We developed an equation of state (EOS) by Ihm, Song, and Mason (ISM) for polar fluids. The model consists of four parameters, namely, the second virial coefficient, an effective van der Waals co-volume, a scaling factor, and the reduced dipole moment. The second virial coefficient is calculated from a correlation that uses the heat of vaporization, and the liquid density at the normal boiling ...

We describe a simple derivation of virial relations, for arbitrary physical systems that are governed by an action. The virial theorem may be derived directly from the action, A, with no need to go via the equations of motion, and is simply a statement of the stationarity of the action with respect to certain variations in the degrees of freedom. Only a sub-class of solutions that obey appropri...

We reconsider the virial theorem in the presence of a positive cosmological constant Λ. Assuming steady state, we derive an inequality of the form ρ ≥ A(Λ/4πGN ) for the mean density ρ of the astrophysical object. The parameter A depends only on the shape of the object. With a minimum at Asphere = 2, its value can increase by several orders of magnitude as the shape of the object deviates from ...

On the basis of the stationary Schrödinger equation, the virial theorem in an inhomogeneous external field for the canonical ensemble is proved. It is shown that the difference in the form of virial theorem is conditioned by the value of the wave-function derivative on the surface of the volume, surrounding the system under consideration. The stress tensor in such a system is determined by the ...

We report on the discovery of a new correlation between global parameters of the hot interstellar gas in elliptical galaxies. We reanalyze archival Chandra data for 30 normal early-type systems, removing the contributions of resolved and unresolved point sources to reveal the X-ray morphology of the hot gas. We determine the half-light radius, RX , and the mean surface brightness, IX , from the...