Correction of the Gas-Thermometer. 81 



17. Interpretation of the Index n. 



Some idea of the meaning of the index n may be obtained 

 by considering the expression above given for the Energy E. 

 The energy of an imperfect gas is less than that of the gas in 

 the ideal state at the same temperature by the term nop, 

 which represents the loss of energy due to coaggregation of 

 the molecules, corresponding to the diminution of volume 

 c per unit mass. Considering first the case of a monatomic 

 gas, in which the whole of the kinetic energy of the molecules 

 consists of energy of flight (corresponding to three degrees 

 of freedom), we have the well-known relation pv = H0 = 2s0/3. 

 In a diatomic gas, regarded as consisting of pairs of atoms 

 rigidly joined together like dumbbells, it appears probable, as 

 suggested by Boltzmann, that the energy of a molecule may 

 be equally distributed between each of three degrees of 

 freedom of translation and two degrees of freedom of rotation, 

 supposing that the rotation of a molecule about its axis could 

 not be altered by intermolecular collisions. Such a molecule 

 would have five equal degrees of freedom, and the specific 

 heat at constant volume should be 5R/2, which is amply con- 

 firmed by experiment. Supposing that two monatomic mole- 

 cules each with three degrees of freedom coaggregate to form 

 a diatomic molecule possessing five degrees of freedom, there 

 would be a loss of energy equivalent to one degree of freedom, 

 or one third of the energy of flight, since the energy of flight 

 of the resulting diatomic molecule would be the same as that 

 of a single monatomic molecule at the same temperature. 

 If the diminution of volume per unit mass due to coaggre- 

 gation be represented by c. the loss of energy on this 

 hypothesis would be represented by cp/2, since the product 

 cp represents two-thirds of the energy of flight in a volume c. 

 We ought therefore to have the index n=l/2, in the case of 

 a monatomic gas, on the simple hypothesis of coaggregation 

 in pairs, provided that the coaggregation is a purely physical 

 effect, and that there is nothing in the nature of chemical 

 combination involving evolution of heat. 



In the case of a diatomic gas, a similar line of reasoning- 

 fails to give a definite result, because we have no sure experi- 

 mental guide or mechanical analogv to enable us to estimate 

 the number of degrees of freedom of the resulting tetratomic 

 aggregate. If we supposed with Maxwell that the number of 

 degrees of freedom could not exceed six, as for a rigid body, 

 the loss of energy for a pair of diatomic molecules each 

 possessing five degrees of freedom would be equivalent to four 

 degrees of freedom on coaggregation, which would make 



Phil. Mag, S. 6. Vol. 5. No. 25. Jan. 1903. G 



