ON THE THERMODYNAMIC PHASE DIAGRAMS OF HELIUM THREE

Journal Article · Wed Nov 01 04:00:00 EST 1961 · Annals of Physics (New York) (U.S.)

DOI:https://doi.org/10.1016/0003-4916(61)90036-7· OSTI ID:4828137

Goldstein, L

An analysis of thermodynamic consequences resulting from the observed anomaly at the temperature T/sub a/ of the melting pressure line P(T) of He/sub 3/ through the formation of a minium at this temperature is given. The anomalous character of the volume line V/sub 1/(T) of the liquid, in equilibrium with the solid, is proved on the basis of data available on the high temperature side of T/ sub a/ and at T/sub a/. This volume anomaly consists in a maximum of V/sub 1/(T) at T/sub a/. The similar anomaly of the solid volume line V/sub s/ (T) at T/sub a/ resuits from the temperature double-valuedness of the isobaric and isochoric states of the liquid and solid along the phase equilibrium lines. The saddle point type character of the states STAP(T/sub a/), V/sub 1/(T/sub a)! and STAP(T/ sub a/), V/sub s/ (T/sub a/)!, combine d with the existence of the locus of vanishing expansion coefficients of the liquid, led to recognizing the oscillatory character of the isobar of pressure P(T/sub a/) and isochore of volume V/sub 1/(T/sub a/) of the liquid. The oscillations result from the vanishing of the second partial temperature derivatives of these isobar and isochore of anomaly at three different temperatures, the temperature T/sub a/ being one of these. These impose the occurrence of probably observable anomalies in constant pressure and constant volume henat capacities of higher pressure, p approximately - P(T/sub a/), and smaller volume V approximately - V(T/sub a/). The anomalous isobaric lines yield a fairly complete description of the associated expansion coefficients of the liquid. The vanishing expansion coefficient of both the liquid and the solid at the states of anomaly will be shown to resuit directly from the saddle point type character of these states of the two phases. Features of the isothermal compressibility of the liquid will be derived, togenthenr with its evaluation at isolated states of these two phasens in equilibrium from local behavior of the equilibrium linens P(T), V/sub 1/(T), and Vsub s/ (T). (auth)

• Research Organization: Los Alamos Scientific Lab., N. Mex.
• NSA Number: NSA-16-003545
• OSTI ID: 4828137
• Journal Information: Annals of Physics (New York) (U.S.), Journal Name: Annals of Physics (New York) (U.S.) Vol. Vol: 16; ISSN APNYA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

DIFFERENTIAL EQUATIONS
EXPANSION
HELIUM 3
ISOBARS
MELTING POINTS
OSCILLATIONS
PHASE DIAGRAMS
PHYSICS
PRESSURE
SOLIDS
SPECIFIC HEAT
STABILITY
TEMPERATURE
THERMODYNAMICS
VOLUME