Sentences with word «virial»
The word "virial" usually refers to a mathematical formula used in physics to measure the force or motion of particles in a system. It helps scientists understand the behavior and stability of things like gases or stars by calculating the relationship between their kinetic energy (energy of motion) and potential energy (stored energy). Full definition
scienceofdoom.com
Miskolczi also provides empirical evidence of the two laws he applies (Krichhoff's law and Virial Theorum) for both the Earth and Mars.
To determine the mass of Eridanus A, Gould uses the «virial theorem», which states that the faster the galaxies in a cluster move, the greater the mass of the cluster.
But Gould says that Eridanus A's mass - to - light ratio, derived from the virial theorem, is 2500.
Even a more conservative estimate, which does not use the virial theorem, indicates that the mass - to - light ratio of Eridanus A must be at least 600.
The virial theorem indicates that Eridanus A has a mass of 90 million million times that of the Sun — the equivalent of 90 times the mass of the Milky Way.
The virial masses are approximately of the order of 1000 Msolar and 500 Msolar for the clumps in IRS 1 - 3 and IRS 9 regions, respectively.
If the fact that it sas published in an obscure Hungarian meteorological journal were not enough to raise your suspicions, his rather «creative» application of the virial theorem ought to peg any reasonable BS detector.
The critical bit seems to be the incorporation of the virial theorem, which at the same time provides the novel means to enforce the required balance and is also the bit I haven't figured out yet.
· He applies the Virial Theorem to the atmosphere, which states that the kinetic energy of a system is half of the potential energy.
The Virial theory and its application is not as straightforward as you think.
In terms of the usual definition of KE (for which the average KE of a molecule = (3/2) kT), the straightforward result of applying the Virial Theorem to a homogeneous gravitational field is: (2/3)[KE] = [PE], as I have demonstrated previously (and also I have updated the text to recover a Word version, in the last few days).
However, I don't wish to focus on the MEP now, as we are still coming to terms on the Virial - Theorem discussion.
However, strictly speaking, this is a separate issue from the Virial Theorem.
«We derive a version of the virial theorem that is applicable to diatomic planetary atmospheres that are in approximate thermal equilibrium at moderate temperatures and pressures and are sufficiently thin such that the gravitational acceleration can be considered constant.
Stothers, R.B., 2006: A virial theorem investigation of magnetic variations in the Sun.
«The virial theorem may be expressed in a variety of different forms and also may be interpreted in a number of different ways.
Toth's presentation of the Virial Theorem is insufficiently general and lacks perspective; and in my experience, Jan Pompe can not write three consecutive equations without erring in one of them.
-- The paper by Toth, as well as the more general approach taken in the paper he references by Pacheco and Sañuco, show that a careful application of the Virial Theorem to the planetary - atmosphere situation results in:
-- The result attributed by Miskolczi to the Virial Theorem is: 2 avg (K) = avg (U) This is inconsistent with the above results.
My point of reasoning for the link to that paper is to show that the Virial Theorem «alone» isn't enough for an accurate demonstration of phenomenological energy transition.
SoD has reminded us of the Eu / KE question (Section 3.1), which is how the Virial - Theorem discussion gets coupled into this paper.
I now realise how I, as an engineer, rely heavily on «Equivalence» and a pertinent version of «The Virial Theorem»!
I started to think about all this SoD and had a dreadful feeling of deja vu; this discussion on the Tau and eqn 7 and Virial and Kirchoff will explain why:
The virial theorem has been misapplied, or 3.
In the abstract to his paper, he made a special point of highlighting the relationship that was supported (somehow) by the Virial Theorem.
The atmosphere is a gravitationally bounded system and constrained by the virial theorem: the total kinetic energy of the system must be half of the total gravitational potential energy.
The Virial Theorem applies to translational kinetic energy (in 3 dimensions).
A couple of years ago, I believe you had some detailed questions about the Virial Theorem, at Niche Modeling.