i 



THE DIELECTRIC 105 



K : 1, and so the energy assigned to unit volume will be less in the 

 ratio 1 : K, or, instead of energy 27rD 2 per cubic centimetre, we 

 have 2-7rD 2 /K per cubic centimetre, D being the same in each 

 system since the charges are the same. 



But this is only the distribution of the energy which is added 

 by the work done in charging the system. If K varies with the tem- 

 perature heat has to be added or subtracted as well, if the tempera- 

 ture is to be kept constant. Just the same consideration comes in with 

 a wire undergoing stretch. The energy put in per unit volume by 

 the stretching force is \ stress x strain', but heat must be added or 

 subtracted to keep the temperature constant, and the total energy 

 added is stress X strain + Q, 

 where Q is the heat given to 

 unit volume. 



We can calculate the heat _pull 

 added in the electrical case by 

 taking a charged condenser 

 with a fluid dielectric through 

 a thermodynamic cycle, repre- 

 sented in Fig. 7^, where 

 al)M -ivsse represent distance apart 

 and onlinates represent pull per 

 unit area. Let the condenx r lx 

 charged with a- per unit area. 

 The pull per unit area is STT^/K. FIG. 72. 



Let the distance of the plates 



apart be increa>e<l bva small quantity / = AB, so slowly that there 

 i^ no change in the temperature #, and let heat dQ.l be added to 

 each volume / x I 2 in order to keep the temperature constant. Now 

 make a further adiabatic increase in the distance, the change being 

 represented by BC, the temperature in the dielectric which flows 

 in through the changes represented by AB and BC falling to 



dO, and the specific inductive capacity falling to K J7\d' 



Now make an isothermal decrease CD in the distance, at d0, 

 carrying it so far that a further adiabatic decrease along DA com- 

 pletes the cycle. Then if the process is exceedingly slow it is 



reversible, and the work done is dQ.l. -3- by the second law. But 

 the work done is also equal to the area A BCD, which is 



dK 



the negative >irn being given to ABCD because it is work done 

 on the system. Equating the two expressions 



