R. Feistel et al.: Oceanographic application and numerical implementation of TEOS-IO: Part 1 
651 
www.ocean-sci.net/6/633/2010/ 
Ocean Sci., 6, 633-677, 2010 
Certain properties of interest are very specific for a com 
posite system and not listed in Table S7. Using Eq. (5.35), 
the isobaric evaporation rate, i.e. the decrease of the brine 
fraction b=Ssv/SA upon warming is 
3 b\ bAsvM 
9t) Ssv ,p = “ D S 
(5.37) 
The isobaric heat capacity of sea vapour computed from 
Eqs. (5.30), (S7.6) and (5.35), 
c P — — T 
9 2 g sv 
dT 2 
Ssv,P 
= (1 
b)cj, + be 
sw 
p 
sv 
3 b\ 
dT ) S S y,P 
(5.38) 
consists of the single-phase contributions of vapour, cj,, and 
brine, c® w , as well as a latent part, and is implemented as 
sea_vap_cp_seavap_si. In the latter term, the coefficient 
in front of the evaporation rate (Eq. 5.37) is the isobaric latent 
heat L® v of seawater, 
¿sv = _ TAsvlrj] = - A SV M 
'dh sw \ 
= h v -h 
sw 
Sa 
3S a 
t,p 
(5.39) 
which is available from the function 
sea_vap_enthalpy_evap_si in the library. The brine 
enthalpy, /z sw , is computed from Eq. (S7.3), and the vapour 
enthalpy, /z v , from Eq. (S2.3). 
5.6 Osmotic equilibrium seawater-liquid 
If pure water is separated from seawater by a semi-permeable 
membrane which lets water molecules pass but not salt parti 
cles, water will penetrate into the seawater, this way diluting 
it and possibly increasing its pressure, until the chemical po 
tential of water in both boxes will be the same (or the pure 
water reservoir is exhausted). In the usual model configura 
tion, the two samples are thermally coupled but may possess 
different pressures; the resulting pressure difference required 
to maintain equilibrium is the osmotic pressure of seawater. 
An example is desalination by reverse osmosis; if the pres 
sure on seawater in a vessel exceeds its osmotic pressure, 
freshwater can be squeezed out of the solution through suit 
able membrane walls (Sherwood et al., 1967). 
The defining condition for the osmotic equilibrium is 
equality of the chemical potentials of pure water at the pres 
sure P w and of water in seawater at the pressure P s , 
«w(r,P W )=gSW^ A ,r,pS)_S A ^^j . (5.40) 
In terms of the Primary Standard functions and their indepen 
dent variables (Sect. 2), Eq. (5.40) is expressed as the system 
f w + pW/ w = /S + pS/ s + _ SAg s (5. 41) 
(p W ) 2 / p W = P W (5-42) 
(p S ) 2 fp = P\ (5.43) 
which exploits the relations (Eqs. S2.6, S2.11, 4.4 and S7.12) 
to avoid stacked numerical iterations. The function 
/ F (P,p w ) is abbreviated here by / w , and similarly for 
/ s computed at the liquid-water density p s related to the 
pressure P s , as well as their partial derivatives. Equa 
tions (5.41), (5.42), (5.43) provide three conditions for the 
six unknownsSA, T, P s , P w , p s and p w , so three of these 
parameters must be specified to complete the system. Once 
this choice is made, the remaining parameters can be deter 
mined as in Appendix A8. 
Once the solution for Sa, T, P s , P w , p s and p w has been 
found, the desired properties of the equilibrium can be com 
puted, in particular the osmotic pressure, P osnl =P'' — P w . 
The related function sea_liq_osmoticpressure_si is 
implemented in the library. 
5.7 Triple point sea ice - vapour 
The equilibrium between sea ice and vapour includes three 
phases, solid, liquid and gas, and two components, water 
and salt. Air is not involved. This equilibrium state extends 
the ordinary triple point of pure water to non-zero salini 
ties, i.e. along a one-dimensional manifold. This curve is 
shown in Fig. 3 by the “Triple Line” which has the same 
T — P relation as the sublimation line because ice is in sub 
limation equilibrium with water vapour at any given brine 
salinity. Note that saturation is defined as the equilibrium 
state between water vapour and liquid water above the freez 
ing point of pure water, or, below that temperature, between 
water vapour and ice (IAPWS, 2010). Hence, as soon as ice 
is present in an equilibrium system, the water vapour in the 
gas phase is regarded as saturated. 
The equilibrium conditions for temperature, pressure and 
chemical potentials that determine the locus of triple points 
are expressed in terms of the Primary Standard as 
f + P w fj = f w + P w fj + g s - S A gl (5.44) 
/ v + p w fj = g lh (5.45) 
P=(p W ) 2 fJ (5-46)