SECT. 1] PHYSICAL PROPERTIES OF SEA -WATER 17 



If an element of sea-water, at an initial temperature &i and pressure pi, is 

 raised to the surface of the ocean with no exchange of heat or salt with its 

 surroundings, its final temperature, d'f, at atmospheric pressure will be 



^f = & =-&i+r r{&', p, s) dp, (38) 



where 



&' = d'i+ r r{&, p, s) dp. 



Jpi 

 The final temperature & is called the potential temperature. 



Table IV 



Formula" for the Cooling A@ of Sea-Water of Temperature d'°C and Salinity 

 S%o for an Adiabatic Change of Pressure from a Pressure p db to Atmospheric 



Pressure 



A0CC) = 111 Aiikp^Sm 



i j k 



« Fofonoff and Froese, 1958. The minimum precision of the formula is ± 0.004°C. 



The potential temperature is useful in discussing the movement of deep 

 water in the ocean, because the effects of pressure on temperature are removed. 

 Thus, temperatures of the water at different depths may be compared. Graphs 

 giving values of the difference &i -■&■/, denoted hy A0, are shown in Fig. 5. 

 Coefficients for an empirical formula for A© are given in Table IV. Absolute 

 accuracy of both the graphs and formula is uncertain because of our inadequate 

 knowledge of the thermal expansion coefficient of sea- water (see Table I). 



4. Chemical Potential Difference 



The chemical potential difference, fx, and the partial chemical potential, jUw, of 

 water in sea-water can be determined in terms of the colligative properties of 

 sea-water, i.e. vapour-pressure lowering, freezing-point depression, boiling-point 

 elevation and osmotic pressure. 



