176 THOMSON ON CARNOT'S 



Note on the curves described in Clapeyron's 

 graphical method of exhibiting Carnot's TJieory of 

 the Steam-Engine. 



39. At any instant when the temperature of the 

 water and vapor is t, during the fourth operation 

 (see above, 16, and suppose, for the sake of sim- 

 plicity, that at the beginning of the first and at 

 the end of the fourth operation the piston is ab- 

 solutely in contact with the surface of the water), 

 the latent heat of the vapor must be precisely equal 

 to the amount of heat that would be necessary to 

 raise the temperature of the whole mass, if in the 

 liquid state, from t to S.* Hence, if v' denote the 

 volume of the vapor, c the mean capacity for heat 

 of a pound of water between the temperatures S 



* For at the end of the fourth operation the whole mass 

 is liquid, and at the temperature S. Now, this state might 

 be arrived at by first compressing the vapor into water at 

 the temperature t, and then raising the temperature of the 

 liquid to 8 ; 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-re- 

 ceived ideas connected with "Watt's law," the "latent 

 heat of steam," and "the total heat of steam." 



