SECT. 1] PHYSICAL PROPERTIES OF SEA -WATER 19 



If we define r to be the fractional lowering of vapour pressure, {pv^ — pv)lpv^, 

 where ^v" is the vapour pressure of pure water at the same temperature, we 

 can write (41) as 



(42) 



neglecting Vw in comparison with Vy. The constant R has the value 46.15 db cm/g 

 "'C for pressure in decibars (db). From (42), we see that jjlv, can be expressed 

 in the form 



/xw = [x^^ + RT\n{l-r), (43) 



where />tw° is the chemical potential of pure water at the same temperature. 



A similar comparison of two sea-water systems of slightly differing salinities 

 in equilibrium with ice yields 



'Ys = -(^--^i-)-aJ' (4*) 



where T{7]v/ — r)ice) is the heat of fusion of ice. Again, at the boiling point of sea- 

 water, we have 



S-=irj^-rj^)—, (45) 



where T{rjy — rjw) is the heat of vaporization of sea-water. 



We can find the osmotic pressure, tt, by considering it to be the excess of 

 pressure required to bring sea-water into equilibrium with pure water across a 

 semi-permeable membrane. In the equilibrium, we have 



fl^^ip) = fl^{p + 7T). (46) 



Comparing two such systems containing sea-water of slightly different salinities, 

 we obtain 



= /\^.^^A.-s^As, 

 dp 8s 



so that 



da 8av! 8iT Stt RT 8r ,^„. 



ds dp ds ds 1—r 8s 



The change of osmotic pressure with temperature is given by 



dn 



dlT /AO\ 



Vy,^^ = T7w-i7w" (48) 



