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I have noticed that when I microwave an ice cube it appears to melt more slowly than I would expect. For example, an equal volume of water starting at 0 deg C would probably be at boiling point before an ice cube that was at -15 deg C had melted. I realize there is enthalpy of fusion to take into account in the melting process but I believe there is more to it than that.

As I understand it a microwave oven works by exciting the water molecules in whatever is being cooked and if memory serves the frequency used is one that causes rotation of the molecule. Since the ice cube is solid I'm assuming the molecules aren't free to rotate and therefore the microwaves have a much reduced effect. In fact I'm wondering if a perfect single crystal of water would respond at all to being microwaved. Does this sound right?

I've been trying to rack my brain for a way of testing this theory but I can't think of a way of getting an perfectly dry ice cube into a microwave to see if anything happens. Even a tiny amount of surface water, caused from interaction with a warm atmosphere, would encourage melting.

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Just spit-balling here...I see at least two issues (a) the rotational modes are suppressed, but they will be coupled to phonon modes in the bulk so there is still a channel for energy to be transferred from the radiation field to the material, but (b) the modes will be shifted by virtue of the molecules being bound so you may be off-resonances. A detailed consideration is beyond me. –  dmckee Jul 23 '11 at 19:11
    
I don't think it's a resonance phenomenon at all. Microwaves would probably be in the same part of the spectrum as the rotational bands of water, but the discrete rotational bands you'd see in a gas are not observable in liquids or solids. I actually don't think there's any quantum mechanics required at all, except in the sense that quantum mechanics ultimately determines facts like the nonvanishing dipole moment of the water molecule. –  Ben Crowell Jul 23 '11 at 19:35
    
In the Question you said equal volume of ice and liquid water. But to equal volumes correspond different amounts of mass of H2O. –  Helder Velez Jul 24 '11 at 8:22

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The unusual thing is the really high absorption of microwaves by bulk water, whereas the ice behaves more normal like most solids and liquids. In liquid water we have an effect of relaxation of orientational polarisation. The polarisation is achieved not by rotation (not possible in liquid water) but by shift of hydrogen atoms along the hydrogen bonds. This is a kind of Kohlrausch conduction mechanism. This process is extremely fast, so polarisation of water is one of the fastest processes in liquids. There is debate, whether tunneling plays a role to enhance the shift of the protons. The same mechanism is responsible for the extraordinary (about tenfold) mobilities of H+ Ions in water.

Here is a plot of Water spectrum in microwave domain. Note the incredible absorption maximum with k about 3 !

http://books.google.com/books?id=bj1EnQPB0CMC&pg=PA184#v=onepage&q&f=false

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You refer to "orientational polarisation," but then you claim that rotation is "not possible in liquid water." A molecule can't change its orientation without rotating. I think what you really mean here is that (classically) rotation is damped in much less than a full rotational cycle, or (quantum-mechanically) there are no discrete rotational bands. These statements are completely different than saying that rotation is impossible in general. Rotation through a small angle is still rotation. The WP article on dielectric heating has a nice discussion of all this. –  Ben Crowell Jul 24 '11 at 16:43
    
No not at all. You want to correlate orientation to rotation. This is wrong. As I recommended already, read about ice structure, local order in liquid water, and on hydrogen bonds. You will have to look into physical Chemistry textbooks. This is outside the scope of most physics research and books. –  Georg Jul 24 '11 at 19:02

This is a nice application of $W=F\Delta x$ for mechanical work, or its rotational analogue $W=\tau\Delta\theta$. Molecules in a liquid are free to rotate, so $\Delta\theta$ can be large. If you think of the lattice in an ice crystal as being built out of individual water molecules, then $\Delta\theta$ is limited by the ability of the lattice to deform, and you get a much smaller amount of work done by the electric field.

If you try melting a stick of butter in the microwave, you'll see that it doesn't melt evenly. The melting starts in a certain spot, and then the spot spreads. The idea here is that once you get even a tiny bit of liquid, that liquid becomes efficient at absorbing energy, so the process snowballs. For this reason, I don't think you can test the theory by trying to use ice that has been thoroughly dried. As soon as the tiniest amount of liquid forms, it starts to grow.

Some possible experimental tests:

The explanation is independent of the detailed nature of the substance, so it should be true for all substances that the solid heats more slowly than the liquid. This seems to be verified by the fact that butter acts the same way as water.

An insulating liquid without any electric dipole moment should heat more slowly than one like water that has a dipole moment. I don't know of a safe, easy example, though.

[EDIT] Reading a little more on the web, it turns out that there are four qualitatively different effects by which microwaves can heat matter:

  1. dielectric heating -- This is the effect I described above.

  2. ionic conductivity

  3. electronic conductivity

  4. hysteresis

In most foods, 1 and 2 are of approximately equal strength. 3 can occur in soot particles formed when food burns. In pure water and ice, only 1 is significant.

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""Molecules in a liquid are free to rotate, "" This is wrong in 99 % of materials. (Rotation is possible when the molecules rotate in the solid as well eg Camphor and similar rather spherical molecules) For ice with the diamond structure and 4 hydrogen bonds per molecule it is totally wrong. The unusual thing is not why the uptake of energy is so low in ice, but why it so exceptionally high in liquid water. Re butter, the start is where some droplet of bulk water is in or at the butter. –  Georg Jul 23 '11 at 19:38
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@Georg: I'm happy to be corrected if I'm wrong, but I'm not able to follow the logic of your post. Could you explain at greater length? You quoted my statement about liquids, but all your own statements are about solids. –  Ben Crowell Jul 24 '11 at 2:35
    
That is some very lengthy thing . I' recommend to read about lattice of ice and then about structures in liquid water. The density anomality of water is another effect from that locally ordered structures. You mentioned that the rotational frequencies of water in gas phase are not found in liquid, another hint that rotation is not at work. (BTW even when rotation were at work, this would not explain why the absorption is that high.) –  Georg Jul 24 '11 at 10:08
    
@Georg: "You mentioned that the rotational frequencies of water in gas phase are not found in liquid, another hint that rotation is not at work." No, that's incorrect. Discrete rotational bands are not observed in liquid. That doesn't mean that rotation doesn't exist. By analogy, we don't observe discrete energy levels in the emission spectrum of a tungsten lightbulb filament, but that doesn't mean that there are no possible electronic excitations in solid tungsten. It just means that they appear classical because of the large number of particles. –  Ben Crowell Jul 24 '11 at 16:19
    
If rotation in liquid water would "go on", one would expect two broad bands centered at the same frequencies as the rotational gas phase lines were. –  Georg Jul 24 '11 at 18:57

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