88 Prof. Clausius on the Internal Work 



together, or subtracted from one another, however various the 

 forces may be to which they are referable. 



It is therefore convenient to alter the form of the above theorem 

 by introducing, instead of the forces themselves, the work done 

 in overcoming them. In this form it reads as follows : — 



The mechanical wm*k which can he exerted by heat in any altera- 

 tion of the arrangement of a body is proportional to the absolute 

 temperature at which this alteration occurs. 



§ 4«. The theorem does not speak of the work which the heat 

 does, but of the work which it can do ; and similarly, in the first 

 form of the theorem, the resistances which the heat can overcome 

 are spoken of. This distinction is necessary for the following 

 reasons. 



Since the external forces which act upon a body while it is 

 undergoing an alteration of arrangement may vary very greatly, 

 it may happen that the heat, while causing an alteration of 

 arrangement, has not to overcome the whole resistance which 

 it would be possible for it to overcome. A well-known and 

 often- quoted example of this is afforded by a gas which expands 

 under such conditions that it has not to overcome an oppo- 

 sing pressure equal to its own expansive force, as, for in- 

 stance, when the space filled by the gas is made to communi- 

 cate with another which is empty, or contains a gas of lower 

 pressure. In order in such cases to determine the force of the 

 heat, we must evidently not consider the resistance which actu- 

 ally is overcome, but that which can be overcome. 



Also in alterations of arrangement of the opposite kind, that 

 is, where the action of heat is overcome by the opposing forces, a 

 similar distinction may require to be made, but in this case only 

 as far as this — that the total amount of the forces by which the 

 action of the heat is overcome may be greater than the active 

 force of the heat, but not smaller. 



Cases in which these differences occur may be thus charac- 

 terized. When an alteration of arrangement takes place so that 

 the force and counterforce are equal, the alteration can take 

 place in the reverse direction also under the influence of the same 

 forces. But if it occurs so that the overcoming force is greater 

 than that which is overcome, the transformation cannot take 

 place in the opposite direction under the influence of the same 

 forces. We may say that the transformation has occurred in the 

 first case in a reversible manner, and in the second case in an 

 irreversible manner. 



Strictly speaking, the overcoming force must always be more 

 powerful than the force which it overcomes ; but as the excess 

 of force does not require to have any assignable value, we may 

 think of it as becoming continually smaller and smaller, so that 



