# Theory of Heat (Maxwell, 4th edition)/Chapter 7

CHAPTER VII.
ON THE PROPERTIES OF A SUBSTANCE WHEN HEAT IS PREVENTED FROM ENTERING OR LEAVING IT.
Hitherto we have considered the properties of substance only with respect to the volume occupied by a pound of the substance, the pressure acting on every square foot or inch, and the temperature of the substance, which we have assumed to be uniform. We suppose the temperature measured by a thermometer, and when, in order to change the state of the body, heat must be supplied to it or taken from it, we have supposed this to be done without paying any attention to the quantity of heat required in each case. For the actual measurements of such quantities of heat we must employ the processes described in our chapter on Calorimetry, or others equivalent to them. Before entering on these considerations, however, we shall examine the very important case in which the changes which take place are effected without any passage of heat either into the substance from without or out of the substance into other bodies.
For the sake of associating the statement of scientific facts ​with mental images which are easily formed, and which preserve the statements in a form always ready for use, we shall suppose that the substance is contained in a cylinder fitted with a piston, and that both the cylinder and the piston are absolutely impermeable to heat, so that not only is heat prevented from getting out or in by passing completely through the cylinder or piston, but no heat can pass between the enclosed substance and the matter of the cylinder or piston itself.
No substance in nature is absolutely impermeable to heat, so that the image we have formed can never be fully realised; but it is always possible to ascertain, in each particular case, that heat has not entered or left the substance, though the methods by which this is done and the arrangements by which the condition is fulfilled are complicated. In the present discussion it would only distract our attention from the most important facts to describe the details of physical experiments. We therefore reserve any description of actual experimental methods till we can explain them in connexion with the principles on which they are founded. In explaining these principles we make use of the most suitable illustrations, without assuming that they are physically possible.
We therefore suppose the substance placed in a cylinder, and its volume and pressure regulated and measured by a piston, and we suppose that during the changes of volume and pressure of the substance no heat either enters it or leaves it.
In order to represent the relation between the volume and the pressure, we suppose a curve traced on the indicator diagram during the motion of the piston, exactly as in the case of the isothermal lines formerly described. The only difference is that whereas in the case of the isothermal lines the substance was maintained always at one and the same temperature, in the present case no heat is allowed to enter or leave the substance, which, as we shall see, is a condition of quite a different kind.
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The volume of the superheated steam also increases in a regular manner, being proportional to its absolute temperature reckoned from –460° F.
CHAPTER VIII.
ON HEAT ENGINES.
Hitherto the only use we have made of the indicator diagram is to explain the relation between the volume and the pressure of a substance placed in certain thermal conditions. The condition that the temperature is constant gave us the isothermal lines, and the condition that no communication of heat takes place gave us the adiabatic lines. We have now to consider the application of the same method to the measurements of quantities of heat and quantities of mechanical work.
At p. 102 it was shown that if the pencil of the indicator moves from B to C, this shows that the volume of the substance has increased from O $b$ to O $c$, under a pressure which was originally B $b$ and finally C $c$.
The work done by the pressure of the substance against the piston during this motion is represented by the area B $c$ C $b$, and since the volume increases during the process, it is the substance which does the work on the piston, and not the piston which does the work on the substance.
In heat engines of ordinary construction, such as steam engines and air engines, the form of the path described by the pencil depends on the mechanical arrangements of the engine, such as the opening and shutting of the valves which admit or carry off the steam.
For the purposes of scientific illustration, and for obtaining clear views of the dynamical theory of heat, we shall describe