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A body which is either emitting heat, or altering its dimensions against resisting forces, is doing work upon matter external to it. The mechanical effect of this work, in one case is the excitation of thermal motions, and in the other the overcoming of resistances. The body must itself be altering in its circumstances, so as to contain a less store of energy within it, by an amount precisely equal to the aggregate value of the mechanical effects produced; and conversely, the aggregate value of the mechanical effects produced, must depend solely on the initial and final states of the body, and is therefore the same, whatever be the intermediate states through which the body passes, provided the initial and final states be the same.

The total intrinsic energy of a body might be defined as the mechanical value of all the effect it would produce, in heat emitted and in resistances overcome, if it were cooled to the utmost, and allowed to contract indefinitely or to expand indefinitely according as the forces between its particles are attractive or repulsive, when the thermal motions within it are all stopped: but in our present state of ignorance regarding perfect cold, and the nature of molecular forces, we cannot determine this “total intrinsic energy” for any portion of matter; nor even can we be sure that it is not infinitely great for a finite portion of matter. Hence it is convenient to choose a certain state, as standard for the body under

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