Pulse speeds in a non-degenerate gas in equilibrium

3.5 Pulse speeds in a non-degenerate gas in equilibrium

We recall the discussion of characteristic speeds in Section 2.4 which we apply to the system (23

) of field equations. The characteristic equation of this system reads

or, by (11

This equation determines the characteristic speeds $V$ , whose maximal value $Vmax$ is the pulse speed. In the case of moments and for a non-degenerate gas at rest and in equilibrium this equation reads, by (42

$fE$ is the Maxwellian phase density, so that all integrals in (47

) are Gaussian integrals, easy to calculate. Weiss [49 ] has calculated the speeds $V$ for different degrees n of extended thermodynamics. Recall that $α$ , $β$ range over the values 1 through n. He has made a list of $Vmax$ which is represented here in Table 1. $Vmax$ is normalized in Table 1 by $∘ 5kT- co = 3m$ , the ordinary speed of sound, sometimes called the adiabatic sound speed.

Inspection of Table 1 shows that the pulse speed increases monotonically with the number of moments and there is clearly a suspicion that it may tend to infinity as n goes to infinity. This suspicion will presently be confirmed.