January 24, 1913] 



SCIENCE 



125 



ular heats of gases like elilorine and bro- 

 mine, which have more loosely connected 

 atoms than have the so-called permanent 

 gases, are nearly a calorie too high ; that, 

 further, they grow higher as the tempera- 

 ture rises. Recent work,^'' too, shows that 

 as the temperature is slowly raised from 

 300° to 1,200° C. the molecular heats of all 

 the permanent gases rise from 5 to 6 ca- 

 lories, while at the tempera tvire of 2,000° 

 C. they have gone up to nearly 7, just as 

 though two new degrees of freedom had 

 gradually been added. This we should ex- 

 pect if at high enough temperatures energy 

 begins to go into vibrations of the atoms 

 along their line of connection in the diatom. 

 Very recent work,^'' too, which seems to be 

 reliable, shows that when the temperature 

 of the diatomic gas Hj falls from 200° ab- 

 solute to 60° absolute, its molecular heat 

 falls from 5 calories to 3 calories. In other 

 words, at 60 degrees absolute, and pre- 

 sumably at lower temperatures, H, acts 

 like a monatomic gas. 



Now, say the quantum theorists, all these 

 facts are beautifully explained by our 

 hypothesis. For, according to it, no atomic 

 vibrator can absorb any energy at all ex- 

 cept in whole units of size Jiv, or multiples 

 of hv. The diatomic vibrator then, consist- 

 ing of the 2 atoms of a diatomic gas, can 

 absorb no energy at all from the molecular 

 impacts experienced by the molecule as a 

 whole, until the energy of these im- 

 pacts exceeds hv. Then it begins to ab- 

 sorb, and as the temperature rises still 

 farther the number of atomic vibrators 

 which begin to take on an energy load in- 

 creases as rapidly as it can in view of the 

 limitations imposed by the law of distribu- 

 tion of energy among the molecules, and 

 the necessity of absorbing only in whole 



'"Nernst, Zeit. f. Elek. Chem., 17, p. 272, 1911. 

 " Euken, Ber. der Preuss. Akad., February, 1912, 

 p. 141. 



multiples of Iw. In the end, as the tem- 

 perature rises, each atomic vibrator takes 

 on the share of the energy which properly 

 belongs to it in accordance with the law of 

 equi-partition. The atomic vibrators of the 

 chlorine and bromine molecules begin to 

 do this at lower temperatures than those of 

 the other diatoms, because the bonds hold- 

 ing the chlorine and bromine atoms to- 

 gether are relatively weak, and conse- 

 quently their frequencies are small. Hence 

 the energy units hv, characteristic of these 

 absorbers, are correspondingly small, and 

 therefore the temperature at which the 

 kinetic energy of the molecular impacts 

 reaches this value is low. 



The explanation of the fact that Hj acts 

 like a monatomic gas at low temperatures 

 is this. The two rotational degrees of free- 

 dom of the H, molecule drop out at low 

 enough temperatures, for the reason that 

 these rotations correspond at a given tem- 

 perature to a definite mean rotational fre- 

 quency V, and when the energy of impact 

 falls below this value of hv no energy can 

 go into these rotations. 



Coming now to the atomic heat relations 

 of solid bodies, these have been much studied 

 of late and are interpreted by Nernst and 

 others in terms of this same form of 

 quantum theory. Dulong and Petit 's law 

 of the equality of the atomic heats of the 

 elements, and Kopp's law of the additive 

 properties of atomic heats in compounds, 

 were, until very recently, the most sugges- 

 tive of the unexplained laws of experi- 

 mental physics. Boltzmann^^ gave a fasci- 

 nating interpretation of these relations by 

 assuming that the atoms of solids have nat- 

 ural periods of vibration, and, if so, that 

 they must be in thermal equilibrium with 

 a gas when their mean vibratory kinetic 

 energy is the same as the mean transla- 

 tional energy of the gas molecules. If this 



" Boltzmann, Wien. Sitz. Ber., 63, 2 abt., p. 731. 



