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• W2085228316 abstract "The density $ensuremath{rho}$ of ${mathrm{He}}^{4}$ as a function of temperature and pressure has been measured along several different paths in the vicinity of the critical point. The results of the measurements are interpreted in terms of power-law descriptions near the critical point: For the coexistence curve, $|ensuremath{rho}ensuremath{-}{ensuremath{rho}}_{mathrm{c}}|ensuremath{propto}{({T}_{mathrm{c}}ensuremath{-}T)}^{ensuremath{beta}}$; for the critical isotherm, $|Pensuremath{-}{P}_{c}|ensuremath{propto}{|ensuremath{rho}ensuremath{-}{ensuremath{rho}}_{c}|}^{ensuremath{delta}}$; for the critical isobar, $|Tensuremath{-}{T}_{c}|ensuremath{propto}{|ensuremath{rho}ensuremath{-}{ensuremath{rho}}_{c}|}^{ensuremath{pi}}$; for the isothermal compressibility along the coexistence curve, $(frac{1}{ensuremath{rho}}){(frac{ensuremath{partial}ensuremath{rho}}{ensuremath{partial}P})}_{T}ensuremath{propto}{|Tensuremath{-}{T}_{c}|}^{ensuremath{-}{ensuremath{gamma}}^{ensuremath{'}}T}$; and for the thermal expansion coefficient along the coexistence curve, $(frac{1}{ensuremath{rho}}){(frac{ensuremath{partial}ensuremath{rho}}{ensuremath{partial}T})}_{P}ensuremath{propto}{|Pensuremath{-}{P}_{c}|}^{ensuremath{-}{ensuremath{gamma}}^{ensuremath{'}}P}$. The subscript $c$ identifies the value of a quantity at the critical point. It is shown why simple power-law descriptions might be inadequate to describe all the behavior at the critical point and how this problem can be partly solved by the use of additional, non-singular factors. The values of the exponents are found to be $ensuremath{beta}=0.354ifmmodepmelsetextpmfi{}0.010$, $3.8ensuremath{le}ensuremath{delta}ensuremath{le}4.1$, $3.8ensuremath{le}ensuremath{pi}ensuremath{le}4.2$, ${{ensuremath{gamma}}^{ensuremath{'}}}_{T}=1.1ifmmodepmelsetextpmfi{}0.1$, and ${{ensuremath{gamma}}^{ensuremath{'}}}_{P}=1.5ifmmodepmelsetextpmfi{}0.2$. Combined with Moldover's specific-heat measurements, which give for the exponent ${ensuremath{alpha}}^{ensuremath{'}}$ of the expression ${C}_{mathrm{V}}ensuremath{propto}{|Tensuremath{-}{T}_{c}|}^{ensuremath{-}{ensuremath{alpha}}^{ensuremath{'}}}$ a value of ${ensuremath{alpha}}^{ensuremath{'}}=0.017ifmmodepmelsetextpmfi{}0.008$, we can test various inequalities proposed for the exponents. For Rushbrooke's and Fisher's inequality, ${{ensuremath{gamma}}^{ensuremath{'}}}_{T}+2ensuremath{beta}+{ensuremath{alpha}}^{ensuremath{'}}ensuremath{ge}2$, we obtain 2.0 for the maximum value of the left side; for Griffiths's inequality, $frac{{{ensuremath{gamma}}^{ensuremath{'}}}_{T}(ensuremath{delta}+1)}{(ensuremath{delta}ensuremath{-}1)}+{ensuremath{alpha}}^{ensuremath{'}}ensuremath{ge}2$, we obtain 2.2 for the maximum value of the left side; but for Griffiths's inequality, $ensuremath{beta}(ensuremath{delta}+1)+{ensuremath{alpha}}^{ensuremath{'}}ensuremath{ge}2$, we obtain only 1.9 for the maximum value of the left side. Possible reasons for this discrepancy are discussed." @default.
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• W2085228316 date "1968-06-05" @default.
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• W2085228316 title "Pressure-Density-Temperature Surface of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=normal>He</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>near the Critical Point" @default.
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• W2085228316 doi "https://doi.org/10.1103/physrev.170.213" @default.
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