# gsw_internal_energy_first_derivatives_CT_exact

    SA, CT and p partial derivatives of internal energy

## Contents

- USAGE:
- DESCRIPTION:
- INPUT:
- OUTPUT:
- EXAMPLE:
- AUTHOR:
- VERSION NUMBER:
- REFERENCES:

## USAGE:

    [u_SA, u_CT, u_P] = gsw_internal_energy_first_derivatives_CT_exact(SA,CT,p)

## DESCRIPTION:

    Calculates the three (3) partial derivatives of internal energy with
    respect to Absolute Salinity, Conservative Temperature and pressure.
    Note that the pressure derivative is done with respect to pressure in
    Pa, not dbar.

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

## INPUT:

    SA  =  Absolute Salinity                                        [ g/kg ]
    CT  =  Conservative Temperature                                [ deg C ]
    p   =  sea pressure                                             [ dbar ]
           (ie. 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  =  partial derivative of internal_energy with respect to
                 Absolute Salinity          [ (J/kg)(g/kg)^-1 ] i.e. [ J/g ]
    u_CT  =  partial derivative of internal_energy with respect to
                 Conservative Temperature                    [ (J/kg) K^-1 ]
    u_P   =  partial derivative of internal energy with respect to
                 pressure in Pa                             [ (J/kg) Pa^-1 ]

## 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;]
    p =  [     10;      50;     125;     250;     600;    1000;]

    [u_SA, u_CT, u_P] = gsw_internal_energy_first_derivatives_CT_exact(SA,CT,p)

    u_SA =

       0.071139670398649
       0.070985698896531
       0.070875347230962
       0.069718904132060
       0.049038995942071
       0.002993869194885

    u_CT =

       1.0e+03 *

       3.991835755044116
       3.991835861005662
       3.991839264045344
       3.991844967675450
       3.991815063256475
       3.991738931101772

    u_P =

       1.0e-03 *

       0.978707643200608
       0.978463914364685
       0.976704233211509
       0.974063884806538
       0.973627203540062
       0.973297117446459

## AUTHOR:

    Paul Barker and 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.

    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.

    The software is available from http://www.TEOS-10.org