# gsw_enthalpy_second_derivatives_CT_exact

`second derivatives of enthalpy`

## USAGE:

`[h_SA_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_second_derivatives_CT_exact(SA,CT,p)`

## DESCRIPTION:

```Calculates the following three second-order derivatives of specific
enthalpy (h),
(1) h_SA_SA, second order derivative with respect to Absolute Salinity
at constant CT & p.
(2) h_SA_CT, second order derivative with respect to SA & CT at
constant p.
(3) h_CT_CT, second order derivative with respect to CT at constant
SA & p.```
```Note that this function uses the full Gibbs function.  There is an
alternative to calling this function, namely
gsw_enthalpy_second_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 second 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_SA  =  The second derivative of specific enthalpy with respect to
Absolute Salinity at constant CT & p.    [ J/(kg (g/kg)^2) ]
h_SA_CT  =  The second derivative of specific enthalpy with respect to
SA and CT at constant p.                  [ J/(kg K(g/kg)) ]
h_CT_CT  =  The second derivative of specific enthalpy with respect to
CT at constant SA and p.                      [ J/(kg K^2) ]```

## 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_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_second_derivatives_CT_exact(SA,CT,p)`
`h_SA_SA =`
```   0.000082767011576
0.000414469343141
0.001089580017293
0.002472193425998
0.006103171596320
0.010377465312463

h_SA_CT =

0.000130320164426
0.000655016236924
0.001879127443985
0.005468695168037
0.014315709000526
0.025192691262061

h_CT_CT =

0.000714365642428
0.003584965089168
0.009733337653703
0.024044402143825
0.061449390733344
0.107333638394904```

## 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.
See Notes on the first and second order isobaric derivatives of
specific enthalpy.```
```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`