# gsw_entropy_first_derivatives

    first derivatives of entropy

## Contents

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

## USAGE:

    [eta_SA, eta_CT] = gsw_entropy_first_derivatives(SA,CT)

## DESCRIPTION:

    Calculates the following two partial derivatives of specific entropy (eta)
     (1) eta_SA, the derivative with respect to Absolute Salinity at
         constant Conservative Temperature, and
     (2) eta_CT, the derivative with respect to Conservative Temperature at
         constant Absolute Salinity.

    Click for a more detailed description of the first
    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 =  The derivative of specific entropy with respect to
              Absolute Salinity (in units of g/kg) at constant Conservative
              Temperature.  The eta_SA output has units of:
                                           [ J/(kg K(g/kg))]  or [ J/(g K) ]
    eta_CT =  The derivative of specific entropy with respect to
              Conservative Temperature at constant Absolute Salinity.
              The eta_CT output has units of:                 [ J/(kg K^2) ]

## 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, eta_CT] = gsw_entropy_first_derivatives(SA,CT)

    eta_SA =

      -0.263286800711655
      -0.263977276574528
      -0.255367497912925
      -0.238066586439561
      -0.234438260606436
      -0.232820684341694

    eta_CT =

      13.221031210083824
      13.236911191313675
      13.489004628681361
      14.086599016583795
      14.257729576432077
      14.386429945649411

## AUTHOR:

    Trevor McDougall.                               [ 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. (A.12.8) and (P.14a, c) of this TEOS-10 Manual.

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