I Have The Coolest Hobbies, Ctd.

Seriously you guys what’s going on here? Now Liz Clark sends along a video of three cheese cubes melting in the microwave on the same plate. Spoiler: they melt in the opposite order of my video.

Cheese Cubes pt. II from Dan Meyer on Vimeo.

This isn’t funny anymore.

Related: Guided Inquiry and Surface to Volume Ratio

2011 Feb 27. Liz Clark writes back in, having taken the rotating tray out of the microwave and melted one cube at a time (per Matt’s recommendations). Our results now agree.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. I thought the microwave created standing waves within the microwave, creating local mininum and maximum points, thus making some parts of the microwave heat up more than others.

    I believe this is one of the reasons you’re supposed cook things for a couple of minutes, take them out of the microwave, stir them, and put them back in.

    Also the reason why you should wait a couple of minutes after microwaving the food before you eat it, so the heat can transfer from the hotter parts of the meal to the ones which haven’t been in the local maximum.

  2. Great link, Jean-Marc, and thanks, both of you, for dropping some knowledge on me. Is the appropriate test here to switch the order of the small, medium, and large cubes several times to see what happens when each cube intersects or avoids the local maxima?

  3. You might also try three cubes in your microwave at once, rather than separately, and see if your results duplicate Liz’s, since that is the way she melted hers.

  4. You are seeing the standing wave nature of microwaves at work here, for sure. I have a feeling that if she had arranged the cheese blocks differently on the plate, her results would have been different.

    You can switch the order of the cubes, or you can use a bunch of cubes of the same size and try to find the “hot spots” in the microwave.

    Or you could find the minima and avoid the burning cheese smell by using maxwell’s equations ; ). That video would be WAY less interesting…

  5. Good point about the standing waves. I’ll try changing the order of the cubes on the plate, however I’m wondering if there will be no affect because the plate rotates. Also I got the same result at home and at school using two very different microwaves.

  6. Remove the rotating plate :) That way you won’t have problems with cheese moving around.

    The only problem is the EM wave in the microwave has only 2 max points lengthwise if i remember it correctly. I did the light speed experiment Jean-Marc proposed above, but with a row of chocolate, and you get strong melting at two points (max), and no melting at 3 points (min) – so it would be a bit touchy to place 3 cubes of cheese in such a way that they get the same amount of energy. Maybe your microwave uses a different frequency so you would get a different standing wave.

    I think the best way to do a controlled experiment would be to measure the melting of the cubes separately, each time placing the cube in the middle.

  7. I think the reason is that in a microwave food is heated from the inside, not from the outside.
    The air surrounding the cheese is not very hot (as it would be in an oven) but cool, at least a lot cooler than the cheese.
    So the cheese gets cooled by its surface. The larger the surface, the harder it is to heat.

  8. OK, I should have read the comments to the earlier post… of course this had come up before. Never mind.

  9. My homework is to melt identical cheese cubes in an oven, just so I can verify that it is the microwave waves maximum and minimum.

  10. Do fill us in on that, okay? My last experiment depleted a lot of capital around here with my (extremely) patient wife. This one is on someone else.

  11. Microwaves definitely cook from the outside in, though the microwaves penetrate more deeply than the infrared and convection heating of conventional ovens.

    Standing waves should not be a big problem in a microwave with a rotating plate, though there will still be some variation with placement.

    Note that melting several blocks at once raises the question of how the microwave energy is distributed to the different cubes. There is no reason to assume that each absorbs the same amount of energy (which you could assume when there was only one block in the oven absorbing essentially all the energy).

    I think that the amount absorbed should be proportional to something like the volume of cheese absorbing the energy, but since the amount absorbed decreases with depth into the block, it is a complicated integral to figure out the effective volume.

    Think spheres instead of cubes for a moment. Pretend that the absorption is a simple step function of depth instead of
    some sort of gradual decay. Say the first inch is uniformly absorbing energy and deeper gets none.

    For a small sphere, the amount of energy absorbed would be proportional to the volume, but for a huge sphere the absorption would be proportional to the surface area.

    It is DEFINITELY simpler to do the melting one item at a time, since you at least know how much energy is being absorbed, if not how it is distributed within the chunk.

  12. gasstationwithoutpumps is correct. The rotating plate is used to partially negate the fact that the wave only hits in certain places. As the food moves, it should “intercept” the wave in various places.
    Dan’s cheeses were placed in the same place within the microwave, or so it appeared. So I would expect the blocks to be affected in roughly the same way.
    Liz’s cheeses were moving around, therefore being affected differently as they spun.
    Therefore, I’d expect the cheeses to melt differently than Dan’s.

    This might also explain a bit of what is happening: http://tuhsphysics.ttsd.k12.or.us/Research/IB99/Tanski/kate.htm

    I think:
    1) the rotating plate should be removed.
    2) the same type of cheese should be used.
    3) the cheeses should be placed in the same place within the microwave.

    Between the two videos, none of these variables were controlled.

  13. Could this also be a function of the cheese type? Since the microwaves heat by causing water molecules to vibrate could moister cheeses have a different melting behavior? The smaller cube will have less water and therefore not heat as quickly. There are also different microwave designs. Some have more than one gun. The problem is getting lots of confounding variables involved.

  14. Dan, one key aspect in my microwave is height from the base ie… microwave popcorn bag will work faster if I put it on an upturned bowl than if I place it directly on the turntable …..

  15. From what I have read, it will be important to 1) remove the rotational aspect of the microwave and 2) make sure that each cube of cheese is placed in the same spot of the microwave. This will probably change the data in Dan’s table of melting times, but will it be a significant change?

  16. wouldn’t this be a great integrated math/science lesson? knowing the ‘whats’ seeking the ‘whys’?

  17. Hi Dan,

    I think this doesn’t conflict with your other data. The way I calculate it, if the 3 cheese blocks here are cubes of side x, then we can calculate a volume/surface area ratio as

    V/SA = x^3 / (6x^2) = x/6.

    If that’s the case, then the bigger the cube, the faster it heats up relative to how fast it can radiate heat, and so the biggest cheese block should melt first. Isn’t this the result you found?

    I posted a model of this under your original data, with a proposed explanation of the reason for the exponential fit. Let me know if I’ve missed something.

  18. I have a problem with the characterization of that experiment as measuring the speed of light. You’re only measuring the wavelength — you’re relying on the manufacturer to provide you the frequency. But what if they themselves determined the frequency from the wavelength and the speed of light?

  19. I tried the demonstration again putting each cube into the microwave individually. The results agree with Dan’s video.

    Small cube begins to melt at 8 seconds and takes 3 seconds to melt.

    Medium cube begins to melt at 5 seconds and takes 4 seconds to melt.

    Large cube begins to melt at 9 seconds and takes 14 seconds to melt.

    The point of my lesson was the surface area to volume ratio, much like the comments on cell biology and baby in the car.

  20. This also reminds me of the question of “what shape should ice be?” Using either cheese or ice melting, students could investigate various shapes and dimensions.

    Spheres should melt the slowest as they have the lowest SA:Volume ratio. Getting a sphere of ice is tricky though. Alton Brown of the Food Network had an episode where he froze water in a balloon to use in a punch bowl.