Page:Scientific Papers of Josiah Willard Gibbs.djvu/87

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 $\eta$. This might be called the capacity for entropy of the body in the given state.^[1]

1. 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 ot 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 of 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 ${\tfrac {1}{273}}-{\tfrac {1}{373}}=0.00098$, 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).
   

   

   The relations of these quantities to one another and the surface of dissipated energly 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. $Q_{\epsilon }$ and $Q_{\eta }$ are sections of the planes $\eta =0$ and $\epsilon =0$, and therefore parallel to the axes of $\epsilon$ and $\eta$ respectively. $AD$ and $AE$ are the energy and entropy of the body in its initial state, $AB$ and $AC$ its available energy and entropy of the body in 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