Question is inspired by a recent burst of perpetuum mobile-type questions. It would be nice if one could simply discard them all (or at least the huge class that assumes some kind of perfect vacuum to eliminate friction) 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 ruling out all these elaborate constructions requiring specific arguments from the get-go. My question is therefore twofold:
- Does it take infinite energy to create a perfect vacuum (in a macroscopic box)?
- If yes, can you include a derivation? If no, can you give an explicit construction with a finite amount of work being done?
Best Answer
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.