50 REPRESENTATION BY SURFACES OF THE 



such as at the close of the processes are left in their initial con- 

 dition. 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 the body is in a state represented by any point of the surface of 

 dissipated 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 represented by a point in the 

 thermodynamic surface, if this point is not in the surface of dissipated 

 energy, because the equilibrium of the body is unstable in regard to 

 discontinuous changes, a certain amount of energy will be available 

 under the conditions for the production of work. Or, if the body is 

 solid, even if it is uniform in state throughout, its pressure (or tension) 

 may have different values in different directions, and in this way it 

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

 body are in different states, this will in general be a source of avail- 

 able 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, entropies, 

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

 viva of sensible motions.) These values of v, r\, and e will determine 

 the position of a certain point which we will speak of as representing 

 the initial state. 



Now the condition that no heat shall be allowed to pass, to ex- 

 ternal bodies, requires that the 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 

 without increasing its volume or diminishing its entropy. This 

 quantity will be represented geometrically by the distance of the 

 point representing the initial state from the surface of dissipated 

 energy measured parallel to the axis of e. 



Let us consider a different problem. A certain initial state of the 

 body is given as before. No work is allowed to be done upon or by 

 external bodies. Heat is allowed to pass to and from them only on 

 condition that the algebraic sum of all heat which thus passes shall 

 be 0. From both these conditions any bodies may be excepted, which 

 shall be left at the close of the processes in their initial state. More- 

 over, it is not allowed to increase the volume of the body. It is 

 required to find the greatest amount by which it is possible under 

 these conditions to diminish the entropy of an external system. 

 This will be, evidently, the amount by which the entropy of the 



