290 E. G. Spaulding 



Conversely, if work is done on the system, the value of this equa- 

 tion v^ill be negative. Transposing equation [i] we get: 



E=W+{U,-U,) [2] 



The considerations leading to the formulation of the Second 

 Law must be presented in some detail; for on its derivation in this 

 form there hinges the demonstration that the computation of the 

 energy of segmentation means the application of the Four Laws. 

 Now it is well known, that, if we have a system by which, for exam- 

 ple, a definite quantity of heat energy is transformed into work, 

 while the system itself is not permanently modified, and granted 

 that the process is taking place at different temperatures, the con- 

 ditions which under it will give the maximum amount of work are: 

 first, that there is no passage of heat by such direct processes as 

 conduction or radiation; second, that there is no attendant irrevers- 

 ible process, such as friction; and third, and positive, that all the 

 changes must take place under equilibrium conditions; that is, 

 the intensity of the energy form undergoing change (within the 

 system) must be compensated by an intensity externally applied 

 and sensibly equal to it; this must simply be as great as is consistent 

 with the occurrence of the change, since the work therewith pro- 

 duced is the greater, the greater the value of the compensating 

 intensity. For the occurrence of the change, then, this external 

 intensity need be less by only an infinitesimal amount than that 

 within the system. These three conditions are, however, simply 

 those which must be set up in order to bring about the reversibility 

 of a process in a system; in fact, only on condition that the process 

 is cyclical and reversible, will the system not be modified and the 

 maximum amount of work be produced. 



Now such a process will, as is well known, have four phases, 

 the detailed analysis of which is, therefore, not required here. 

 Their examination leads to the familiar expression 



^ = e. ^'^=^' [3] 



for the amount of work produced in such a cyclical process in terms 



