Re: strange definition of temperature
- From: "Timo A. Nieminen" <timo@xxxxxxxxxxxxxxxxx>
- Date: Wed, 12 Dec 2007 05:56:50 +1000
On Mon, 10 Dec 2007, mrdarrett@xxxxxxxxx wrote:
Voyager 2 finds solar system's shape is 'dented'
http://www.reuters.com/article/scienceNews/idUSN1044867120071211
"Voyager scientists had expected the temperatures within the
termination shock to be about 1,000,000 degrees Fahrenheit (555,500 C)
as material normally slows down and is heated up when it encounters an
obstacle in a normal shock wave.
But according to Edward Stone of California Institute of technology,
the temperatures registered were much lower, at around 200,000 degrees
F (111,100 C). Also, Voyager 1 made only one crossing into the
termination shock while Voyager 2 has made at least five shock
crossings over several days which allowed them to collect more data."
Methinks the Voyager spacecraft will start to disintegrate at around
2000 degrees C... eh?
Put your hand into boiling water, and you will regret it very quickly. Put your hand into an oven at 200C, and despite the local environment being hotter, you can keep your hand there for a while. If the walls of the oven weren't hot (just the air inside), and heating your hand up by radiation, you could keep your hand there for longer.
What is the density of the gas at the edge of the solar system? Low, so it only heats up the space probes very slowly. Meanwhile, the electromagnetic radiation is distant stars (including our sun) and the chilly 3K microwave background radiation. The probes can cool down quickly by radiation.
You might ask why the gas (ie the interplanetary/interstellar medium) doesn't also cool down quickly. Something must be heating it as quickly as it can cool down. It's being heated by (a) radiation and (b) the shock wave. (a) probably won't do too much, since this is the same radiation the probes see. What about (b)? Since the density is very low, a small amount of heat (ie energy) delivered by the shock wave can raise the temperature by a lot. Finally, why can't the gas cool down quickly? It's mostly ionized hydrogen, which is a very poor radiator, especially in a very low density gas (well, really a plasma) where collisions are rare - you'll only get radiation when the protons or electrons collide.
You get similarly high temperatures in the solar corona, where radiation from the sun is important for heating.
In neither of these cases is there really thermodynamic equilibrium, since that requires the local electromagnetic radiation to be at the same temperature as the gas. I wouldn't be surprised if the gas isn't even in "local thermodynamic equilibrium" (LTE), in which case, the "temperature" will probably just be a measure of how much of the gas is ionized. A hydrogen plasma needs to be very hot to be mostly ionized, so if the gas is mostly ionized, it must be very "hot", by this definition of temperature.
Purists could quite reasonably argue that this isn't "temperature", and should be given a different name. However, the simple approach is to point at Saha's equation and say "Look, that T is temperature. That's what I'm calculating." The purist replies "Saha's equation assumes thermodynamic equilibrium (or at least LTE)."
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
.
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