The properties of He
4 in thermal equilibrium, especially the phase transitions observed in He
4, are investigated on the basis of orthodox quantum statistical mechanics. Dealing with the Ursell expansion [obtained in part I (ref.1)] by the method proposed by one of us(ref.2), and using the properties of the composite clusters [defined in part I], we have discussed the thermodynamical properties of the system and have obtained the following results :
(i) In the gaseous phase, only “small” clusters exist and the Bose statistics does not play any essential role ; therefore the Bose condensation does not occur.
(ii) At sufficiently low temperatures the liquefaction of He4 occurs and the liquid phase is represented by a “large” composite cluster. (iii) At a certain temperature To a phase transition owing to the Bose statistics (the Bose condensation) occurs in the liquid phase and it is generally of 2nd order. (iv) If we compress the gaseous He
4 at a temperature below To, the liquefaction and the Bose condensation occur at the same time;and if We compress the gaseous He
4 at a temperature above To, the liquefaction only occurs. The analytical properties of the condensation points in those two cases may be different from each other.
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