125-128] Avogadro's Law 111 



Hence it follows that the mean translational energy per molecule in A is 

 equal to the mean translational energy per molecule in B, so that, in accord- 

 ance with our definition of temperature, the temperature in A is equal to the 

 temperature in B. 



127. J. J. Thomson* considers two gases in a tube separated by a piston 

 of mass which is very great compared with that of a molecule of either gas. 

 The condition that there shall be no transfer of energy from one gas to the 

 other by means of the motion of the piston is found to be that the mean 

 kinetic energy of a molecule is the same for the two gases. 



Professor Thomson arrives at this result by a detailed calculation of the 

 effect of individual collisions. The result is, however, obvious upon repre- 

 senting the whole system in a generalised space of the appropriate number 

 of dimensions. For since the motion of the piston only represents one 

 degree of freedom, the kinetic energy of its motion will only be an 

 infinitesimal fraction of the whole energy. This energy may therefore be 

 treated as the interrnolecular potential energy <E> was treated in Chapter V., 

 and we arrive at once at the conclusion that the mean energy of each type of 

 molecule must be the same. 



Maxwell's system of two gases separated by a diaphragm can be treated 

 in the same way, if we assume that there are sufficient quantities of each of 

 the two gases for their energies to be considered as infinite in comparison 

 with the energy of the diaphragm. 



INFINITELY SMALL MOLECULES (continued). 

 Avogadro's Law. 



128. Replacing ^- by RT in equation (262), we have 



(267). 



Hence if two gases are at the same temperature and pressure, the molecular 

 density is the same for both, namely, p/RT. 



This is the well-known law of Avogadro : 



Two different gases, when at the same temperature and pressure, contain 

 equal numbers of molecules in equal volumes. 



* Applications of Dynamics to Physics and Chemistry, p. 91. 



