268 PRINCIPLES OF THE MECHANICAL THEORY OF HEAT. 



r 1 



and 



or 



A<pu=.^^ 



AT' 



424 • 



u=- 



T 



(11) 



if for — we place its numerical value 424. From this equation, which is regarded 



as the second gevteral equation of the mechanical tlieorn of heat, the appropriate 

 value of w at every given temperature admits of being calculated, as r, T, and 

 ^ are known magnitudes. Thus, for example, for t^= 120° we have 

 ^^^ 424 • 522.04 ^Q 3^3 



393 • 645.1 ' 



and for ^=150°, 



424 • 500.8 



=0.3834. 



423 • 1309.3 



Our table contains in the seventh column the value of u for the temperatm'es 

 given in the first vertical series. 



To these values of ii we have only to add 0.001, (the volume of one kilogram 

 of water expressed in cubic metres,) in order to obtain the volume v, which one 

 kilogram of saturated vapor of the corresponding temperatnre occupies. The 

 numerical values of v are presented in the eighth column of our table. From 

 this wc see, for example, that one kilogram of saturated vapor of 100°, of 130°, 

 of 160°, &c., occupies the volume of 1.6459, of 0.6529, of 0.3002, &c., cubic 

 metres. 



If the saturated vapors of water followed Mariotte Gay-Lussac's law, then the 



product —^ — must be a constant magnitude. But this product is 



J. "y*^ V 



46376 for ^=100° 



37832 for /=130° 



32374 for ^=160°; 

 thus for increasing temperatures it becomes continually smaller. From the appli- 

 cation of the mechanical theory of heat to saturated vapors it results, therefore, 

 as Clausius first showed, that these do not follow Lussac's law ; that rather the 

 elasticity of saturated vapor increases less rapidly with increasing temperature 

 than the density thereof. 



Since the quotient — indicates the weight of one cubic metre of saturated 



vapor, — is the weight of one cubic decimetre, consequently, also, the spe- 

 cific weight or density of the same. The numerical values of the density of satu- 

 rated vapor are given under y in the 9tli column of our table. 



If we multiply the enlargement of volume u, which ensues from the trans- 

 formation of one kilogram of water at t° into saturated vapor of ^°, into the 

 corresponding pressure p, we obtain the external work performed through this 

 operation, while the quantity of heat spent in the performance of this work is 

 Apii. The numerical values of Apu, which stand in the 10th column of our 

 table, are, however, not calculated in the above-cited manner, but according to 



the empirical equation proposed by Zeuner: Apw=: 30.456 • log • — - , whose 

 results so nearly accord with those computed after the above theory that we may 



