109 



(One recognizes the same relation as in tlic problem of the 

 wall.) 



Cooling will result from the withdrawal of heat at a 

 rate determined by the fact that every miit of weight of the 

 body requires the removal of a number of calories repre- 

 sented by the specific heat in order to be cooled by one miit 

 of temperature (say, from S to 9i). Calling m the mass 

 of the body and s its specific heat, one has 



Q=(9-90ms (b) 



Bringing the value of Q from (b) into (a) one obtains 



^^cc^'(9-t) (4) 



z ms 



that is, the cooling velocity is proportional to the area of 

 the body, to the coefficient C, to the difference between the 

 temperature of the body and that of the bath, and inversely 

 proportional to the mass and the specific heat of the body. 

 A consequence of the assumption that the cooling velocity 

 is proportional to the difference between the temperature 

 of the object and that of the bath is that, when the time is 

 increasing arithmetically by one unit, the temperature 

 decreases to a set fraction of its own value, that is geo- 

 metrically; in other words, the cooling curve is an ex- 

 ponential. Calling 9^ the temperature at the time z and 9o 

 the original temperature of the object, one has 



9. = 9„e-^^ (5) 



where e is the base of natural logarithms. 



The formulas (4) and (5) express two aspects of New- 

 ton 's ' ' Law of Cooling. ' ' 



The assumptions on which the law is based are funda- 

 mentally the same as those previously given for the prob- 

 lem of the wall. An additional condition is that the body be 

 entirely surrounded by the bath. 



If no heat escapes by radiation or convection and if all 

 contact-conductivity can be overlooked, C is the coefficient 

 of heat conductivity of the object. 



