250 Ice in the Sea 



According to p. 247 if Sr is the salinity of the salt solution 



(1 - ar)S, = 1, 



so that 



da, 1 dSr 



and 



Cr = C + Xr 



S2 dr ' 



S dSr 



5? dt ' 



According to the investigations of Pettersson (1878) A^ = 80 + 0-5t, The factor of 

 Xj can be calculated from investigations made by Ringer, so it is therefore possible to 

 evaluate the above equation for different temperatures and salinities (Table 94). 



Table 94. The specific heat of sea ice 

 (According to Malmgren) 



Malmgren has also determined the specific heat of ice samples experimentally, 

 and has obtained values in excellent agreement with the theoretical. At higher tem- 

 peratures the heat capacity of sea ice is quite high, at — 2°C and 15%o salinity it reaches 

 16-0 g cal. These high values can be explained either by melting or freezing of large 

 amounts of pure ice in the salt cells of the ice at temperatures close to freezing point 

 and fjr temperature changes of about 1 °C, which is accompanied by release or uptake 

 of large amounts of heat from the latent heat of melting. For sea ice the specific heat 

 and the latent heat of melting are properties closely related to each other. 



The dependence of the latent heat of melting on temperature and salinity can also 

 be calculated theoretically from Sr the salinity of the ice, and r^, the freezing tempera- 

 ture of sea-water of salinity S. If t is close to zero, the latent heat of melting for pure 

 ice will be constant between r and r^ and will be 80 g cal. The amount of heat required 

 to melt 1 g of sea ice will be made up of: (1) the heat = 80[1 — ^(1 — a-r)] required 

 to melt pure ice; and (2) the heat required to raise the temperature of the pure ice 

 and the salt solution from r to Tj,. Since the specific heat of pure water is 0-5 this 

 quantity of heat will be approximately 0-5 (xg — T)aT. The latent heat of melting of 

 sea ice will thus be given by 



U 



= ^°('-|) 



+ 0-5(t. - t) 



