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Question is inspired by a recent burst of perpetuum mobile-type questions. It would be nice if one could simply discard them all by an argument that shows it's impossible to create a perfect vacuum. Intuitively, I have some hope that there will be a thermodynamics/statistical mechanics argument that we can never even eliminate air friction completely, thereby eliminating all these elaborate constructions requiring specific arguments from the get-go. My question is therefore twofold:

  1. Does it take infinite energy to create a perfect vacuum (in a macroscopic box)?
  2. If yes, can you include a derivation? If no, can you give an explicit construction with a finite amount of work being done?
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One minor thing of note: the majority of perpetual motion claims explicitly purport to violate conservation of energy and generate energy from nothing. As a result, the main problem with these claims is not necessarily that they are complicated by the existence of air friction, but rather the problem is much larger: they fundamentally violate the laws of physics. –  DumpsterDoofus Feb 24 '14 at 20:50
@DumpsterDoofus Of course. This question was merely inspired by this perpetual motion crap, but should be considered separately. –  Danu Feb 24 '14 at 20:55

5 Answers 5

The answer is no, or at least it is in the classical vacuum sense. I also don't see a rationale for why creating a vacuum would require infinite energy.

An explicit construction is to use a solid-phase reactive chemical "getter" to eliminate (nearly) all gas molecules present; in experimental practice, virtually all man-made materials still outgas slightly, which means that for practical purposes a true vacuum is difficult to achieve. As an example, one of the highest vacuums made on Earth was at CERN, with a density of 1 molecule per $\text{cm}^3$. However, this inability to create perfect vacuum is a problem of material science, rather than a side effect of theoretical impossibility.

In interstellar space, vacuums can approach 1 molecule per liter, which for all practical intents and purposes is perfect vacuum.

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My interpretation of his question is: is it possible to remove all those small leaks and virtual leaks, and is it possible to create a pump that can remove every single atom. –  garyp Feb 24 '14 at 19:25
My interpretation of his question is: is it possible to remove all those small leaks and virtual leaks, and is it possible to create a pump that can remove every single atom, creating an absolute vacuum. I can't see how that can be done. Using getters, cryopumps, or any kind of pump, you have to wait for the atom to hit the pumping surface. Also, you can't stop atoms from diffusing in. You can slow that down by putting your vessel in outer space, and wait a long time. But it's practically impossible to create absolute vacuum. Is there a thermodynamic argument preventing it? Don't know. –  garyp Feb 24 '14 at 19:34
Yeah, but "all intents and purposes" is engineering. The OP wants a really truly vacuum. And statistically that won't happen on a macro scale, because all materials have a nonzero partial pressure and so on. –  Carl Witthoft Feb 24 '14 at 19:41
@CarlWitthoft: True, but it's still an engineering problem regardless, seeing as the OP motive is perpetual motion. Also, is it true that all materials have a nonzero partial pressure? What about fully-crosslinked polymers, where the entire object is basically one giant molecule? Any vaporization would require direct bond scission, which would be unlikely at low temperatures such as 2 Kelvin. Make a 1L container out of it, let it outgas, put it in interstellar space, and close the lid. You have a perfect vacuum inside with 50% probability. –  DumpsterDoofus Feb 24 '14 at 19:46
@DumpsterDoofus Sorry, but you've misunderstood. I'm asking a theoretical question here, not an engineering one. –  Danu Feb 24 '14 at 20:12

Given an ideal piston/cylinder, starting with the piston completely inserted and zero volume, the work to make a perfect vacuum is simply:

(distance the piston moves) X (force) = (distance) X (area of the piston) X (exterior pressure).

So the work to make a vacuum of volume V, is V X P, where P is the exterior pressure, such as atmospheric pressure.

However, all real materials have a vapor pressure unless they are at a temperature of absolute zero. Molecules or atoms of the material of which the box is constructed will enter the vapor phase at all non-zero tempertures. A perfect vacuum in a macrosopic box cannot be made because reaching absolute zero in a finite number of steps is contrary to the third law of thermodynamics.

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But is it really true that all materials will have a vapor pressure? That would imply that even our best alloys would be slowly evaporating out into space when used in space probes. Alternatively, you could say that the stray solar wind particles keeps them held in lattice by their miniscule pressure. Either proposition is extremely difficult to accept. Some quantum tunneling out of the bond energy must obviously happen, but if it's only a handful of atoms that escape every year, that doesn't prevent the creation of a perfect vacuum in the classical sense. –  Alan Rominger Feb 24 '14 at 20:34

In quantum scale, particles are appearing and disappearing out of random everywhere all the time, meaning that if you are actually able to create a perfect vacuum at a macro scale, it would be instantly denied by the quantum scale. Also, in the quantum world, there's a small chance of random "teleportation" of any particle or atom from your container to any place in the Universe, creating a whole that would allow other particles to come in the system. Or the other way around, randomly bringing particles or atoms into the system.

Even using infinite energy, a Three-dimensional container can not be able to create a perfect vacuum in our Universe.

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I guess he meant in the classical context. –  jinawee Feb 24 '14 at 20:14
@jinawee is right about that. I think there should be some method to average such that fluctuations vanish. Then, a 'classical' vacuum might be established? Of course, in the quantum case it's clear a perfect vacuum isn't what the intuitive notion of a vacuum tells you it should be. –  Danu Feb 24 '14 at 21:15

Perfect vacuum can't be created. Even if you somehow get rid of all material particles, there still will be blackbody photons from the container, not to mention virtual gravitons.

Generally, you can't be 100% sure that some part of space is perfect vacuum - to know that you should measure precisely the energy of that region, but it's forbidden by Heisenberg's uncertainity principle: $\Delta E \Delta t \geq \hbar$ where $\Delta E$ is uncertainity of energy measurement. I'd say that making sure that something is perfect vacuum would take infinite time.

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Well, you should first prove that gravitons exist. And virtual particles are not real particles. –  jinawee Feb 24 '14 at 20:50
Patryk, your argument is a bit handwavy. Can you make it more precise? –  Danu Feb 24 '14 at 21:13
Theoretically, a macroscopic box without any fluid inside is possible to make, although I have no idea what engineering method should be used to make a such. Assume that you have this box without any fluid inside and no particles from the box are disconnecting from it. Still, you will have blackbody radiation from the box. –  Patryk Hes Feb 24 '14 at 21:27

Perpetual motion machines

Take a UV-grade fused silica vessel with 1 cm walls, annealing point 1140 C. Heat it to 900 C under hard vacuum both sides (turbopump plus titanium sublimation pump) with electrodeless low pressure 184.9 nm Hg vapor UV flood to dissociate everything not silica. Let that proceed for a few days, then flame off the connection. Cool. Cool in superfluid liquid helium. There's your "perfect" vacuum. It still has zero-point energy (Casimir effect) plus thermal emission.

Here's a "perfect" perpetual motion machine of the Second Kind. Why is it crap?

A hermetically isolated hard vacuum envelope contains two closely spaced but not touching, in-register and parallel, electrically conductive plates having micro-spiked inner surfaces. They are connected with a wire, perhaps containing a dissipative load (small motor). One plate has a large vacuum work function material inner surface (e.g., osmium at 5.93 eV). The other plate has a small vacuum work function material inner surface (e.g., n-doped diamond "carbon nitride" at 0.1 eV). Above 0 kelvin, spontaneous cold cathode emission runs the closed isolated system. Emitted electrons continuously fall down the 5.8 volt potential gradient. Evaporation from carbon nitride cools that plate. Accelerated collision onto osmium warms that plate. Round and round. The plates never come into thermal equilibrium when electrically shorted. The motor runs forever.

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I'd like to see a theoretical derivation which indicates that your vacuum is indeed perfect, i.e. contains literally zero particles (at least classically)... –  Danu Feb 24 '14 at 21:13
What would be in there that is volatile at 4 kelvin? Put it in a South African gold mine if muons bother you. Neurtrinos won't matter. –  Uncle Al Feb 25 '14 at 3:05

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