MOLECULAR ENERGY 291 



Let us now see what value of C v we should expect 

 for various types of molecules. In addition to trans- 

 lation a monatomic molecule should have three degrees 

 of rotation, that is of spin, about three mutually per- 

 pendicular axes through its center. With the fact 

 that a body has such degrees of freedom we are familiar 

 from our experience with golf balls. 1 Unless the centers 

 of two molecules are moving along the same line 

 or unless they are perfectly smooth spheres, a collision 

 results in a change in their rotation. In an impact 

 the points of contact come to rest relatively. The 

 centers, and in fact all other points, do not, but con- 

 tinue in their original directions because of their 

 inertias. If the impact is elastic the molecules bounce 

 apart, but their rotational speeds will have been altered. 



The k.e. of rotation of the various molecules of a 

 gas will, therefore, be different and that of the same 

 molecule will vary from time to time. It will, how- 

 ever, have an average value just as in the case of trans- 

 lation. According to the conclusions of the mathema- 

 ticians the two average values will be equal, that is, 

 there will be equipartition between translation and 

 rotation and hence between all the degrees of freedom. 



Corresponding to an increase of 1 C. in a mole of 

 gas each degree of freedom of translation is increased 

 by R/2 ergs. From page 218 we have # = 83.2 XlO 6 



the initial and final volume be Vi and F 2 , respectively. The 

 pistonmoves (F 2 - Fi)/a against aforce, pa, and hence A = p(V 2 Vi). 

 But pVi=RT and pV 2 = R(T+l), hence A = R. 



1 In this case we usually recognize the existence of a spin by a 

 deflection of the ball from its rectilinear path due to the difference 

 in air pressure on the two sides, which is occasioned by its rotation 

 in combination with its translation. 



