Using water vapor to concentrate and to disperse heat

See the comment. I spoke too soon about the water vapor idea: it doesn't help much.

An interesting posting on thinkcycle.org by Pranab Jyoti Ghosh led to my response. I mirror it here:

Hello Pranab,I have examined your description, and I see a fatal flaw: you have no cold sink. You hope to create one by allowing compressed air to expand, but it just doesn't happen that way. The condenser will get too hot to condense the water vapor.

On the other hand, the idea of using some work to pump water vapor out of a container of water vapor over water, lowering the water temperature so that heat will flow in from the surroundings, is a good idea. Nearly 1000 times more heat flows in than was invested in work. I can easily believe this.

The problem is how to make use of this latent heat. The water vapor coming out of the vacuum pump will be at approximately the vapor pressure of water at the ambient temperature. Thus, it will not condense on a surface at ambient temperature and deliver heat to it.

What you have really done is to concentrate heat from the surroundings into the water vapor at the same temperature as the surroundings. (I'm ignoring your idea for heating up the water vapor. That just isn't going to work.)

Concentrating heat is a good thing. It increases the heat flow which can be extracted from the surroundings because heat flow goes as the temperature difference, and investing some work in pumping water vapor results in a lower temperature and more heat flow.

Now if you have a lot of compressed air stored up from the night before, you can allow the compressed air to expand doing work, and let the water vapor condense on the tubes holding the compressed air, warming it back up so you get isothermal expansion. You save up the work in some form of potential energy like pumped water. The work available per mole of compressed air is RT ln(Pmax/Pmin), with T the daytime temperature.

At night, you reverse the process. Using work extracted from descending water, you compress air. You cool the tubes containing the air by using the vacuum pump to pump water vapor out of a container, cooling the water, and use the cold water to cool the tubes. By this method you extract heat from the tubes faster than merely exposing them to the ambient temperature would do. The result will be an excess of compressed air, which is useful for many things, or else and excess of pumped water, also useful.

The amount of excess energy available depends on the temperature difference from day to night, and on the capacity of the compressed air and pumped water storage. If night is 275K and day is 305K, you need to store 10 times the output energy as raised water during the day, and as compressed air at night. (The energy isn't really in the compressed air, but was dissipated into the surroundings at night in the form of the latent heat of water vapor exhausted from the vacuum pump).

This text will be mirrored at the Renewable Energy Design wikia, and at Archimerged's blog.

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2 Responses to “Using water vapor to concentrate and to disperse heat”

  1. archimerged Says:

    Posted on thinkcycle.org May 17, 2006 10:49 pm

    I am sorry to say I see another separate problem from the lack of cold sink.

    To evaporate water using a pump without expending much energy, you need a big tank full of vacuum first. But making one takes a lot of work. If you have one, you just sweep the low pressure vapor into the vacuum using hardly any energy, and more vapor will form.

    For a simple view, take a very long cylinder with some water in the end and piston up against the water. Pull the piston out against atmospheric pressure. The water will vaporize and absorb all of its heat of evaporation from the surroundings. But to get this to happen you had to do work against atmospheric pressure. I believe the experiment quoted was not exactly as described. I haven’t looked at it recently but google for OTEC or look on wikipedia. I think they have a big cold sink, namely, cold water from the bottom of the ocean.

    If the cylinder were evacuated first, then it wouldn’t take much (if any) work to move the piston.

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