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[Physltest] [Phys-L] Re: expansion of gases



In your example of an expanding gas, it's not always true that the ex=
panding gas cools and the surroundings warm up. In the special case o=
f an ideal gas expanding freely and adiabatically ("adiabatic" means =
no heat is exchanged with the surroundings, as in a fast process or i=
n a well-insulated container) into a vacuum, the temperature of the g=
as does not change. This situation is described as "free expansion o=
f an ideal gas" in a large number of textbooks. The process can be u=
nderstood in terms of the conservation of energy. Because the gas ex=
panding into a vacuum does no work and does not exchange energy with =
its surroundings, its internal energy (and therefore its temperature)=
remains constant.

The second part of the riddle has to do with the Big Bang. In the Bi=
g Bang, the gas did not expand "into" anything. Space itself expande=
d, and there was no such thing as an "outside" to expand "into." Thi=
s is a very subtle point, and one that is very difficult to conceptua=
lize, but one that is central to understanding cosmological physics. =
Our common sense tells us that there must have been some external vo=
lume into which to expand, but this is not the case for the Big Bang.=
As to whether the total amount of energy in the universe is truly c=
onserved for all time and space, this is one of the great ongoing my=
steries of cosmology. I think that for now, we have to be satisfied =
with saying that for all practical purposes involving non-cosmologica=
l processes, energy is conserved. Certainly no significant violation=
s of energy conservation have ever been observed for non-cosmological=
phenomena.

Physics is a series of approximations, and nothing is as simple as th=
e carefully selected examples in the textbooks make it seem. Most of=
the standard equations in intro textbooks only work in special cases=
(for example, ideal gas only, or non-relativistic only, or no air re=
sistance only), which is why I teach my students to pay attention to =
the "fine print" that goes with each equation.

Vickie Frohne

-----Original Message-----
=46rom: Forum for Physics Educators on behalf of Anthony Lapinski
Sent: Mon 1/3/2005 3:30 PM
To: PHYS-L@LISTS.NAU.EDU
Subject: expansion of gases
=20
My physics colleague brought a puzzling idea to me today regarding
cosmology. We all know that when a gas expands, it cools. By conserva=
tion
of energy, the expanding gas cools and its surroundings warm up.

But what happens when a gas expands in a vacuum? If it cools, is the =
total
energy still conserved? More specifically, what about the Big Bang? I=
f the
Universe was very hot in the beginning and expanded (into a vacuum), =
then
it should cool. And it has -- to 2.7 K. But does this violate conserv=
ation
of energy? We were both baffled. Can anyone help us with this apparen=
t
dilemma?
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