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A vacuum requires little power to be created and when spread over a large surface area can lift thousands of pounds. Is there a way to generate enough work out of this to create more power than was required?

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    $\begingroup$ "Could a vacuum provide exponential power?" Exponential in what? The word "exponential" does not mean "a lot". "Exponential" refers to the function $\exp$ defined by the equation $\exp(x) = e^x$. If you want to talk about something being exponential, you should specify what thing (dependent variable) is growing exponentially with what other thing (independent variable). $\endgroup$ – DanielSank Mar 27 '18 at 4:20
  • $\begingroup$ A vacuum requires little power to be created.. This is a false premise. To create a vacuum, you have to do work against the ambient pressure so you have to put energy in. You get exactly the same energy out when the vacuum collapses. [P.S. I presume we're talking about traditional atmospheric vacuums that you get in a piston or bicycle pump - not quantum field vacuums?] $\endgroup$ – Oscar Bravo Mar 27 '18 at 6:11
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No - The easy answer is that would violate conservation of energy.

In this case, yes you can create a vacuum over a wide area producing a large force, but any movement of the piston would similarly amplify the amount of pressure lost. The maximum energy gained is the integral of the force (pressure times surface areas) over the distance. If you make a very wide piston that is super shallow it doesn’t take a lot of energy to create the vacuum, but the piston can’t move very far and you don’t get much energy out.

To get a lot of energy you need to let the piston move a lot. That means you would need to pump a lot of air out. That costs a lot of energy. At least as much as you could gain from the piston moving.

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Your premise that a vacuum requires very little energy to produce is false. Creating a vacuum in a volume $V$ with atmospheric pressure $P$ requires at least $E=PV$ of energy, in order to displace that quantity of air in the atmosphere.

Then imagine you use this vacuum to raise a piston of cross sectional area $A$. The piston can go up a distance $h=\frac VA$ before it runs out of vacuum. The force on the piston due to the pressure differential is $PA$, and so overall the work done is:

$$ W = Fh=\left(PA\right)\left(\frac VA\right)=PV$$

So, best case scenario, you get out exactly what you put in, and you've accomplished nothing.

Realistically, vacuum pumps require more than $PV$ of energy, and some of the work in the piston is lost to friction, so you get back less than $PV$ of energy, and so you've accomplished less than nothing.

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A vacuum requires little power to be created

That's a very debatable statement. Creating a vacuum depends on what you start from and what you have to do to make one. Start from a jar of water in the sea and try to create a vacuum - it's going to be harder than starting from a jar filled with air standing in the open.

and when spread over a large surface area can lift thousands of pounds.

A vacuum will lift precisely nothing.

You are confusing e.g. the effect of external pressure or air flowing into a vacuum with the vacuum doing work. The vacuum is doing nothing, it's just being filled. It's the something else that it's filling with (or that is trying to fill it) that is doing the work.

Imagine a box containing a vacuum with air all around the box. There is a force on the surface of the box, but it's from the air, not the vacuum. The vacuum has no effect itself. The net force is inward precisely because the vacuum supplies no outward pressure to match the inward pressure from the air.

The vacuum does nothing. It will lift nothing, it will pull nothing, it will push nothing. It is the other forces outside the vacuum that do the work.

Is there a way to generate enough work out of this to create more power than was required?

Not from the vacuum. You can stop or reduce the force that's maintaining the vacuum (and that could be the intermolecular force keeping the container unbroken against external pressure). That will mean the external pressure source will try to fill or compress the space the vacuum occupies (because the vacuum can't resist it).

That generates power, but it cannot possibly generate more power than you used to create the vacuum in the first place.

How did you create the vacuum ? You had to e.g. move the air out of the way. What happens when you let the air back in - it does the same movement in reverse (more or less). So the net work been done is, at best, zero.

This is all about thermodynamics and thermodynamics is a game you can't win.

This is all discussed formally in physics under the title of Thermodynamic Work.

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