Re: energy distribution

[John Denker <jsd@MONMOUTH.COM>]

At 10:57 AM 5/12/99 -0600, Jim Green wrote:
> Suppose there are 4 particles with energies of 2, 4, 6, 8 -- their average
> energy is of course 5 but the total energy of the system is 20 -- NONE of
> the particles can ever have an energy >20.   NOW what did I do wrong?

Sorry, I misread your E as intensive energy per particle, not the extensive
energy of the whole system.  Your note was syntactically clear enough, but
I was led astray by the expressions of the form
  p (of an extreme particle) = sqrt (2mE)?
which is a very unusual form, with an intensive quantity on the LHS and an
extensive quantity on the RHS.

Such a p is, just as you orignally asserted, an absolute upper bound on the
accessible momenta, but for a macroscopic system it is so exceedingly
unlikely for a particle to have such an extreme momentum that the equation,
while syntactically correct, has no relevance to the the physics as far as
I can tell.

If there are N particles making up the total energy E, then a reasonable
estimate of a typical momentum is
  p (typical) = sqrt (2 m E / N)
and this is what I would use to estimate the number of plausibly-accessable
states.

OK? --- jsd