Conservation and Innovation : Helmholtz's Struggle with Energy ...

approach is discussed at length and criticised: only for gases the law established
by Clapeyron on the assumptions of the caloric theory had received empirical
support, but in the case of gases it is equivalent to Holtzmann's.
Holtzmann assumed that if a certain quantity of heat "enters" in a gas it either
produces an increase of temperature or an expansion. In this second case the
work done gives, following Helmholtz's account of Holtzmann, the possibility to
calculate the mechanical equivalent of heat. On the grounds of Dulong's values
for the specific heats of gases, Holtzmann's equivalent is 374 Kgm 182. Helmholtz
warned that this could be accepted in the framework of the conservation of force
only if all the living force of the heat communicated was actually given as work,
that is, if the sum of the living forces and the tension forces, or, in the old
terminology, the quantity of free and latent heat, of the expanded gas was the
same as the one of the denser gas at the same temperature. This approach is in
agreement with the above quoted one of Joule, and Helmholtz compared the
equivalents of Holtzmann and Joule. The 374 Kgm of the former are compared
with a series of results of the latter, who is credited with having actually
performed the experiments and not to have only reinterpreted previous data. Five
values were given from Joule's results 183: two are the already recalled ones of 452
and 521 (which, as already explained, should be 424 and 488) deriving from the
friction of water, and three (481, 464, 479 which should be 451, 435, 449) are
quoted without reference. My view is that these three values are taken from
Joule's 1845 paper: "On the Existence of an Equivalent Relation". The first
(481/451) refers to the 1843 experiments with an electromagnetic engine, the
second (464/435) to the 1845 experiments on air referred to above, and the third
one to the final average mentioned in Joule's paper 184. As noted above, the
comparison of the results of the two researchers is deeply distorted by the
systematic error in the conversion of Joule's units of measurement. The chapter
ends with a detailed discussion and comparison, which includes a table, of the
laws of Clapeyron and Holtzmann 185.
182 Helmholtz Erhaltung P. 35.
183 Helmholtz Erhaltung P. 36.
184 Going back from Helmholtz's values to British ( and not French) foot-pounds we
get 822, 793, 819 that are reasonably close to Joule's figures of 823, 795, 817 respectively.
185 Helmholtz Erhaltung P.37. Helmholtz was later to claim priority in the
interpretation of Carnot's function: see Wolff "Clausius".