Hhyphen;TandVhyphen;Pcurves for various types of phase transitions are shown. In secondhyphen;order transitions a discontinuity in the curvature of the free energy occurs. It appears to follow that some change in the system must be occurring in the phase of high heat capacity, and that this change is such that it has gone to completion at the transition, so that an extrapolation of the phase is meaningless. It is shown that it is extremely difficult uniquely to prove, by calorimetric or equationhyphen;ofhyphen;state data alone, the presence of an anomalous firsthyphen;order transition, in which heat capacity and compressibility approach infinity continuously as the transition is approached. This type of transition can be distinguished by obtaining two phases of differing density in equilibrium, or by sound velocity measurements.A tentative discussion of phase transitions, based on a suggestion of Frenkel, is given. It is shown that the factors determining the type of transition can be partially unraveled. A positive surface free energy between the phases necessitates a simple firsthyphen;order transition.The relation of the Band and Frenkel developments, for an imperfect gas, to the method based on Ursell's development is discussed, and it is shown that the two methods are not identical.
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