150 



nu'lrii' iti-(»>;-rc'ssi()ii i-('i)r('s('iitiii,u- llif ('(tursc of tempera- 

 ture: 13: 15 = ().S()(). Willi lliis latio one ealeulates 1lie 

 temjH'rntiire after ii minutes, wliieli is 15 X 0.86()". hi 

 general, there is a uood agi^eemeiit hdwceii the ex})eri- 

 mental and the calcnhited eooiiiiu' eui'ves. 



As to the portion Bf (Figure 17), it is a straight line in 

 the ideal conditions assumed. When the decreasing tem- 

 perature reaches 0°, water begins to freeze and, by liberat- 

 ing heat, it ])revents a further dro]) of the temperature. 

 Theoretieally, if the entii'e mass of watei- were at 0° and if 

 the heat liberated could be eliminated instantly, freezing 

 would be completed at once. But a portion only of water is 

 at 0° and freezes, the remnant is at a slightly higher tem- 

 perature and stays liquid. The heat liberated by the part 

 which freezes contributes to maintain the temperature of 

 the non-frozen i)ortion above 0° and delays the complete 

 freezing of the mass. The curve then stays horizontal, 

 there being an exact balance between the quantity of heat 

 which is withdrawn by the bath and which would bring the 

 temperature down, and the quantity of heat which is pro- 

 duced by f i-eezing and which would bring the temperature 

 up. 



The length of the horizontal portion of the curve depends 

 on two main factors : the velocity of withdrawal of heat, and 

 the mass of liquid to be frozen. Concerning the rate of 

 withdrawal of heat from the freezing mass one should 

 remember that it does not remain constant during the 

 process of freezing, even if the temperature of the cooling- 

 bath stays constant. While the material is being solidified, 

 there is a gradual increase in heat conductivity and conse- 

 quently the rate of withdrawal of heat increases. It is 

 evidently necessary to take into account this change when 

 one calculates the length of BC. The change in specific 

 heat can be neglected in as much as the system consisting 

 of the substances separating the freezing mass from the 

 cooling bath can be compared to a wall limited by two 

 surfaces at constant tem])eratures (see, above, the treat- 

 ment of the "Problem of the wall")- iVnother factor 



