eta_SA_CT has units of:     [ J/(kg (g/kg) K^2) ]

    eta_CT_CT =  The second derivative of specific entropy with respect
                 to Conservative Temperature at constant Absolute
                 Salinity.  eta_CT_CT has units of:           [ J/(kg K^3) ]

## EXAMPLE:

    SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
    CT = [28.8099; 28.4392; 22.7862; 10.2262;  6.8272;  4.3236;]

    [eta_SA_SA, eta_SA_CT, eta_CT_CT] = gsw_entropy_second_derivatives(SA,CT)

    eta_SA_SA =

      -0.007627718929669
      -0.007591969960708
      -0.007528186784540
      -0.007455177590576
      -0.007441108287466
      -0.007414368396280

    eta_SA_CT =

      -0.001833104216751
      -0.001819473824306
      -0.001580843823414
      -0.000930111408561
      -0.000717011215195
      -0.000548410546830

    eta_CT_CT =

      -0.043665023731109
      -0.043781336189326
      -0.045506114440888
      -0.049708939454018
      -0.050938690879443
      -0.051875017843472

## AUTHOR:

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

## VERSION NUMBER:

    3.01 (17th 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 Eqns. (P.14b) and (P.15a,b) of this TEOS-10 Manual.

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