THERMODYNAMIC PROPERTIES OF SUBSTANCES. 



51 



body can be increased without changing the energy of the body 

 or increasing its volume, 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 rj. This might 

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



* 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 question 

 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 the 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 length, 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 

 TH~Tfj = 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 the body of which the temperature 

 remains fixed at the freezing point, and impart to another of which the temperature 

 remains fixed at the boiling point). 



Q 



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

 energy are illustrated by figure 3, which represents a plane perpendicular to the axis 

 of v and passing through the point A, which represents the initial state of the body. 

 MN is the section of the surface of dissipated energy. Qe and QT; are sections of the 

 planes r) = and e = 0, and therefore parallel to the axes of e and 77 respectively. AD and 

 AE are the energy and entropy of the body in its initial state, AB and AC its available 

 energy and its capacity for entropy respectively. It will be observed that when either 

 the available energy or the capacity for entropy of the body is 0, the other has the same 

 value. Except in this case, either quantity may be varied without affecting the other. 

 For, on account of the curvature of the surface of dissipated energy, it is evidently 

 possible to change the position of the point representing the initial state of the body so 

 as to vary its distance from the surface measured parallel to one axis without varying 

 that measured parallel to the other. 



As the different sense in which the word entropy has been used by different 

 writers is liable to cause misunderstanding, it may not be out of place to add a 



