# gsw_enthalpy_first_derivatives_CT_exact

`first derivatives of enthalpy`

## 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.```
```Note that this function uses the full Gibbs function.  There is an
alternative to calling this function, namely
gsw_enthalpy_first_derivatives(SA,CT,p),which uses the computationally
efficient 75-term expression for specific volume in terms of SA, CT and
p (Roquet et al., 2015).``` ```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).                     [ m^3/kg ]```

## EXAMPLE:

```SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
CT = [28.7856; 28.4329; 22.8103; 10.2600;  6.8863;  4.4036;]
p =  [     10;      50;     125;     250;     600;    1000;]```
`[h_SA, h_CT] = gsw_enthalpy_first_derivatives_CT_exact(SA,CT,p)`
`h_SA =`
```  -0.070224183838619
-0.351159869043798
-0.887036550157504
-1.829626251448858
-4.423522691827955
-7.405211691293971```
`h_CT =`
`1.0e+003 *`
```   3.991899712269790
3.992025674159605
3.992210402650973
3.992283991748418
3.992685275917238
3.993014370250710```

## AUTHOR:

`Trevor McDougall.                      [ 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.
See Eqns. (A.11.18), (A.11.15) and (A.11.12) of this TEOS-10 Manual.```
```Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate
polynomial expressions for the density and specifc volume of seawater
using the TEOS-10 standard. Ocean Modelling.```
`This software is available from http://www.TEOS-10.org`