Q & A: The temperature of a vacuum

What is a vacuum in physics? Does it have a temperature?
- Anonymous

Well, our idea of a vacuum is a bit of space with nothing in it. We don’t know of any examples of a perfect vacuum, but know some bits of space that get pretty close. Space beyond the Earth’s atmosphere isn’t a bad approximation to a vacuum, but it is filled with solar wind particles, light from the sun, cosmic rays and cosmic microwave background radiation. It’s probably also filled with dark matter which doesn’t interact with other stuff (except gravitationally, and possibly only through the feeble weak interaction), as well as neutrinos.

If you manage to pump all the air out of a steel can, for example, you will have a vacuum in there, but there will be photons constantly radiated off of the walls and re-absorbed by them. This soup of photons will be in thermal equilibrium with the walls, and therefore will have a defined "temperature". In fact, even the deepest of deep space (outside the galaxy, for example), is in a radiation bath of temperature 3K, left over from the Big Bang. There may be other stuff, like the neutrinos, for example, which are not in thermal equilibrium with the 3K radiation because they don’t interact with it, and so space may have two or more "temperatures".

But we said a vacuum is a region of space with nothing in it, and that means those photons have to go. Cooling the walls down to as close to absolute zero as you can get (and the limit here is that photons of energies that would be radiated by a wall of a cold temperature would have wavelengths longer than the size of the can -- that’ll let you freeze out all of the photons) will give you a vacuum. You have to also shield it from outside sources of energy. There’s little you can do about the neutrinos and dark matter -- they penetrate ordinary matter, but also don’t really interact with it so to a good approximation you can neglect them.

Tom

p.s. So the answer really depends on what you mean by vacuum. If you mean what’s left when all the atoms etc. are pumped out, yes it still has a temperature of electromagnetic radiation. If you want, though, you could choose to only call that a vacuum if the temperature is zero. By the way, the third law of thermodynamics says nothing can ever get to zero temperature, so by that definition there wouldn’t be any vacuums.

Mike W.

(published on 10/22/2007)

why temperature go up in vacuum?
- jbeauty (age 25)
singapore

We didn't say that temperature must go up in a vacuum. We just said that an ordinary vacuum can have a temperature due to the electromagnetic waves in it. That temperature will become the same as the temperature of the material surrounding the vacuum.

Mike W.

Lee H

(published on 03/03/07)

What temperature is ther in vacuum? Or is there any heat at all?
- Olle (age 12)
Sweden

Hi Olle- There seems to be a glitch in our search engine, so that the terms "vacuum temperature" fail to turn up our previous answer to this question. Hence I'm posting your question as a follow-up. See the answers above.

Mike W.

(published on 01/20/11)

So if you took an infrared camera to a vacuum would it show up as the temperature of the room or what?
- Ryan (age 13)

What will the IR camera see? It should be kept cold, so that it can more easily sense thermal IR. The IR that hits it will be largely absorbed. The time it takes to get an image is very long compared to the time it takes light to reach the camera from the opposite wall. So the image will depend not on the thermal equilibrium IR density (which depends only on temperature) but rather on the IR emissions from the wall. Those depend on both the temperature of the walls and their emissivity/absorptivity, i.e. whether they tend to absorb or reflect IR. The more absorptive, the more they will show up.

Mike W.

(published on 05/21/11)

Sorry, let me rephrase my question. I was wondering more of what it would feel like. Let's just say hypothetically that I could stick my arm into a vacuum. What would it feel like because I just can't wrap my head around no temperature.
- Ryan (age 13 )
Canada

I think it wouldn't feel very hot or cold. Say you stick your arm into a vacuum room at some normal temperature, say 22°C. Your arm is at ~37°C internally,  somewhat cooler on the surface but still well above 22°C. So there's a net flow of radiant heat out from your arm to the room. If there were air in the room, there would also be some convective cooling of your arm by the air. So not having the air around should make your arm feel a bit warmer than it would otherwise. However, even without any cooling via sweat evaporation, heat is leaving your arm, so it will feel about like it would in a room that was warmer than 22°C but cooler than 37°C. 

If you sweat a little, it should evaporate easily (the relative humidity is zero) so it should feel cooler than our recent muggy weather here, with very high relative humidity and temperature around 34°C.

Of course the lack of pressure from the vacuum will feel weird. I'm not sure if it would pop blood vessels or something.  But that's another issue.

Mike W.

(published on 06/05/11)

I still want to ask, what is the temperature of vacuum? The real one, with nothing in it. No elements, no radiation, no magnetic or other fields. I understand, that it's very difficult to get, but what is the temperature of NOTHING(vacuum in our case)?
- Sergei
Israel

If there is no electromagnetic radiation then the temperature would be absolute zero. The third law of thermodynamics says that's not reachable. So the vacuum you describe is not "the real one" but an unattainable ideal one. It's fair to say, however, that as the density of thermal radiation approaches zero the temperature (assuming the radiation can be described by a thermal spectrum) approaches 0 K.


Mike W.

(published on 07/23/11)

I know there is a limit on how small a volume is that we can refer to, but still, if i look at a volume very small, smaller than the size of particles we know, wouldn't that volume be considered as vacuum, the "ideal" one you were talking about? And another thing troubles me, when we look at the position of matter as a probability function of space we find that a particle is spread all over the place, so in what sense are the walls of a vacuum cell not filling it up with themselves?
- joe (age 27)
israel

Many of our particles (electrons, muons, neutrinos, quarks,...) have no known size. That means that one could have their wave functions squashed in more and more, at least until things start to happen beyond our current laws of physics. Those would be things like the formation of tiny black holes for which the as yet undeveloped quantum theory of gravity would be needed. That's not the sort of event which would be called "nothing". So  I don't know of any way you can describe a piece of space so small that it has to be empty. Some of the books on string theory might be a good place to start looking at what people are trying to do about small-scale physics.

The walls of a box will indeed have some quantum spread, just like anything else. However, the magnitude of the quantum wave typically falls off exponentially with a characteristic distance scale of less than an angstrom, so you have effectively none in the bulk of the box.

Mike W.

(published on 07/29/11)

Following Sergei's question regarding an "ideal" vacuum with absolutely no form of matter or energy (just plain space-fabric): I've learned that the temperature of something is the average kinetic energy of its particles, which is to say the total kinetic energy divided by the number of particles. Wouldn't by that definition the temperature of a vacuum be 0/0, and so undefined?
- David (age 17)
California

What you learned is wrong. There are certain familiar special cases where the "energy per particle" definition of absolute temperature isn't too bad. For example for an ideal monatomic gas, the average thermal energy per particle is (3/2)kT, where k is Boltzmann's constant.  However, in general that definition breaks down in serious ways. In a vacuum, if you choose to call photons particles, the very number of the particles depends on temperature, going as T³. (The average energy per photon does still go as T.) Since the number of photons only goes to 0 when T -> 0, if there are no particles of any type then T=0.

Mike W.

p.s. In many other cases, e.g. for crystalline solids, the formulation of T as energy per particle breaks down in very different ways. At low T, the thermal energy in a piece of diamond goes as T⁴, not T. The thermal energy per particle is then much less than kT at low T.

(published on 08/04/11)

what is the exact temperature of vaccum?
- sabin duwal
nepal

If you want to insist that a vacuum have no electromagnetic radiation in it, then its temperature is 0K. However, no such thing exists. If you want a vacuum that at least is empty of more conventional particles, then its temperature must be well under that needed to excite particle-hole pairs.  To be free of electron-positron pairs, that means T would be much less than 5x10⁹ K. To be free of neutrinos in equilibrium would require a lower temperature. Since the neutrino masses aren't known, I can't give much of a clear figure. In principle some neutrinos might be around in equilibrium at room temperature. However, neutrinos interact so slowly with ordinary matter that they won't reach equilibrium for an extremely long time.

Mike W.

(published on 09/27/11)

to the first reply, i disagree that vacuum can have a temperature. for example, say in an enclosed vacuum, you can only measure the temperature of the measuring probe itself, caused by surrounding radiation. when we measure the temperature of something that exist, for example the human body, we are yet again trying to measure the temperature of the measuring probe, which temperature however, is in thermal equilibrium with our body. Hence i think it is pointless to say "the temperature of vacuum", although electromagnetic waves can travel through it, but that doesn't mean vacuum does indeed have a temperature.
- lawrence (age 25)
singapore

The definition of T is that 1/T= dS/dU |_V, where S is the entropy and U is the internal energy. The thermal radiation has U and it has S. When it's got a thermal spectrum, it has a defined T. We measure that T in various ways, but perhaps the most obvious is by measuring the spectrum. The temperature of remote space, for example, is 2.7255 +/- 0.0006 K.

 I don't see what the problem is.

Mike W.

(published on 04/15/12)

Can a certain T be assigned to a vacuum?
- Charlene (age 16)
Philippines

Sometimes it can. If the distribution of different frequencies of radiation in the vacuum follows the right form, then there's a temperature. If it has a different form, then if you look at one frequency range you'd get one temperature and if you look at another frequency range you'd get another temperature.  For example, far from a star, the microwave radiation in space looks like it has a temperature of 2.72548 K. However, if you look in the visible range, the little bit of light would fit a
much higher temperature.

Mike W.

(published on 12/12/12)

You said nothing can reach absolute zero because space is permeated by background radiation leftover from the big bang. Is the background radiation decreasing as the universe ages? Will it ever reach a maximum zero?
- Shane (age 22)
Linden, NJ, USA

Actually, the argument that one couldn't get things to absolute zero goes back to basic thermodynamics, long before anybody knew about the cosmic microwave background. Roughly, it's that the efficiency of heat pumps as coolers falls to zero as the temperature falls to zero. So with any heat leak, no matter how small, it would require an infinite amount of work to cool something to absolute zero.

On your main question, yes, the background temperature keeps falling as the universe expands. In principle, if nothing interesting happens, the infinite-time limit of this process will give T=0. It's possible that some sort of vacuum phase transition will interrupt that process. We don't know enough to predict the very long term with confidence.

Mike W.

(published on 04/15/13)