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I.

GRAPHICAL METHODS IN THE THERMODYNAMICS OF FLUIDS.

[Transactions of the Connecticut Academy, II., pp. 309–342, April–May, 1873.]

Although geometrical representations of propositions in the thermodynamics of fluids are in general use, and have done good service in disseminating clear notions in this science, yet they have by no means received the extension in respect to variety and generality of which they are capable. So far as regards a general graphical method, which can exhibit at once all the thermodynamic properties of a fluid concerned in reversible processes, and serve alike for the demonstration of general theorems and the numerical solution of particular problems, it is the general if not the universal practice to use diagrams in which the rectilinear co-ordinates represent volume and pressure. The object of this article is to call attention to certain diagrams of different construction, which afford graphical methods co-extensive in their applications with that in ordinary use, and preferable to it in many cases in respect to distinctness or of convenience.

Quantities and Relations which are to be represented by the Diagram.

We have to consider the following quantities:—

⁠ $v$ , the volume,	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right\}\,}$ of a given body in any state,
⁠ $p$ , the pressure,
⁠ $t$ , the (absolute) temperature,
⁠ $\epsilon$ , the energy,
⁠ $\eta$ , the entropy,
also $W$ , the work done,	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$ by the body in passing from one state to another.
and $H$ , the heat received^[1],

↑ Work spent upon the body is as usual to be considered as a negative quantity of work done by the body, and heat given out by the body as a negative quantity of heat received by it. It is taken for granted that the body has a uniform temperature throughout, and that the pressure (or expansive force) has a uniform value both for all points in the body and for all directions. This, it will be observed, will exclude irreversible processes, but will not entirely exclude solids, although the condition of equal pressure in all directions renders the case very limited, in which they come within the scope of the discussion.

g.i.

A

[1] Work spent upon the body is as usual to be considered as a negative quantity of work done by the body, and heat given out by the body as a negative quantity of heat received by it. It is taken for granted that the body has a uniform temperature throughout, and that the pressure (or expansive force) has a uniform value both for all points in the body and for all directions. This, it will be observed, will exclude irreversible processes, but will not entirely exclude solids, although the condition of equal pressure in all directions renders the case very limited, in which they come within the scope of the discussion.

[1]