### 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 , whose maximal value 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),
is the Maxwellian phase density, so that all integrals in (47) are Gaussian integrals, easy to calculate.
Weiss [49] has calculated the speeds for different degrees n of extended thermodynamics. Recall that
, range over the values 1 through n. He has made a list of which is represented here in
Table 1. is normalized in Table 1 by , 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.