342 HERMANN VON HELMHOLTZ 



no necessary remainder' merely signifies that when the process 

 is carefully conducted, the remainder which is lost in, e.g., 

 friction, elastic after-effect, electrical resistance, and so on, and 

 converted into heat, may be made minimal. Conversion with- 

 out remainder can only be an ideal limit for our terrestrial 

 conditions, to which we can approximate more or less closely. 

 Still there is a great difference between these losses of the 

 freely convertible energy and those which we encounter in 

 heat, where an important fraction, which cannot be diminished 

 by any precautions known to us, necessarily remains over in 

 the form of heat. 



' We already know that chemical forces can develop not 

 merely heat, but mechanical work also, either immediately or 

 by setting up electric currents. This brings in the question, to 

 what part of their work the free energy corresponds, and what 

 other part on the contrary appears exclusively in the form of 

 heat. It is well known that an extraordinary number of 

 chemical changes in the state of aggregation occur ; in these 

 also heat may become free or bound. Of this heat we already 

 know that it is subject to the limitations of Carnot's law. 

 Moreover, it has long been known and proved in thermo- 

 chemical work that this binding and loosing of heat plays its 

 part in the alteration of the state of aggregation ; and that we 

 may even have chemical processes that are self-initiated and 

 self-developed, as in the mixture of ice and salt, which engenders 

 cold, and in which external heat must be introduced before the 

 initial temperature can be reinstated. Here then the salt 

 solution that results has more internal energy than the dry 

 salt and snow had previously. 



' Further it is clear that the sudden alterations of the state 

 of aggregation represent only the most striking cases of such 

 binding and loosing of latent heat. We are equally justified 

 in regarding the cooling which occurs when a gas expands 

 as a binding of heat ; it is true that with slow expansion this 

 will in the latter case be reconverted wholly or almost entirely 

 into mechanical work, but even the latent heat of steam includes 

 the work done in overcoming the pressure on the steam. In 

 the sudden expansion of a gas without resistance, as in Joule's 

 experiments, there is indeed no cooling, but this is only because 

 the initial work performed in producing the vis viva of the 



