Re: Temperature applied to small group of particles

[John Denker <jsd@AV8N.COM>]

Quoting alex Brown <aesbrown77@YAHOO.CO.UK>:

> Is the term temperature of a system of say, 50 particles meaningful?

Yes.

> If
> not What macroscopic(?) state variable would be most appropiate to define
> the energy of the system?

Energy is not the same as temperature.
 -- Everything has an energy.
 -- Not everything has a temperature.

The most appropriate variable to describe the energy is THE ENERGY,
which is indeed a macroscopic variable and a state variable.

> Intuatively I don't think you can define temp
> here as there are not enough particles to give a statistically accurate
> measure of the speed.

There are two ideas in that sentence.
 -- In the abstract, I agree with the major premise that *if*
    you don't have enough particles *then* it might be pointless
    or impossible to talk about temperature.
 -- I totally disagree with the minor premise that 50 isn't
    enough.  People deal with systems of this size all the
    time.  Those who say it can't be done simply don't know
    what they're talking about.

Also......  I assume the question was intended to pertain to a
50-particle group that was _isolated_ from its surroundings,
although this assumption is not necessary.

In contrast, if we have a small group (or even a single particle)
in contact with a heat bath, then the concept of temperature is
very easy to define and very useful.

> By this I mean that the velocity of a particular
> particle  could easily be far away from the mean speed and hence skew the
> results.

1) What means "easily"?  It is exponentially unlikely that the
outlier will be far away from the mean.

2) If you have 49 prosaic data points and one outlier, it won't
skew the results very much ... assuming you use reasonable
statistical procedures.