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Temp of Universe (was Definitions of Temperature)



DSCHROEDER@cc.weber.edu says:

But you've already given yourself away: You say you can *derive* this
relation between energy and temperature, starting from the ideal
gas law. I absolutely agree. Which proves that the relation is not
a definition. You can't derive a definition. So you need some *other*
definition of temperature to determine what the T in the ideal gas
law stands for. Even in an upper-division course, I think this other
definition should be an operational one (how to make a thermometer).
Then, when students ask what temperature really *is*, even in an
introductory course, you need to tell the truth: it's a measure of
the willingness of an object to spontaneously give up energy. In many,
but not all cases, this "willingness" happens to be proportional to
how much energy the object already has.


This reminds me of a problem given us in graduate stat. mech., on which I'd
be interested to hear opinions.

The problem was "What is the temperature of the universe?" There were
probably simplifying assumptions allowed, but I don't remember them, and
they are important for the following.

The "correct" (i.e., the one given by the grader) answer was that a
temperature cannot be defined for the universe, because there is no object
outside the universe with which you could check to see how willing the
universe is to give up energy.

This always bothered me. Once you've derived a relation between energy and
temperature, why isn't the temperature of the universe given by that
relation (under simplifying assumptions and knowing the appropriate
energies)?

So I ask: do you think that the universe has a temperature?

--
--James McLean
jmclean@chem.ucsd.edu
post doc
UC San Diego, Chemistry