278 PRINCIPLES OF THE MECHANICAL THEORY OF HEAT. 



of tlie law of Dnlonor and Petit only when both quantities i and e are completely 

 null. Only in special cases can the qnantities e and i be small enough to admit 

 of their being neglected. This circumstance, however, makes it possible to 

 ascertain the value of the quantity Jc. 



For solid and fluid bodies the expansion which corresponds to an elevation of 

 temperature by 1° is so slight that we may overlook, without sensible error, the 

 external tvork thereby executed ; for this case, therefore, we have 



s=:k + i .... (2). 



On the other hand, it may be assumed that, at least with the ponnanent gases, 

 .the infernal loork is null ; whence, for these we have 



s=lc-\-e .... (3), 



if by s the specific heat ©f these gases under constant pressure be indicated. For 

 the case in which the gas is so eoniined as not to be capable of expanding fi'om 

 subsequent heating, e is also null ; and we then have 



s'=lc .... (4), 



if by s' lie indicated the specific heat f)f gases under constant volume. 



According to the experiments of Regnault, the specific heat is, with constant 

 volume, for oxygen gas, 0.1551 j for hydrogen gas, 2.4153 ; for nitrogen gas, 

 0.1712; whence the atomic heat is for oxygen gas, 0.1551 • 16 = 2.4816; for 

 hydrogen gas, 2.4153-1 = 2.4153; for nitrogen gas, 0.1712-14 = 2.3968. 

 We will take, then, 2.4 for the approximate value of the atomic heat under con- 

 stant volume, for the gases named. 



This value, 2.4, we will now designate as absolute atomic heat. It would l)e 

 the atomic heat for all elements, whether in a fluid, solid, or gaseous state, if all 

 the heat supplied to them inured exclusively to the auguientation of the vibra- 

 tory work, and none of it were employed for internal and external work. 



The knowledge of the absolute atomic heat 2.4 enables us to ascertain what 

 part of the specific heat S of a bod}'^ inures to the elevation of temperature, and 

 what part thereof becomes latent through the performance of internal or external 

 labor. For solid elements the atomic heat is, according to equation (2), 



S2)= {lc-\-i)p. 



For the absolute atomic heat Icp of all elements we have found the value 2.4; 

 whence, 



(s— i)»=2.4, and s—i — "" . 

 P 



2 4. 



The quotient -^, which we will call the absolute specific Jieat, or the absolute 



heat-capacity, is the same quantity which we designated above by /.: ; we find it 



for cacli element if we employ its atonric weighty? as a divisor for 2.4. 



2 4 

 Thus, for exanqde, wo obtain for copper ]c^^-^[^- =0.0378. Of the quan- 



63.4 



tity of heat 0.0949, which must b(! supplied to one gram of copper in order to 



raise its temperature 1°, only 0.0378 units of heat are expended for the elevation 



of temperatm-e, (increase of vibratory work;) the rest, 0.0949 — 0.0378 = 0.0571 



units of heat, are consumed hn- internal work, and hence are latent. In the same 



vvH.y we obtain for certain solid elements, which are exhibited together in the fol- 



