# gsw_enthalpy_first_derivatives_wrt_t_exact

`first derivatives of enthalpy`

## 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`