Re: Upper limit on temperature?


"Edward Green" <spamspamspam3@xxxxxxxxxxx> wrote in message
news:1155609273.146663.286570@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
joshipura@xxxxxxxxx wrote:

This one branches off from my earlier question about "Temperature and
Pressure at atomic level?"

1. Temperature is proportionate to the RMS molecular velocity.
2. No molecule can have a velocity more than that of light.
3. The RMS also can not increase beyond the velocity of light (because
it is actually an average, it should be less than or equal to the
maximum possible).
4. So the temperature that is proportional to RMS, can not raise beyond
some value.
5. This means we can't get colder than 0 degree K and we can't get
hotter than "max hot" degree K.

Do I make sense? What happens when the average molecular velocity
approaches the speed of light?

Lost in the side discussion about the possible meaning of the Planck
temperature, is a simple partial answer to your question: speed of
molecules is limited, but energy is not. So this relativity argument,
by itself, suggests no upper limit on temperature.

BTW, clever types like to point out the "thermodyanmic" definition of
temperature, regarded as more fundamental than anything based on
average energy, and that is, roughly:

1/T = dS/dE

S is entropy, roughly a measure of the number of ways the system can
exist microscopically compatible with its macroscopic (human scale)
condition, and this equation says that, at the absolute zero of
temperature, a small increment of energy produces a large (if not
infinite) increase in entropy, whereas this increment per energy
increment decreases as temperature increases -- and that's why heat
flow from hot to cold, because the universe arranges things to always
increase entropy (on average).

If you wanted to be a real smart aleck, you could point out that in a
two state system (only two energy states for each of a collection of
little bits making up the macroscopic system) a temperature of
"infinity" is easily achieved (equal populations in top and bottom
states), and hence there is no limit on temperature.

I can't off hand see any reason to expect a limit on possible
temperatures based on the thermodynamic definition of temperature even
in more normal systems.


One may not, but one should consider the Planck temperature and the Big
Bang temperature to be one and the same. Each of these, the Planck units and
the Big Bang units should be considered equal to each other and equal to
'unity' ('1'). But I of course have my own agenda in responding thus. That
the Planck and Big Bang Horizons are [the] constant background horizons to
an unlimited number of foregrounds of which we are some.

Both being equal to each other and equal to unity (1), ultimately they are
one and the same background Horizon. As to the absolute zero (0) of
temperature, that is our property and our property alone. One of the strict
properties of foreground universe (the plural infinity of local --
foreground -- universes) versus 'unity' (the Background Universe or the
Universal Horizon).

Now then, consider "flow"! Rather, consider +/- flows! When it comes to
the finite (the relative) absolutes, the rock bottom base can't possibly be
less than base 2.

GLB


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