THERMAL CAPACITY SPECIFIC HEAT. 115 



67. Thermal Capacity Unit of Heat Specific 



Heat. The thermal capacity of a body is the quantity of 

 heat required to raise the temperature of the body one 

 degree. 



The unit of heat which is generally employed is the quan- 

 tity of heat required to raise a unit mass of water through 

 one degree C., the temperature of the water being between 

 C. and 40 C. It is called the thermal unit Centigrade. 



The specific heat of a body is the thermal capacity of a 

 unit of its mass ; and it is always to be understood that the 

 same unit of mass is employed for the body as for the water 

 mentioned in the definition of the unit of heat. Therefore, 

 specific heat is independent of the unit, and is merely the 

 ratio of the quantity of heat required to increase by 1 the 

 temperature of the body to the quantity of heat required to 

 increase by 1 the temperature of an equal mass of water. 



The quantity of heat expended in changing the tempera- 

 ture from t to t' 



varies as t' t when the mass is given, 

 and varies as the mass when t' t is given ; 



and therefore generally it varies as m (f t), if m be the 

 mass. Hence, the quantity of heat expended in changing 

 the temperature of the mass m from t to t' is 



sm (t 1 t), (1) 



where s is the specific heat of the substance, since it is the 

 quantity of heat required to raise by 1 the temperature of 

 the unit of mass, which may be shown by putting m = 1 

 and t' t I. 



Let dH denote the quantity of heat which produces in 

 the unit of mass a change of temperature dt, then the meas- 

 ure of the specific heat is -=7- 



