of the Tlieriiiodi/iKimic PropertieH of Siihstances. 4()1 



witlioiit increasing its Aolume or cliniinisliing its entropy. This 

 quantity will be represented geometrically by the distance of the 

 point representing the initial state from the surface of dissipated en- 

 ergy measured parallel to the axis of e. 



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

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

 external l)odies. Heat is allowed to pass to ajid from them only on 

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

 be 0. From both these conditions any l»odies may be exce])ted, which 

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

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

 required to find the greatest amount by which it is possil)le under 

 these conditions to diminish the entropy of an external system. 

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

 can be increased without changing tlie energy of the body or increas- 

 ing its volnme, which is represented geometrically by the distance of 

 the point representing the initial state from the surface of dissipated 

 energy, measured parallel to the axis of //. This might be called the 

 capacity for entropy of the body in the given state.* 



Thirdly. A certain initial condition of the body is given as before. 

 No work is allowed to be done upon or by external bodies, nor any 

 heat to pass to or from them ; from which conditions bodies may be 

 excepted, as before, in which no permanent changes are produced. 

 It is required to find the amount by which the volume of the body 



* It may be worth while to call attention to the analogy and the difference between 

 this problem and the preceding. In the first case, the question is virtually, how great 

 a weight does the state of the given body enable us to raise a given distance, no other 

 permanent change being produced in external bodies. In the second case, the ques- 

 tion is virtually, what amount of heat does the state of the given body enable us to 

 take from an external body at a fixed temperature, and impart to another at a higher 

 fixed temperature. In order that the numerical values of the available energy and of 

 the capacity for entropy should be identical with tlie answers to these questions, it 

 would be necessary in the first case, if the weight is measured in units of force, that 

 the given distance, measured vertically, should be the unit of lengtli, and in the second 

 case, that the difference of the reciprocals of the fixed temperatures should be unity. 

 If we prefer to take the freezing and boiling points as the fixed temperatures, as 

 Z7 3 — iwu = 0.00098, the capacity for entropy of the body in any given condition 

 would be 0.00098 times the amount of heat which it would enable us to raise from the 

 freezing to the boiling point (i. e., to take from a body of which the temperature re- 

 mains fixed at the_ freezing point, and impart to another of wliich the temperature 

 remains fixed at the boiling point). 



The relations of these quantities to one another and to the surface of dissipated 

 energy are illustrated by figure ?>, which represents a plane perj^endicular to the axis 



