ENERGETICS 29 



are added or removed by units of one electron at a time. The question naturally 

 arises, are there similar phenomena in the case of energy ? Now, in the considera- 

 tion of the solid state of aggregation, certain phenomena have been met with which 

 suggest that energy is dealt with in units at a time, in other words, that it 

 cannot be divided into portions smaller than these units, called "quanta" by 

 Planck (see p. 254 of Nernst's book, 1913). In the treatment of the solid state 

 from the kinetic point of view, it is to be remembered that the molecules are 

 only free to move or vibrate about a mean position, which does not change, 

 contrary to what obtains in gases and liquids. Nernst (1913, p. 252) finds that 

 the atomic heat of substances becomes very small as absolute zero of temperature 

 is approached, and becomes practically nil at quite finite temperatures. In other 

 words, the amount of energy imparted by the impact of vibrating molecules is 

 not what the kinetic theory as applied to gases at ordinary temperatures would 

 lead us to expect. The discrepancy is explained by the theory of quanta of 

 Planck and Einstein, namely, that in the production of vibrations of an atom 

 around its fixed position, as, for example, by the impacts of gas molecules, energy 

 is taken up only in certain "quanta," and that these units are directly pro- 

 portional to the period of vibration of the atom. For a freely movable gas 

 atom this period is, of course, zero, so that in this case kinetic energy can 

 increase steadily and the kinetic theory of gases remains unaffected. In the 

 case of solids, a different state of things exists. 



If this view be correct, it would follow that the curve giving .the energy 

 content, or partition of velocities between the atoms, instead of being a continuous 

 one, would rise in a series of equal steps, each corresponding to a quantum of 

 energy. A certain formula expressing atomic heats has been deduced by Einstein 

 from this point of view, and, in the experiments made by Nernst and his 

 co-workers, it has been found to be confirmed in the case of eight distinct 

 elements. It applies also to the experiments in which the atomic heat of salts 

 was determined by making use of the optical measurements of absorption bands 

 made by Rubens. The absorption bands are taken as representative of the 

 vibration periods of the atoms. Further measurements will be found in the 

 account given by Nernst (1913, pp. 254, etc.), together with more details of the 

 theory itself than can be given here. 



CHEMICAL ENERGY 



Practically all energy available in the animal body is derived from the 

 oxidation of food, and is, therefore, of chemical origin. It is very important 

 to remember that chemical energy is readily transformed into other forms, 

 without necessarily passing through the form of heat. In the various forms of 

 primary batteries, the electric current, derived directly from the chemical 

 reactions taking place, can be used to drive motors without any further change. 

 The experimental facts concerning the relation of the heat produced in the 

 contraction of muscle to the external mechanical work done show that the 

 energy afforded by the chemical changes cannot pass through the stage of heat, 

 since the proportion of work to heat is too high. The "efficiency" of muscle 

 as a heat-engine would be 27 per cent, to 30 per cent, or more, according to 

 various experiments. This would require, by the second law of thermodynamics, 

 in a heat-engine, a difference of temperature between " boiler " and " condenser " 

 of such a degree as to be incompatible with the life of cells. This fact was 

 familiar to Fick (1882, p. 158), who makes the statement that the "chemical 

 forces " must be used directly for mechanical work, and at the present time 

 no physiologist holds the view that heat energy is a stage in the process. 



What are the capacity and intensity factors in the case of chemical energy ? 

 Willard Gibbs (1878) suggested the name "chemical potential" for the latter, 

 although "chemical affinity" is perhaps the better designation. This latter 

 name, however, has been used somewhat vaguely. The capacity factor is clearly 

 the quantity of a substance taking part in a reaction, that is the equivalent or 

 combining weight, so that : 



Chemical energy = equivalent weight x chemical potential. 



