When we look at the critical states and triple points of other gases, we find the situation shown in table 4.34. The liquid phase exists only when the pressure is between the critical and the triple-point pressures. If we cool down hydrogen, helium or water at room temperature and pressure, we will get liquids before we get solids. But if we cool down CO2 from room temperature and pressure, we get dry ice rather than liquid carbonic to obtain liquid carbon dioxide we have to raise the pressure to at least 5.1 atm to exceed the triple-point pressure. The melting point is not as sensitive to the pressure as the boiling point, which is stated usually for a room pressure of 1 atm, which prevails at sea level on Earth and not in Colorado or the Himalayas. [Pg.142]

Using the finite-size scaling method, study of the analytical behavior of the energy near the critical point shows that the open-shell system, such as the lithium-like atoms, is completely different from that of a closed-shell system, such as the helium-like atoms. The transition in the closed-shell systems from a bound state to a continuum resemble a first-order phase transition, while for the open-shell system the transition of the valence electron to the continuum is a continuous phase transition [9]. [Pg.39]

Although the proposed mechanism is consistent for photolysis of iodine in helium, nitrogen and methane (24), substantive deviations were present at low densities and especially near the critical point of ethane. As Figure 3 shows, the quantum yields at these low densities are consistently below one, the value expected in this high diffusivity regime where kd k i. [Pg.39]

Because of the close relationship between the MNM transition and the vapor-liquid transition, it is to be expected that immiscibility in the mercury-helium system reaches up to the critical point, or even into the supercritical region. This expectation is confirmed by measurements of the phase diagram at very low helium concentrations and at pressures close to the critical pressure of pure mercury. The experiments extend up to 1610 °C and to pressures up to 3325 bar (Marceca et al., 1996). The p — T — X phase equilibrium surface obtained is qualitatively like the one shown schematically in Fig. 6.4 for a binary fiuid-fluid system of the first kind. The critical line starts at the critical point of pure mercury (Tc(l) = 1478 °C, Pc(l) = 1673 bar) and runs to higher temperatures and pressures as the helium composition X2 increases. [Pg.205]

For the H ion, Hill [108] proved that there is only one bound state with natural parity. This result, along with Kato s proof [109] that the Helium atom has an infinite number of bound states, seems to suggest that the critical point for the excited natural states is X = 1 [87]. [Pg.38]

It is known that the classical molecular field theory discussed above is not suited for describing a close vicinity of the critical point. Experimentally obtained values of the parameter (called the critical exponent) are essentially less than fio = 1/2 predicted by the mean-field theory. On the other hand, the experimental values of = 0.33-0.34 turn out to be universal for many different systems (except for quantum liquid-helium where [Pg.8]

Addition of a solute molecule that repels solvent molecules leads in general to em increase of the pressure at constant volume, that is, there is a positive value of dpldx)yT- Equations (6.7) and (6.8) then tell us that the partial molar volume of the solute should diverge toward -i-oo at the critical point of the solvent if there is such a repulsive interaction. This is actually the case for mercury-helium mixtures as illustrated by the pressure dependence of V shown in Fig. 6.5. This simple mechanistic [Pg.204]

From the present calculations, the expectation value of the operator r 2 may provide a direct physical picture about the thermodynamic stability and dissociation of Hj-like molecules. As shown in Fig. 16, there is a vertical jump of the mean value ru at Xc. We note that there are similarities and differences between helium-like atoms and Hj-like molecules. In Section V.A of heliumlike systems, based on an infinite mass assumption, we show that the electron at the critical point leaves the atom with zero kinetic energy in a first-order phase transition. This limit corresponds to the ionization of an electron as the nuclear charge varies. For the Hj-like molecules, the two protons move in an electronic potential with a mass-polarization term. They move apart as X approaches its critical point and the system approaches its dissociation limit through a first-order phase transition. [Pg.49]

See also in sourсe #XX -- [ Pg.226 , Pg.228 ]

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