I can’t immediately see why the following isn’t a perpetual motion machine of the first kind, ie. produces work without the input of energy. It would thus violate the first law of thermodynamics: the law of conservation of energy. Further, it’s based on a classical rather than quantum effect and would have been known to all the pioneers of thermodynamics.

I’ll describe the machine first. It relies on an effect variously known as the “Joule-Thompson effect”, “Kelvin equation” or “Ostwald-Freundlich equation”.

Start with a thermally isolated closed box containing a liquid (such as water) under a vacuum (it would also work under air). The liquid would evaporate and the space above the liquid would increase in pressure until it was filled with vapour at 100% relative humidity. Nothing more would happen.

Now place a thin (~10 nm diameter) capillary tube in the liquid in this box. The liquid will rise up the tube (for liquid mercury it would drop down but the end result would still be the same) until it reaches equilibrium. So you’ve got the idea. A capillary tube sits in a liquid and liquid has risen up the tube, all under a vacuum filled with vapour. (According to several technical papers, quantum effects are negligible for tubes > 4 nm diameter).

The Kelvin equation says that, because of surface tension effects, the liquid will condense in the capillary tube at below 100% relative humidity (for 10 nm diameter at 90% relative humidity, for 100 nm diameter at 99% relative humidity). The latent heats of evaporation and condensation balance. So the steady state condition is liquid evaporating from the bulk liquid and an equal amount of liquid condensing in the capillary tube driving a circulation of liquid. A minuscule propeller under the capillary tube could extract energy from the flow, despite it being a thermally isolated system.

Where did I go wrong? I still don’t see it. All Wikipedia “Perpetual motion” says is:

> there are concepts and technical drafts that propose “perpetual motion”, but on closer analysis it’s revealed that they actually “consume” some sort of natural resource or latent energy, such as the phase changes of water or other fluids … A capillarity based water pump functions using small ambient temperature gradients and vapour pressure differences.

PS. I came across this while working on movement of and condensation of water passing through a porous iron oxide layer on top of corroding iron. I really need an answer as it affects the rate of steel corrosion.

Water will not leave a capillary tube without extra energy being added.

Stealth said:

Water will not leave a capillary tube without extra energy being added.

Good, you understand the problem, If you’re talking about the bottom of the capillary tube, why not? There’s no surface tension effect stopping it. If you’re talking about the top of the tube, again there’s nothing to stop the ingress of gas.

mollwollfumble said:

Stealth said:

Water will not leave a capillary tube without extra energy being added.

Good, you understand the problem, If you’re talking about the bottom of the capillary tube, why not? There’s no surface tension effect stopping it. If you’re talking about the top of the tube, again there’s nothing to stop the ingress of gas.

Except that the tube will be full of water right to the top due to capillary action.

Stealth said:

Water will not leave a capillary tube without extra energy being added.

But the mollwoll PMM has the water condensing and flowing down the capillary tube, rather than the usual system where it evaporates and water rises up the tube.

I haven’t thought this through, but perhaps the water would cool until some equilibrium state was reached.

Stealth said:

Except that the tube will be full of water right to the top due to capillary action.

No no no. The tube is only full part way up. The top only has water vapour in it.

mollwollfumble said:

Stealth said:

Except that the tube will be full of water right to the top due to capillary action.

No no no. The tube is only full part way up. The top only has water vapour in it.

Why? Why does normal capillary action not work in this system?

Before condensation, the system will be in equilibrium, so after condensation there is no doubt that water will need to flow down the tube, to restore static equilibrium.

You could make the tube as tall as you like, so even if there is a range over which the capillary column was stable, with enough condensation you would reach a state where water had to flow.

Stealth said:

mollwollfumble said:

Stealth said:

Except that the tube will be full of water right to the top due to capillary action.

No no no. The tube is only full part way up. The top only has water vapour in it.

Why? Why does normal capillary action not work in this system?

It does. The height of capillary rise is governed by the fluid and the tube diameter and material, but it is quite limited.

Maybe this is a sort of macro Maxwell’s Demon.

I’ve always been unconvinced that MD systems are impossible in principle (or at least I’ve always been unconvinced by the usual explanation based on quantum effects).

Just to clear up one point, if there is no air in the system, can you talk of ‘relative humidity’?

morrie said:

Just to clear up one point, if there is no air in the system, can you talk of ‘relative humidity’?

I don’t know. Consider it as short-hand for: “ratio of actual vapour pressure to vapour pressure in equilibrium with liquid in the absence of surface tension effects”.

Can we do without the capillary tube?

If we had a very tall container with flat surfaces near the top, wouldn’t the water tend to condense on these upper flat surfaces? It could then be fed down to the bottom through a turbine, and then allowed to evaporate again.

The Rev Dodgson said:

Can we do without the capillary tube?

If we had a very tall container with flat surfaces near the top, wouldn’t the water tend to condense on these upper flat surfaces? It could then be fed down to the bottom through a turbine, and then allowed to evaporate again.

The condensation on the upper flat surfaces would exactly match the evaporation from those surfaces. It’s an interesting question, though, because of the time lag between condensation and evaporation.

mollwollfumble said:

The Rev Dodgson said:

Can we do without the capillary tube?

If we had a very tall container with flat surfaces near the top, wouldn’t the water tend to condense on these upper flat surfaces? It could then be fed down to the bottom through a turbine, and then allowed to evaporate again.

The condensation on the upper flat surfaces would exactly match the evaporation from those surfaces. It’s an interesting question, though, because of the time lag between condensation and evaporation.

But would it? Wouldn’t the lower, higher pressure region be continually supplying the upper region with excess water molecules?

The Rev Dodgson said:

mollwollfumble said:

The Rev Dodgson said:

Can we do without the capillary tube?

If we had a very tall container with flat surfaces near the top, wouldn’t the water tend to condense on these upper flat surfaces? It could then be fed down to the bottom through a turbine, and then allowed to evaporate again.

The condensation on the upper flat surfaces would exactly match the evaporation from those surfaces. It’s an interesting question, though, because of the time lag between condensation and evaporation.

But would it? Wouldn’t the lower, higher pressure region be continually supplying the upper region with excess water molecules?

I was forgetting the variation in gas pressure with height. The situation would be different depending on whether we’re talking about water vapour in air or water vapour in vacuum. For water vapour in vacuum there would be no condensation on those surfaces because the pressure up high would be lower than 100% RH. For water vapour in air it might depend on whether the lower density of water vapour relative to air is sufficient to counteract the decrease in air pressure with height.

There is also the issue of nanoscale pores on the vertical surfaces but that would bring us back to the capillary problem through surface tension effects.

when I was a kid I used to spend idle hours trying to come up with free energy machines

if only I had known that nuclear and fossil fuels were the answers to our prayers for cheap electricity I would have done something else

Problem solved. I should have looked at Derivation of Kelvin’s Equation

Because of the weight of vapour above the surface of the bulk liquid, the vapour pressure decreases with height. This decrease exactly matches the drop in ‘relative humidity’ associated with the steady-state condition of no evaporation or condensation on the surface of the meniscus in the capillary tube.

wookiemeister said:

when I was a kid I used to spend idle hours trying to come up with free energy machines. If only I had known that nuclear and fossil fuels were the answers to our prayers for cheap electricity I would have done something else

I was familiar with Maxwell’s Demon from an early age, so never bothered looking. I’ve only come up with one false perpetual motion machine before, about ten years ago, and that turned out to be a variation on the Brownian ratchet machine.

While young, I was very concerned about the predictions that fossil fuels would soon run out, and there was a tension between the obvious long term need for fast-breeder reactors and the nuclear weapon proliferation issue.