286 HEAT. 



AB represent, in Fig. 165, the small adiabatic change due to an increase 

 of pressure HB, a unit mass of the body being dealt with. Let the 

 temperature at A be 0, and that at B be + d6. Let BO be the 6 + dd 

 isothermal, and HAG the line of equal pressure through A. Then by 

 the last proposition the heat along AC equals the heat along BC. 

 But heat along BC = a.v6dp t 



while heat along AC = K p d6, 



where K p is the specific heat at constant pressure, as expressed in work 

 measure. Equating 



or 



avOdp 



= - 



If 64, is the adiabatic elasticity, i.e. the elasticity along AB defined by 



HB 



Though the area of ABC is of the 

 second order and vanishes in com- 



^^^^^_^ parison with the heat received 



/i c along either AC or BC, it may be 



of interest to show how it may be 

 used to obtain the above result 

 when equated to the corresponding 

 area on the entropy-temperature 



- ' - diagram, the two areas represent- 

 FIG. 165. * n S *h e work done, and the heat 



transformed, respectively. 



The area ABC = ^HB -AC 



z 



= -dp-avd6 

 On the entropy-temperature diagram, Fig. 166, the corresponding area is 



abc=-ab~bc 



2 



1 db 



= - - area omiic 



2 bm 



But in the limit bmnc = amnc 



= heat along ac 

 = K,d0 



ab d0 



and - 



