212 Prof. Clausius on the Internal Work of a Mass of Matter. 



tity of heat H and the temperature T. If we call the mass of 

 the body m, and its true specific heat c, we have, for an alteration 

 of temperature throughout amounting to dT, the equation 



dll = mcdT (23) 



According to what has been said above, the true specific heat of 

 a body is independent of the arrangement of its particles; and 

 since a condition is known, namely, that of the perfect gases, for 

 which we must regard it as established, partly by existing expe- 

 rimental data, and partly as the result of theoretical considera- 

 tions, that the true specific heat is independent of temperature, 

 we may assume the same thing for the other states of aggrega- 

 tion, and may regard the true specific heat as always constant. 

 Thence it follows that the amount of heat present in a body is 

 simply proportional to its absolute temperature, inasmuch as we 

 can write 



H=mcT (24) 



The foregoing equation still remains applicable even when the 

 body is not homogeneous, but consists of different substances, 

 all, however, at the temperature T, if for c we substitute the cor- 

 responding mean value. On the other hand, if different parts of 

 the body have different temperatures, we must in the first instance 

 apply the equation to the separate parts, and then unite the 

 various equations by summation. If, for the sake of generality, 

 we assume that the temperature varies continuously, so that the 

 body must be conceived as divided into an infinite number of 

 parts, the equation takes the following form : 



H 



= I cTdm (25) 



Applying this expression to the integral given above for the 

 transformation-value of the heat in the body, and denoting the 

 initial temperature by T , we obtain, for the more simple case in 

 which the temperature is uniform throughout, 



1 -jjr—mc\ T^wclogjjr, . . . (26) 



and, as a general expression embracing all cases, 



I -Tp- = j c log ^ . dm. ..... (27) 



If the disgregation of a body is altered, without heat being 

 supplied to or withdrawn from it, by an external object, the 

 amount of heat contained in the body must be changed in con- 

 sequence of the production or consumption of heat attendant on 

 the alteration of disgregation, and a rise or fall of temperature 



