Continuum Mechanics and Thermodynamics

, Volume 29, Issue 2, pp 361–371

# The virial theorem and the kinetic energy of particles of a macroscopic system in the general field concept

Original Article

## Abstract

The virial theorem is considered for a system of randomly moving particles that are tightly bound to each other by the gravitational and electromagnetic fields, acceleration field and pressure field. The kinetic energy of the particles of this system is estimated by three methods, and the ratio of the kinetic energy to the absolute value of the energy of forces, binding the particles, is determined, which is approximately equal to 0.6. For simple systems in classical mechanics, this ratio equals 0.5. The difference between these ratios arises by the consideration of the pressure field and acceleration field inside the bodies, which make additional contribution to the acceleration of the particles. It is found that the total time derivative of the system’s virial is not equal to zero, as is assumed in classical mechanics for systems with potential fields. This is due to the fact that although the partial time derivative of the virial for stationary systems tends to zero, but in real bodies the virial also depends on the coordinates and the convective derivative of the virial, as part of the total time derivative inside the body, is not equal to zero. It is shown that the convective derivative is also necessary for correct description of the equations of motion of particles.

### Keywords

Virial theorem Acceleration field Pressure field General field Kinetic energy

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© Springer-Verlag Berlin Heidelberg 2016

## Authors and Affiliations

1. 1.PermRussian Federation