Do big sugar granules have a big surface area?

Answer 1

Let's think about this a bit. Imagine a large sugar granule: for ease of illustration, we'll think of, say, a cube that's 1 cm on a side. (Yes, I know this is unreasonably large, but the argument works on smaller pieces as well.) Think of how much surface area it has, which is just the sum of the areas of the six square sides. Now think of cutting that granule into 1/2-cm cubes, one cut in each dimension, so where you had one cube, you now have eight. Notice that the surface area of all the 'outside' faces of those 1/2-cm cubes add up to the same surface area of the original 1-cm cube. There are 3 'outside' faces per 1/2-cm cube, and the other three are 'inside,' i.e., before cutting, they were attached to each other, so there were no faces there. With this kind of argument, it's very easy to see that a teaspoon of smaller granules has much more surface area than a teaspoon of large granules. (There's another, usually less important, effect at work here too. Think of a teaspoon of dice—maybe you'll get one die in the spoon. Now think of a teaspoon of fine sand. The sand packs more efficiently, so you don't have as much air space, so small granules are denser than large ones—you can pack more weight (a physicist would say 'mass') into the same volume.) If you're comparing the individual granules, certainly a big one has more area than a small one, but now you're comparing, say, 1 tsp large granules with 1/8 tsp small granules (i.e., the same number of granules in each case, but the smaller ones are...well...smaller). Hope that helps.