Josiah Willard Gibbs. 289* 



If we adhere to the Kelvin order of ideas, we can reason as follows. 

 The dissipation of energy in any material system must be relative to 

 some standard state of the system, for with regard to the absolute zero 

 of temperature all energy is mechanically available. Any group of 

 states of the system, which are mutually convertible by reversible 

 adiabatic processes, are on the same plane as regards dissipation, and 

 can serve as equivalent standard states, those namely of equal! 

 entropy . In any working process, for each infinitesimal amount of 

 heat 6H or 6 0, which is acquired in a specified state of the system at 

 temperature 0, let the portion & H ultimately arrive at one of these 

 standard states, say the one whose temperature is ; this process 

 involves somehow waste, relative to this standard state, of a part of 

 this energy, originally existing at temperature 9, of amount 

 H e SH /0 , that is 00 0<p or ((90 6>0 ) (0 )0. Thus- 

 the total unutilised energy in the given state, relative to this standard,, 



f* 



is 00 00o (0 $o)d9, where 0o is constant. In this expression the 



J0 



integral is perfectly definite ; in it is to be expressed as a function of 

 and the constitution of the system, and is the temperature at 

 which with this constitution the value of is . This dissipation is- 

 readily represented on the temperature-entropy diagram for a given 

 constitution of the system. 



For isothermal change, in which 9 is not altered by the addition of 

 the heat &H, the dissipation for an infinitesimal change is the increment 

 of 006>0o ; thus E 00 + 00 , of which the last item is now a constant, 

 serves as a function representing the mechanically available energy 

 for changes of state conducted isothermally : its gradient is therefore 

 downward in spontaneous change. 



This last result may be reached more directly, following Planck's 

 mode of exposition, by including in the system the surrounding medium 

 in thermal equilibrium with it. The change of the total entropy 

 is now &E/0, for heat of amount E has been lost from 

 the surroundings; this must be positive; thus as before it is 

 E/0 that tends to a maximum in a system maintained at 

 constant temperature. 



But neither of these ways of arriving at the adaptation of the- 

 principle of dissipation of energy, or of maximum entropy, to use in 

 the practical case of slow reaction proceeding at constant temperature,, 

 is as direct or comprehensive as Gibbs' original analytical statement. 

 As Maxwell remarked, the key to his advance on Kirchhoff and other 

 writers who had previously treated some cases of physico-chemical 

 change in more complex manner, was in definitely introducing the 

 functions of thermodynamics E and as generalised co-ordinates of the 



