400 J. TFi Gihbs on a Hepresentation by Sxrfaees 



surface of dissipated energy on the one hand, nor luive the theoreti- 

 cal interest of the primitive surface on the other. 



Problems relating to the Surface of Dissipated Energy. 



The surface of dissipated energy has an important application to a 

 certain class of problems which refer to the results which are theo- 

 retically possible with a given body or system of bodies in a given 

 initial condition. 



For example, let it be required to find the greatest amount of 

 mechanical work which can l)e obtained from a given quantity of a 

 certain substance in a given initial state, without increasing its total 

 volume or allowing heat to pass to or from external bodies, except 

 such as at the close of the processes are left in their initial condition. 

 This has been called the available energy of the body. The initial 

 state of the body is supposed to be such that the body can be made 

 to pass from it to states of dissipated energy by reversible processes. 



If tlie body is in a state represented by any ])()int of the surface of 

 dissij>ated energy, of course no work can be obtained from it under 

 the given conditions. But even if the body is in a state of thermody- 

 namic equilibrium, and therefore in one I'epresented by a point in the 

 thei'modynamic surface, if tliis jxtint is not in the surface of dissipated 

 energy, because the ecpiilibrium of the l)ody is unstable in regard to 

 discontinuous changes, a certain amount of energy will be available 

 nader the conditions for tlie })roduction of work. Or, if the body is 

 solid, even if it is uniform in state throughout, its pressure (or ten- 

 sion) may liave diiferent values in different directions, and in this way 

 it may have a certain available energy. Or, if different parts of the 

 body are in difterent states, this will in general be a source of availa- 

 ble energy. Lastly, we need not exclude the case in which the body 

 has sensible motion and its vis viva constitutes available energy. In 

 any case, we must find the initial volume, entropy, and energy of the 

 body, which will be equal to the sums of the initial volumes, entro- 

 pies, and energies of its parts. (' Energy ' is here used to include the 

 vis viva of sensible motions). These values of v, //, and f will deter- 

 mine the position of a certain point which we will speak of as repre- 

 senting the initial state. 



Now the condition that no heat shall 1)e allowed to pass to exter- 

 nal bodies, requires that tlie final entropy of the body shall not be 

 less than the initial, for it could only be made less by violating this 

 condition. The problem, therefore, may be reduced to this, — to find 

 the amount by which the energy of the body may be diminished 



