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LXXIII. On the Dynamical Theory of Heat. — Part V. On the 

 Quantities of Mechanical Energy contained in a Fluid in Dif- 

 ferent States, as to Temperature and Density. By William 

 Thomson, M.A., Professor of Natural Philosophy in the Uni- 

 versity of Glasgow*. 



[Continued from vol. iv. p. 434.] 

 81. A BODY which is either emitting heat, or altering its 

 •£*- dimensions against resisting forces, is dping 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 work 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. 



82. The total mechanical 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 inde- 

 finitely 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 

 mechanical 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 consideration, and to use the un- 

 qualified term, mechanical energy, with reference to this standard 

 state; so that the ''mechanical energy of a body in a given 

 state " will denote the mechanical value of the effects the body 

 would produce in paving from the state in which it is given, to 

 the standard state, or the mechanical value of the whole agency 

 that would be required to bring the body from the standard state 

 to the state in which it is given. 



83. In the present communication, a system of formuke 

 founded on propositions established in the first part of my paper 

 on the Dynamical Theory of Heat, and expressing relations be- 

 tween the pressure of a fluid, and the thermal capacities and 

 mechanical energy of a given mass of it, all considered as func- 

 tions of the temperature and volume ; and Carnot's function of 



* Prom the Transactions of the Royal Society of Edinburgh, vol. xx. 

 j>art '.i ; read December 15, 1851. 



