INVARIANT RELATIVISTIC THEORY OF IDEAL GAS
DOI:
https://doi.org/10.31489/2021No4/88-101Keywords:
distribution function, relativistic ideal gas, arithmetic mean and mean square velocity, equation of state, massless limit.Abstract
The purpose of this study is to develop an original theory of a relativistic ideal gas and to prove the validity of the postulate of the special theory of relativity for the characteristic (i.e., arithmetic mean, root-mean-square) velocities of particles of a relativistic ideal gas even in the massless limit. In this work, the following original methods are used for the first time in the theory of a relativistic ideal gas: the method of nonlinear transformation to prove of the distribution function to find the distribution function of the velocities of particles of a relativistic ideal gas; the equation of state of a relativistic ideal gas was first obtained by averaging the relativistic - invariant components of the energy - momentum tensor of a system of noninteracting particles, i.e. ideal gas by the distribution function of the velocities of their particles. The uniqueness and definiteness of the distribution function of the velocities of the particles of a relativistic ideal gas are proved on the basis of the well-known relativistic invariance of the distribution function. For the first time, expressions were obtained for the arithmetic mean and mean square velocities of particles of a relativistic ideal gas. For the first time, a fundamental conclusion is made about the validity of the postulates of the special theory of relativity for the characteristic velocities of particles of a relativistic ideal gas. An equation of state for a relativistic ideal gas is obtained, which relates its pressure, average energy density and temperature.
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