Page:Scientific Papers of Josiah Willard Gibbs.djvu/39

On the other hand $W$ and $H$ are not functions of the state of the body (or functions of any of the quantities $v$, $p$, $t$, $\epsilon$ and $\eta$), but are determined by the whole series of states through which the body is supposed to pass.

Fundamental Idea and General Properties of the Diagram.

Now if we associate a particular point in a plane with every separate state, of which the body is capable, in any continuous matter, so that states differing infinitely little are associated with points which are infinitely near to each other,^[1] the points associated with states of equal volume will form lines, which may be called lines of equal volume, the different lines being distinguished by the numerical value of the volume (as lines of volume 10, 20, 30, etc.). In the same way we may conceive of lines of equal pressure, of equal temperature, of equal energy, and of equal entropy. These lines we may also call isometric, isopiestic, isothermal, isodynamic, isentropic,^[2] and if necessary use these words as substantives.

Suppose the body to change its state, the points associated with the states through which the body passes will form a line, which we may call the path of the body. The conception of a path must include the idea of direction, to express the order in which the body passes through the series of states. With every such change of state there is connected in general a certain amount of work done, $W$, and of heat received, $H$, which we may call the work and the heat of the path.^[3] The value of these quantities may be calculated from equations (2) and (3),

$dW=pdv$,

$dH=td\eta$,

i.e., $W=\int pdv,$

(5)

$H=\int td\eta ,$

(6)

1. The method usually employed in treatises on thermodynamics, in which the rectangular co-ordinates of the point are made proportional to the volume and pressure of the body, is a single example of such an association.
2. These lines are usually known by the name given them by Rankine, adiabatic. If, however, we follow the suggestion of Clausius and call that quantity entropy, which Rankine called the thermodynamic function, it seems natural to go one step farther, and call the lines in which this quantity has a constant value isentropic.
3. For the sake of brevity, it will be convenient to use language which attributes to the diagram properties which belong to the associated states of the body. Thus it can give rise to no ambiguity, if we speak of the volume or the temperature of a point in the diagram, or of the work or heat of a line, instead of the volume or temperature of the body in the state associated with the point, or the work done or the heat received by the body in passing through the states associated with the points of the line. In like manner also we may speak of the body moving along a line in the diagram, instead of passing through the series of states represented by the line.