184 Dr. Schroeder van der Kolk on Gases. 



^90.00 



We have consequently for carbonic acid k = — = 19*1923, 



k 

 and, from the formula, c t — c= y =0*045468, towards which 



value the numbers of the Table also converge. 



In the case of air and of carbonic acid, either c or c v or both, 

 change with the pressure and temperature. 



§ VII. On the Internal Work of Gases. 



Heat which is imparted to a body is in general used for three 

 purposes — in increasiug the temperature, and in internal and 

 external work. Of these three, that which is changed into ex- 

 ternal work can be most easily determined; and if this quantity 

 is subtracted from the total heat used, the sum of that applied to 

 the other two purposes is obtained. Let us suppose a kilogramme 

 of air at 4° and 0*76 metre pressure. Let the quantity of heat 

 necessary to raise this through 1° C. under constant volume be 

 c, the quantity used under constant pressure is a 4-0*069470. 

 But in the latter case work is performed, the magnitude of which 

 is easily determined. Under constant pressure the formulae 

 before and after the heating are 



pv = kr, /™i = (t + 1)(&+^J, 

 from which is obtained 



p{v\ — v)=k+ — (t+1). 

 dr 



The external work done is therefore in thermal units 



1 f 7 dk , ■ 1 



J |, + _ (T+1) | 



dk 

 In this case k and -y- must be calculated from the formulae pre- 

 viously obtained for 0*76 metre and 4°; 



t+1=273-15 + 5 = 278-15, 



and J is the mechanical equivalent of heat. This quantity of 

 heat is found to =0069420. 



Hence if a kilogramme of air, under a constant pressure of 0*76 

 metre is heated from 4° to 5°, the excess of heat which the air 

 contains at 5° over that which it contains at 4° is 



= c + 0-06947 - 0-06942 = c + 0-00005. 



In heating under constant volume, the heat c is to be added, by 

 which the pressure increases from 0*76 metre to 



278 



~- xO m - 76 = 0-7626. 



