400 M. R. Clausius on the Deportment of Vapour 



carried on until the tension sinks to 1 atmosjjliere. According 

 to Regnault's determination, we must set /, = 152°"2 or = 180°*3, 

 and ^0 = 100'^; from this we obtain the values 



Qi = 5.2-1 or =74-9 units of heat. . . . (I.) 



As second case, wc will again assume that a unit of weight of 

 saturated vapour at the temperature /, above 100° is enclosed in 

 a vessel separated from water, and that an orifice is made in the 

 vessel through which the vapour can issue into the atmosphere. 

 We will follow it at the other side of the orifice until a distance 

 is attained where its expansive force is exactly equal to the atmo- 

 spheric pressure, the vapour being supposed to remain unmixed 

 with air, and inquire how much heat must be imparted to the 

 entire mass of vapour during its passage, so that it may remain 

 throughout gaseous and saturated. 



The interior work which the vapour has to execute during this 

 expansion is exactly the same as in the first case ; for here the 

 state of the vapour at the commencement and at the end is the 

 same as there. Tlie exterior Avork, on the contrary, is much less ; 

 for while, in the first case, the resistance at the commencement 

 was equal to the tension which corresponds to the temperature 

 /j, and decreased slowly to one atmosphere, in the present in- 

 stance the resistance is only one atmos]ihere from beginning to 

 end. The amount of heat converted into work is therefore in 

 the present case less, and hence a much smaller quantity is 

 I'equired from without to preserve the vapour gaseous. 



That this difference in regard to the quantity of heat con- 

 sumed actually occurs, is already established with complete di- 

 stinctness by the experiments of Joide vnth atmospheric air*. 

 He found that by pumping air into a rigid vessel, the mode of 

 compression here being analogous to the first of the above two 

 cases, much more heat was developed than disappeared when the 

 compressed air was permitted to stream into a space where the 

 pressure of one atmosphere was exerted, the process here being 

 analogous to our second case. These two quantities were nearly 

 in tlie ratio of the quantities of work calculated according to the 

 foregoing principles. 



In order to carry out the calculation in our case, we must, in 

 reality, besides the resistance of the atmosphere, take two other 

 quantities into account ; namely, the resistance due to the fric- 

 tion of the vapour as it issues, and the work which must be ex- 

 pended to coumiunicate to the vapour the motion which it still 

 possesses at the point where its tension is equal to the pressure 

 of the atmosphere. To overcome the friction, a certain quantity 



* On the Changes of Temperature produced by the Rarefaction and 

 Condensation of Ah-, by J. P. Joule. Phil. Mag. vol. xxvi. p. 369. 



