# gsw_enthalpy_first_derivatives_wrt_t_exact

    first derivatives of enthalpy

## Contents

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

## USAGE:

    [h_SA_wrt_t, h_T_wrt_t, h_P_wrt_t] = ...
                          gsw_enthalpy_first_derivatives_wrt_t_exact(SA,t,p)

## DESCRIPTION:

    Calculates the following three derivatives of specific enthalpy, h.
    These derivatives are done with respect to in-situ temperature t (in the
    case of h_T_wrt_t) or at constant in-situ tempertature (in the cases of
    h_SA_wrt_t and h_P_wrt_t).

     (1) h_T_wrt_t, the derivative with respect to Absolute Salinity at
          constant t and p.
     (2) h_T_wrt_t, derivative with respect to in-situ temperature t at
         constant SA and p.
     (3) h_P_wrt_t, derivative with respect to pressure P (in Pa) at constant
         SA and t.  This output has the same dimensions as specific volume,
         but is not equal to specific volume.

    Note that this function uses the full Gibbs function.  This function
    avoids the Nan that would exist in h_sub_SA at SA=0 if it were
    evaluated in the straightforward way from the gibbs function.

## INPUT:

    SA  =   Absolute Salinity                                       [ g/kg ]
    t   =   in-situ temperature (ITS-90)                           [ deg C ]
    p   =   sea pressure                                            [ dbar ]
            (i.e. absolute pressure - 10.1325 dbar)

    SA & t need to have the same dimensions.
    p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & t are MxN.

## OUTPUT:

    h_SA_wrt_t  =  The first derivative of specific enthalpy with respect to
                 Absolute Salinity at constant t and p.
                                              [ J/(kg (g/kg))]  i.e. [ J/g ]
    h_T_wrt_t   =  The first derivative of specific enthalpy with respect to
                 in-situ temperature, t, at constant SA and p.  [ J/(kg K) ]

    h_P_wrt_t   =  The first derivative of specific enthalpy with respect to
                 pressure P (in Pa) at constant SA and t.         [ m^3/kg ]

## 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_wrt_t, h_T_wrt_t, h_P_wrt_t] = gsw_enthalpy_first_derivatives_wrt_t_exact(SA,t,p)

    h_SA_wrt_t =

       1.0e+002 *

      -1.676848793933789
      -1.664056485876083
      -1.400297616206127
      -0.779512353439202
      -0.643802328856826
      -0.562565663262413

    h_T_wrt_t =

    1.0e+003 *

       4.002888003958537
       4.000980283927373
       3.995546468894633
       3.985076769021370
       3.973593843482723
       3.960184084786622

     h_P_wrt_t =

    1.0e+003 *

       0.882417098829581
       0.882800084327962
       0.894853437097790
       0.925305056107352
       0.931443001624161
       0.934467194091049

## AUTHOR:

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

## VERSION NUMBER:

    3.05 (16th February, 2015)

## 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.

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