virialn.
/ˈvɪrɪəl/ Physics.
a. In Clausius' kinetic theorem of gases: (see quots.). virial theorem, the theorem that for a steady-state system of particles obeying an inverse square law of force, the time-average of the kinetic energy equals the time-average of the virial; or equivalently, that the potential energy is twice the total energy and the kinetic energy is the negative of the total energy.
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the world > matter > physics > mechanics > types of motion > [noun] > kinetic theory of heat or gases > specific theorem > specific quantity in
virial1870
the world > matter > physics > mechanics > types of motion > [noun] > kinetic theory of heat or gases > specific theorem
virial theorem1925
1870 London, Edinb., & Dublin Philos. Mag. 4th Ser. 40 123 We will therefore give to the mean value which this magnitude has during the stationary motion of the system the name of Virial of the system.
1875 Encycl. Brit. III. 39 When an attraction or repulsion exists between two points, half the product of this stress into the distance between the two points is called the virial of the stress.
1904 J. H. Jeans Dynamical Theory of Gases vi. 144 The virial depends solely on the forces acting upon the molecules, and not upon the motion of the molecules.
1925 London, Edinb. & Dublin Philos. Mag. 6th Ser. 50 414 By the extended theorem of the virial, the effect of the pressure of radiation can be ignored, and thus all consequences of the virial theorem which hold in the absence of radiation hold also when radiation is taken into account.
1965 C. S. G. Phillips & R. J. P. Williams Inorg. Chem. I. i. 11 A useful theorem known as the Virial Theorem, which holds for all coulombic potential energy systems.., states that the equilibrium binding energy is equal to ½V or −T, where V and T are time-average potential and kinetic energies.
1974 Encycl. Brit. Macropædia VI. 852/2 Under such conditions the total potential energy of the cluster is exactly twice as great as the combined kinetic energy of all the cluster stars. This relation is known as the virial theorem.
1980 Nature 29 May 305/1 The virial theorem is often used to calculate a [galaxy] system's mass from its size and velocity dispersion.
b. virial coefficient [translating German virialcoefficient (H. K. Onnes 1901, in Arch. neérlandaises des Sci. exactes & nat. VI. 874)] , each of the (temperature-dependent) coefficients of inverse powers of V in a polynomial series used to approximate the quantity pV/RT in the equation of state of an ideal gas or similar collection of particles; so virial equation, virial expansion.
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1902 Sci. Abstr.: Physics & Electr. Engin. 5 364 The series development pv = A + B/v + C/v2 + D/v4 + E/v6 + F/v8 is applied... The coefficients A, B, &c., are termed virial coefficients, and are functions of the temperature.
1955 H. B. G. Casimir in W. Pauli Niels Bohr & Devel. Physics 121 In the theory of an ideal gas interaction between atoms is neglected, but it is possible to calculate successive approximations, the so called virial coefficients.
1967 E. U. Condon & H. Odishaw Handbk. Physics (ed. 2) v. iv. 49/2 The virial expansion is one of the cleanest-cut developments in the subject of statistical mechanics.
1967 D. Margerison & G. C. East Introd. Polymer Chem. ii. 63 Some idea of the deviations from ideality in these dilute solutions can be obtained by evaluation of the second virial coefficients.
1978 P. W. Atkins Physical Chem. i. 39 Conclusions can be drawn from the virial equation of state only by inserting specific values of the coefficients and taking note of their temperature dependence.
This entry has not yet been fully updated (first published 1917; most recently modified version published online September 2018).
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