[calambrac]

You had to expend the energy to freeze the water. You probably did that with a freezer, which runs using a compressor just like an air conditioner, except that it has to get a lot colder.

I think you're still right that it comes out cheaper, though, because you'd be spending most of the freezer's energy output anyways.

[jacquesm]

The freezes compressor will run longer if you stuff it with things that are not yet at the temperature of the rest of the stuff in the freezer.

This is also why it is a good idea to de-ice your freezer every now and then, keeping all that ice at a low temperature against the leakage through the walls of the freezer costs energy.

[billswift]

The real reason to de-ice is that the ice interferes with the flow of heat between the items you place in the freezer and the cooling coils. It wastes energy, but by making it take longer to cool things down.

[Elepsis]

I'm not so sure this logic makes sense -- in fact I think it might be entirely backwards.

I've always been under the impression that though you pay a penalty for freezing things the first time you put them in, thereafter a full refrigerator (and freezer) is actually much more efficient because it's more difficult to keep air cold than it is to keep any variety of items that are more dense. If we're talking about leakage, too, air obviously exits the freezer much more often than its contents do.

[jacquesm]

reduce it to an absurdity:

If you imagine a giant freezer filled with ice it will eventually melt. This takes energy, a larger freezer will take more, an empty one will take less than a full one.

Counteracting the heat transferred through the freezer walls from the outside in will require an amount of energy proportional to the mass in the freezer and the leakage from the outside.

It takes energy to maintain that imbalance, the bigger the imbalance the faster the heat will transfer.

If the stuff in the freezer is light (air) then it will take less energy to keep it cold than if the stuff in the freezer is heavy (ice), because there simply is less leakage from air (a thermal insulator) to the walls than there is from ice (a pretty good thermal conductor).

Thermal conductivity is not very tightly coupled to mass but it usually is a good indicator, in the case of ice vs air it works pretty good.

So, it takes more energy to keep a freezer full of ice at a low temperature than a freezer full of air...

For an encore, which is heavier: A cubic meter of dry air vs a cubic meter of humid air ?

[derobert]

I believe the inefficiency of an empty freezer/fridge actually comes from it being inefficient to cycle the compressor. The low heat capacity of air leads to the compressor cycling often.

[sokoloff]

Most people will get the last question wrong.

Humid air is less dense (dry air heavier) because water has a lower molecular weight than the average molecule of dry air.

[swombat]

Air has a very low heat capacity. It doesn't take much energy to cool a cubic metre of air quickly (see air con, for example). On the other hand, cooling a cubic metre of water and other watery solids takes a load more energy.

In terms of keeping it cool, that probably depends on how good your freezer's insulation is. If it's really good, it probably doesn't take too much energy to keep things cool (air or otherwise). If it's not so good, you'll incur a constant "your freezer sucks" tax.

In the case being discussed, we're talking about freezing stuff every day, and letting it thaw in/near your bed during the night. So the cost would definitely be there.

[calambrac]

No doubt there's still an additional cost, I just don't think it would be high enough to make it more expensive than running an air conditioner, given that you're going to be running the freezer regardless (depending, of course, on how much we're talking about. I'm picturing a window unit vs. a window fan with a baking pan's worth of ice).

Any ideas on how to be more rigorous about thinking this through or running an experiment?

[swombat]

You could take a certain quantity of ice, figure out how long it takes to melt under a fan in hot weather, then calculate the energy required to get that quantity of water into ice (heat capacity equations), and you'd have a rough figure for energy spent per unit time.

Then compare that with the energy consumption of an air-con unit.

[derobert]

An experiment is easy to run. Obtain a Kill-a-Watt or other power meter, then measure (a) how much power the freezer uses over a day w/o freezing extra ice for fan-ice cooling, repeating several times; (b) how much power the freezer uses over a day with freezing extra ice for fan-ice cooling, repeating several times; (c) how much power the fan uses blowing over the ice; (d) how much power an AC uses to keep the room comfortable, repeated several times; (e) [bonus] how much power an AC set to a higher temp. + a fan blowing on you uses to keep the room comfortable, repeated several times.

You can then compare (b)-(a)+(c) vs. (d) or (e).

Ideally, you'd do these experiments in identical conditions (temp., sunlight, wind, humidity, etc.), of course.

[calambrac]

Of course, but is the marginal cost of adding a few trays of ice really more expensive than running an air conditioner?

The problem is so under-specified at this point it's kind of silly to pretend we could get a meaningful answer yet. Are we talking about the ice/fan and a/c cooling the room to the same temperature? Or are we just talking about the sleeper's comfort, in which case we should take into account that i/f can be put right next the sleeper while an a/c has to sit all the way over in the window? Etc, etc.

[baddox]

Well, that isn't quite a fair comparison, since the ice-fan only cools the small column of air between the fan and your bed, while an air conditioner cools all the air in a room or building. That said, the ice-fan is probably more efficient than a very small air conditioner than performs the same level of cooling (not that such small air conditioners exist), whereas an air conditioner is surely more efficient than the quantity of fans and ice that would be required to cool an entire room or building.

I have another question, since my basic physics knowledge is a bit lacking. Compressed refrigerant system like air conditioners work by expending (electrical) energy to move heat from one system (the inside air) to another system (generally outdoors). With the ice-fan, where does the heat go? This is probably a fallacious way to explain it, but is the energy being removed from the air and used to transfer the state of the H20 from solid to liquid? And if that's the case, if you wanted to cool an entire room rather than a column of blown air, you'd have to have the liquid water end up outside the room, just like the exhaust from an AC system is outside?

[derobert]

With the ice-fan, the heat from the room is going into melting the ice (and, eventually, warming that water to room temperature).

The freezer, of course, works just like an AC: it moves the heat from inside the freezer to outside the freezer — i.e., to the room its sitting in (some large commercial freezers actually use outdoor parts so then can dump the heat outdoors). Assumably, during the day, the windows are open, so that heat will escape outdoors.

Random note: If you could prevent all heat transfer with the outdoors, the freezer/fan/ice cycle would actually heat the room.

[baddox]

Very true. Your comment reminds me of a question I've always had. Does a refrigerator full of stuff take more energy per unit time (after the stuff is all cooled down) than an empty refrigerator? I don't know exactly how to do rough calculations of that sort of thing in my head, but my best guess is that since more food in the frig means less air, the question becomes, is air easier to keep cool than food?