VI. C A L O R I M E T R I C MEASUREMENTS 177 



l"'~ I,' = ^' <>•• (T.,„ - Tr)nn = {T, - T„.)m, (1) 



Temperature loss times mass of the warm portion is equal to tem- 

 perature gain times mass of the cold portion. The ability to raise the 

 temperature of a given amount of cold water is proportional to the 

 mass of the warmer water. 



When different substances are mixed, the relation is more compli- 

 cated. If, for example, tn grams of water at Ti is mixed with m 

 grams of steel at T2 the rise in temperature of the water is only }{o of 

 the loss in temperature by the steel. For a given difference in tem- 

 perature, therefore, a unit mass of steel has only 3^o as much "ability" 

 to raise the temperature of a given amount of a cold substance as 

 does a unit mass of water. To account for this different caloric be- 

 havior of different substances one uses the concept "specific heat," c. 

 The result of a mixing trial with two different substances at different 

 temperatures may then be expressed as follows: 



(r,„ - TOwifi = (T2 - TJm^c, (2) 



where Ti, T2 — original temperature of components, Tm = tempera- 

 ture of the mixture, m = mass (in grams), and c = specific heat. 



For mixtures of several (0 components one may generally formu- 

 late : 



Tm = ^T {miCjl^miCi (3) 



where the product of mass and specific heat (WiCj) represents the heat 

 capacity. The final temperature of a mixture is thus equal to the sum 

 of all the products of temperature times heat capacity of the compo- 

 nents. The latter sum is the heat capacity of the mixture. 



To determine specific heats one may formulate from equation (2) : 



m^JTm - 7^1) ,,. 



C2 = C\ (4; 



yn,{T, - Tm) 



The specific heat of water is arbitrarily chosen as unity, thus if the 

 substance 1 in equation (4) is water, Ci = 1. Heat capacities and 

 specific heat are then expressed in tenns of the heat capacity of 1 

 gram of water. 



The simplifying assumption that heat capacity is independent of 

 temperature is only approximately correct. One might define a 

 temperature scale, say between the freezing and the boiling points of 



