# gsw_entropy_second_derivatives

`second derivatives of entropy`

## USAGE:

`[eta_SA_SA, eta_SA_CT, eta_CT_CT] = gsw_entropy_second_derivatives(SA,CT)`

## DESCRIPTION:

```Calculates the following three second-order partial derivatives of
specific entropy (eta)
(1) eta_SA_SA, the second derivative with respect to Absolute
Salinity at constant Conservative Temperature, and
(2) eta_SA_CT, the derivative with respect to Absolute Salinity and
Conservative Temperature.
(3) eta_CT_CT, the second derivative with respect to Conservative
Temperature at constant Absolute Salinity.``` ```Click for a more detailed description of the second 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_SA =  The second derivative of specific entropy with respect
to Absolute Salinity (in units of g/kg) at constant
Conservative Temperature.  eta_SA_SA has units of:
[ J/(kg K(g/kg)^2)]
eta_SA_CT =  The second derivative of specific entropy with respect
to Conservative Temperature at constant Absolute
Salinity. eta_SA_CT has units of:     [ J/(kg (g/kg) K^2) ]```
```eta_CT_CT =  The second derivative of specific entropy with respect
to Conservative Temperature at constant Absolute
Salinity.  eta_CT_CT has units of:           [ J/(kg K^3) ]```

## 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_SA, eta_SA_CT, eta_CT_CT] = gsw_entropy_second_derivatives(SA,CT)`
`eta_SA_SA =`
```  -0.007627718929669
-0.007591969960708
-0.007528186784540
-0.007455177590576
-0.007441108287466
-0.007414368396280```
`eta_SA_CT =`
```  -0.001833104216751
-0.001819473824306
-0.001580843823414
-0.000930111408561
-0.000717011215195
-0.000548410546830```
`eta_CT_CT =`
```  -0.043665023731109
-0.043781336189326
-0.045506114440888
-0.049708939454018
-0.050938690879443
-0.051875017843472```

## 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 Eqns. (P.14b) and (P.15a,b) of this TEOS-10 Manual.```
`This software is available from http://www.TEOS-10.org`