372 



R. Clausius on the Application of the 



We have consequently arrived at results which differ essen- 

 tially from Pambour's views. While he assumes one and the 

 same law for the two different kinds of expansion which occur 

 in succession in the steam engine, according to which the steam, 

 originally present neither increases nor diminishes, but always 

 remains exactly at a maximum density, we have found two dif- 

 ferent equations, which permit us to recognize an opposite rela- 

 tion. According to the equation just found (xm), new steam 

 must still arise in the first expansion during the influx, and in 

 the further expansion, after the cutting off from the boiler, 

 whereby the steam does the full work corresponding to its ex- 

 pansive force, a portion of the steam present must be precipita- 

 ted according to the equation (vn) already developed. As these 

 two opposite actions of increasing and diminishing the steam, 

 which must also exert a contrary influence upon the quantity of 

 work done by the machine, partly counteract each other, the same 

 final result may occur approximately under certain circumstances, 

 as according to Pambour's more simple assumption. We must 

 not however, therefore neglect to take into consideration the dif- 

 ference found, particularly when we desire to determine in what 

 manner a change in the arrangement, or in the working of the 

 steam engine, acts upon the quantity of its work. 



36. By the help of the quantities of heat cited singly in § 34, 

 we may according to what is stated in §. 8, easily determine the 

 uncompensated transformation which occurs during the expan- 

 sion, by applying the integral which occurs in the equation 



»=-/-f 



to these quantities of heat. 



The communication of the quantities of heat m, r J — m 2 r 2 

 and^ 0 r 0 , occurs at constant temperatures, namely T x1 T 21 T 01 

 and these portions of the integral are therefore : 



and t*o r o 



For the portions of the integral arising from the quanties of heat 

 Mc{T x - T 2 ) and —pc(T 2 - T 0 ), we find, according to the process 

 already applied in § 23, the expressions : 



T T 



Mc lo g Tir an d -pe log y~ . 



1 2 1 0 



By putting the sum of these quantities in the place of the above 

 integral, we obtain for the uncompensated transformation, the 

 value : 



(38.) j^-^ + ^-Jfckgfi-^+^log^. 



X \ ^2 1 2 ^ 0 0 



37. We may now return again to the complete circular pro- 

 cess which takes place during the working of the machine, and 



