Of Cheese, Mice, Men, and Mars

​Here is a cool experiment that you can do at home. You can follow the link, but in a nutshell the experiment involves cutting a piece of cheese into cubes of different sizes. When you place these cheese cubes in a conventional preheated oven you find that the smaller cheese cubes melt first. However, if you place these cheese cubes in a microwave oven it is the larger cubes that melt first! How can this be?

The explanation has to do with something called the surface to volume ratio. If you calculate the surface area of a cube and divide this by the volume of that cube, you will find that the smaller cubes have a greater surface to volume ratio than the larger cubes. So when you place the cheese cubes in a conventional oven, the heat enters the smaller cubes much faster (because they have more surface area relative to their volumes) than it enters the larger cubes. Most people that have tried to heat food in a conventional oven have experienced this. The center of bulky pieces of food may remain cold while the outside is hot, whereas smaller pieces heat up faster.

But just in the same way that heat gets in faster into a small cheese cube that has a high surface to volume ratio, it is also true that heat can get out equally fast (dissipate) from such cubes. The microwave oven generates heat inside the cubes. In the larger cubes the heat has trouble moving out (because of the lower surface to volume ratio) and accumulates, heating the cube and melting it, whereas in the smaller cubes the heat escapes much faster and the cube doesn’t get as hot.

The interesting thing is that this principle also applies to living things. Mice have a very high surface to volume ratio compared to a human being, and tend to lose heat very fast just like the small cheese cubes. This is why mice have a very high metabolic rate (expressed on a per body mass basis) to compensate for this large heat loss. If a mouse had the metabolic rate of a human it would die from hypothermia (lack of heat). Conversely if a person had the metabolic rate of a mouse, he/she would die from over-heating because the heat generated in the large volume of the human body would have trouble getting out through the limited surface area, just like in the large cheese cubes. If an elephant had the metabolic rate of a mouse it would (in theory) boil!

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​But even more interesting is that we owe our very existence to the principle of the surface to volume ratio. Compare our planet teeming with life to the barren wasteland that is Mars. The Earth is larger than Mars and therefore has a lower surface to volume ratio and cools slowly (like the large cheese cubes). All the heat that gets trapped inside the Earth as a result of this has melted its core, and the spinning of this core generates a magnetic field. This magnetic field protects the Earth against the solar wind, which would otherwise strip away our atmosphere. Unlike the Earth, Mars is smaller (has a high surface to volume ratio) and, like the small cheese cubes, it has cooled faster. As a result of this, its core solidified and stopped spinning a long time ago. When this happened, Mars lost its magnetic field and its atmosphere was stripped away by the solar wind.

So there you have it. Who needs expensive labs or particle accelerators? Here is a fundamental physical principle responsible for life that holds true from mice to planets and that you can put to the test in your kitchen. Isn’t that cool?

Now next time you get served cheese cubes and crackers at a cocktail party you can impress everyone by talking about the principle of the surface to volume ratio and heat transfer. Please remember to reference this blog!

Mouse & Cheese
Photo credit: Darny / Foter.com / CC BY-NC-ND
Mars
Photo credit: NASA Goddard Photo and Video / Foter.com / CC BY

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