562 PROFESSOR WILLIAM THOMSON'S ACCOUNT OF 



Note. — On the curves described in Clapeyeon's graphical method of exhibit- 

 ing Carnot's Theory of the Steam-Engine. 



39. At any instant when the temperature of the water and vapour is t, dur- 

 ing the fourth operation (see above, § 16), the latent heat of the vapour must be 

 precisely equal to the amount of heat that would be necessary to raise the tem- 

 perature of the whole mass, if in the liquid state, from ^ to S. * Hence, if tf de- 

 note the volume of the vapour, <• the mean capacity for heat of a pound of water 

 between the temperatures S and t, and W the weight of the entire mass, in pounds, 

 we have 



kv' = c (S-/) W. 



Again, the circumstances during the second operation are such that the mass of 

 liquid and vapour possesses H units of heat more than dm-ing the fourth ; and 

 consequently, at the instant of the second operation, when the temperature is t, 

 the volume v of the vapour will exceed li by an amount of which the latent heat 

 is H. so that we have 



, H 

 k 



40. Now, at any instant, the volume between the piston and its primitive 

 position is less than the actual volume of vapour by the volume of the water eva- 

 porated. Hence, if x and x denote the abscissae of the curve at the instants of 

 the second and fourth operations respectively, when the temperature is t, we have 



x^v—<sv, n! = v' — sv', 



and, therefore, by the preceding equations, 



;e=i=^{H + c(S-OW} .... (a) 

 fc 



■ ^"%(S-OW (6) 



k 



These equations, along with 



y=!/=p («) 



enable us to calculate, from the data supplied by Regnault, the abscissa and 

 ordinate for each of the curves described above (§17), corresponding to any as- 



* For, at the end of the fourth operation, the whole mass is liquid, and at the temperature {. 

 Now, this state might he arrived at by first compressing the vapour into water at the temperature t, 

 and then raising the temperature of the liquid to S ; and however this state may be arrived at, there 

 cannot, on the whole, be any heat added to or subtracted from the contents of the cylinder, since, 

 during the fourth operation, there is neither gain nor loss of heat. This reasoning is, of course, 

 founded on Carnot's fundamental principle, which is tacitly assumed in the commonly-received ideas 

 connected witli " Watt's law," the " latent heat of steam," and '• the total heat of steam." 



