Abstract

Following the original line of argument by Maxwell and Boltzmann (MB) we derive a 4-velocity distribution function for a relativistic ideal gas of massive particles. Most importantly, this distribution function can be factorized and perfectly reduces to non-relativistic MB speed distribution formula in low temperature (non relativistic) limit. Using this distribution function we express the pressure p, and kinetic energy density ρ − ρο as the functions of a parameter λ directly related to the kinetic energy density and hence to the temperature. We compute the adiabatic index γ=c_p/c_v from the relativistic equation of state ρ − ρο = (γ -1)p as a function of the parameter λ. The value of γ exactly reduces to 5/3 and 4/3 in the nonrelativistic and ultra-relativistic limit respectively. We also find the sound speed(a_s) satisfies a_s ≤ 1/√3 (Basu & Mondal 2013, 2011; Mondal & Basu 2011, 2013).