106 THE PHYSICS OF VIRUSES 



where k is Boltzmann's constant. Hie free energy, F, correspond- 

 ing to this class of bond is then (Schrotlinger, 1948, p. 13) 



F = kT hi ^ e-'"'^'' (4.2) 



and by the definition of free energy in thermodynamic terms 



F = U - TS 



where U is the internal energy and S the entropy. 

 Now U, the internal energy per form of vibration, is 



Ie, 



-Er/kT 



r = ^ — (4.3) 



r 



which is sim])ly the energy times the population divided by the 

 population to give total energy. We can, therefore, use these 

 expressions to find »S, the entropy involved. 



We then have explicitly: The internal energy, U {or H), per 

 form of rihrafion is 



XEre-'''''''' 



[ = 



Xe- 



-Er/kT 



The total internal energy will be the sum of terms of this kind. 

 The free energy per form of vibrafion is 



F = I'T In 2 e-"-'"'' 



The total free energy is again the sum of terms of this kind. 

 The Entropy, S, for the case where no volume changes is 



I f^" 



-E,/kT 



S = -^ + /.• In > p-^'^'^''' (4.4) 



2' \ ^-Er/kT / J 



Again this must be summed for each form of vibration. 



