GIBBS' PAPERS I AND II 37 



Lecture XXII (December 18, 1899). A detailed discussion of 

 the characteristics of the thermodynamic surface with respect to 

 increasing entropy.* 



Lecture XXIII {January 11, 1900). The surface hes on the 

 negative entropy side of any tangent plane. If the surface in 

 the immediate vicinity of the point of tangency lies on the nega- 

 tive entropy side of the plane, the substance is in a stable state 

 for infinitesimal variations from the state represented by the 

 point of tangency. In like manner as an isolated system tends 

 to a state of minimum energy it follows that if the surface lies 

 upon that side of the tangent plane upon which energy increases 

 the state represented by the point of tangency will be one of 

 stable equilibrium ; if at a considerable distance from this point 

 the plane again cuts the surface we have a kind of instability 

 (the state is not entirely stable) but there is still stability for 

 small variations. 



then heat up from the reservoir). The work would be less, say w. By 

 the time the medium had absorbed the heat from the reservoir its energy 

 would however be the same. For the two processes we have therefore 

 Q — W = q — w or Q — q = W — w>0 or Q>q. When the heat Q is 

 transferred from the reservoir to the medium isothermally at tempera- 

 ture t, the medium gains entropy to the amount Q/t and the reservoir 

 loses the same amount of entropy. In the adiabatic decompression and 

 subsequent heating the medium gains the same amount of entropy Q/t 

 but the reservoir loses only q/t so that the system consisting of reservoir 

 and medium gains the amount {Q — q)/t of entropy. To put this in 

 another light suppose there are two like cylinders one in condition vi, t 

 which expands adiabatically to state V2, t and then heats up as above and 

 the other in state V2, t which is compressed isothermally in contact with 

 the reservoir to (^i, t) as in stage (4) of the Carnot cycle. The operation 

 of the two will result in work W — w being done on the media. In the 

 final condition the two cylinders have only interchanged states. The 

 reservoir has gained the heat Q — q equivalent to the work done and the 

 system consisting of the two cylinders and medium will have gained the 

 entropy (Q — q)/t representing the irreversibility in the process. 



* This was essentially a review and illustration of the close of the pre- 

 vious lecture, consideration being also given to the kind of isothermals 

 encountered in van der Waals' equation. It does not seem worth while 

 to follow this detail here, though it was helpful to the class in gaining a 

 better appreciation of the subject matter. The long Christmas vacation 

 intervened at this point in the course. 



