Monday, November 22, 2010

Cooking with insulators

Look what I got.

It's a thermal pot!  Also a Kandinsky carpet, but the pot!

It's easy to use. Put all the ingredients in the inner pot, and heat them on a stove. Then put the inner pot into the hot pot, and let it cook.  Then, when you open it again later, the meal is still hot and ready to eat.

 Lentil soup... delicious!

The way it works is simple.  The outer pot is a really good thermal insulator.  The outer pot has two layers, with a vacuum chamber between them.

There are basically three kinds of heat transfer.  The first is convection, which is when hot atoms physically move into a colder space.  Convection doesn't occur in solids, so it's not a problem for my pot.  The second kind is heat conduction, which is when hot atoms transfer energy to cold atoms, essentially by bumping into them.  Conduction occurs in solids, but it can't occur in a vacuum.  So that's why the thermal pot uses a vacuum.

The last kind of heat transfer is thermal radiation.  Random motion of particles will emit electromagnetic radiation (ie light), which carries energy.  Light travels through a vacuum just fine, so that's how the thermal pot loses energy over time.  In fact, we can calculate how much energy the pot loses through the Stefan-Boltzmann Law.

 This basically says that the rate of energy loss (P) is proportional to the fourth power of temperature (T).  It's also proportional to the the surface area of the pot (A).  σ is just a fundamental constant of nature, called the Stefan-Boltzmann constant.

As for ϵ, that is the emissivity.  It turns out that the emissivity is always equal to the percentage of light that the material absorbs (as opposed to what it reflects).  Absorption and emission are basically the same process, only reversed in time, so it's not surprising that their rates are related.  To make the best insulator, we want low emissivity, and thus low absorption and high reflectivity.

Therefore, what we really want is a highly reflective surface, such as silver.  It's likely that the inner surface of the vacuum chamber is coated with silver, though I couldn't be sure without breaking it open and looking.

I tried calculating the rate of change of temperature, and it's about 15 degrees Celsius (or 27 degrees Farenheit) per hour.  That's an overestimate.*  I expect it's a few times smaller than that.  I often leave soup in there for four hours or more, and it's still piping hot when I open it!

Chicken veggie soup!  At least one animal was harmed in the making of this blog.

*Some details: I took the surface area to be 0.5 square meters, the reflectivity to be 90%, and the heat capacity to be the same as two quarts of water.  The pot inside is 100 degrees Celsius, and the temperature outside is 20 degrees Celsius.  15 degrees per hour is almost certainly an overestimate, since the rate of energy loss would decrease as the pot gets closer to room temperature.


schrodingasdawg said...

I want a Kandinsky carpet. Where did you get a Kandinsky carpet?


miller said...

That one's from Overstock, though I don't think they say anywhere that it's Kandinsky.

Actually I wasn't sure if it really was Kandinsky, but I just looked it up. This one is called "Hommage a Grohmann".