# gsw_internal_energy_second_derivatives_CT_exact

second derivatives of internal energy

## Contents

## USAGE:

[u_SA_SA, u_SA_CT, u_CT_CT, u_SA_P, u_CT_P] = ... gsw_internal_energy_second_derivatives_CT_exact(SA,CT,p)

## DESCRIPTION:

Calculates the following five second-order derivatives of internal energy, (1) u_SA_SA, second order derivative with respect to Absolute Salinity at constant CT & p. (2) u_SA_CT, second order derivative with respect to SA & CT at constant p. (3) u_CT_CT, second order derivative with respect to CT at constant SA & p. (4) u_SA_P, second-order derivative with respect to SA & P at constant CT. (5) u_CT_P, second-order derivative with respect to CT & P at constant SA

Note that this function uses the full Gibbs function. There is an alternative to calling this function, namely gsw_internal_energy_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).

## 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:

u_SA_SA = The second derivative of internal energy with respect to Absolute Salinity at constant CT & p. [ (J/kg)(g/kg)^-2 ] u_SA_CT = The second derivative of internal energy with respect to SA & CT at constant p. [ (J/kg)(g/kg)^-1 K^-1] u_CT_CT = The second derivative of internal energy with respect to CT at constant SA and p. [ (J/kg) K^-2 ] u_SA_P = The second derivative of internal energy with respect to SA & P at constant CT. [ (J/kg)(g/kg)^-1 Pa^-1 ] u_CT_P = The second derivative of internal energy with respect to CT & P at constant SA. [ (J/kg) K^-1 Pa^-1 ]

## 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;]

[u_SA_SA, u_SA_CT, u_CT_CT, u_SA_P, u_CT_P] = ... gsw_internal_energy_second_derivatives_CT_exact(SA,CT,p)

u_SA_SA =

1.0e-04 *

-0.083825343496748 -0.083416792635045 -0.084948480848605 -0.085554093346234 -0.014989876934701 0.151822855467358

u_SA_CT =

1.0e-03 *

-0.131960094412962 -0.131426154575457 -0.143661243353954 -0.176542994620612 0.038873103109403 0.578487406867507

u_CT_CT =

-0.000723400187344 -0.000719998992295 -0.000745814518760 -0.000736301199729 0.000456106079104 0.003383686798365

u_SA_P =

1.0e-07 *

-0.002355222222595 -0.007035025555756 -0.016468311540362 -0.035407474852142 -0.084808691842265 -0.141942939648594

u_CT_P =

1.0e-07 *

-0.001718583707015 -0.005204387424044 -0.015207379618322 -0.049042313140502 -0.129085760730138 -0.230817132562563

## 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.

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