# gsw_enthalpy_first_derivatives_CT_exact

first derivatives of enthalpy

## Contents

## 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