Tuesday, June 14, 2011

Physics and Food - Part 2

I've been baking a lot lately, as usual. The other day I made something called Slices of Sin, a chocolate dessert that my mom used to make. It's hard to describe, but it's kind of similar to a very very thick mousse or a cakey fudge. It is baked in a glass loaf pan lined with foil. The recipe says to put the loaf pan directly into a larger pan filled with cool water after taking it out of the oven. I followed these directions, and after letting it sit in the water for a few minutes, I decided to check on it and maybe change the water; I figured that the water would have gotten hot by that point, and I wanted to replace it with cool water again. But when I felt the water, it was still cool, and so was the loaf pan! I realized that this is because water has a high specific heat capacity.

The specific heat capacity of a material is the amount of heat it takes to raise the temperature of one gram of that material by one degree Celcius. In other words it's a measure of how much heat something can absorb before actually getting hotter. So, when I say that water has a high specific heat capacity, I mean that you can put a lot of heat into it without it getting much hotter. That's why the pool is still cold at the beginning of the summer! The sun starts putting heat into it, but the temperature doesn't change much. Heat capacity also has to do with why you would choose to sit on a plastic bench instead of a metal one after both of them have been in the sun. You intuitively know that the metal one will be hotter; it's because metals have low specific heat capacity and therefore get hot even with a small heat input.

Let's address temperature itself first. Temperature can be described as a measure of the amount of kinetic energy in a substance, or how much the molecules are moving around. These molecules can move in different ways: the whole molecule can move, the whole molecule can rotate, or the molecule can vibrate (along the connections or bonds between the atoms that make up the molecule). As you put heat into the substance, the heat gets divided up between these different "modes" of movement, and the temperature is a reflection of the average movement within the substance. However, some substances have more modes than others. For example, if a substance were to consist of single atoms not connected to one another, there would be no opportunity for vibration, as vibration only happens along bonds (like a spring with a ball on each end). In a minute I'll mention another important characteristic that supplies more modes, but for now, consider two substances, one of which has more modes than the other. If you put the same amount of heat into each one, what happens? In each case, the heat will be divided up between the modes. But in the substance that has more modes, the heat will be divided into more portions, and therefore each portion will be smaller. So, the resulting average motion (averaged across more modes), will be smaller than the average motion in the substance with fewer modes. This will result in a smaller temperature increase in the substance with more modes. Let me reiterate that by "modes" I mean the different types of motion that may be available within a substance (translational, rotational, vibrational).

Now let's talk about the structure of water. A molecule of water has one oxygen atom and two hydrogen atoms, and it is a bent molecule, as shown below.

As you can see, the hydrogens are bound to the oxygen, but what you can't see from my simple little image is that the oxygen also has some free electrons, or electrons that aren't part of a bond with another atom. The electrons and the two bonds can't be too close to one another, so the electrons hang out on one side of the oxygen, and the hydrogens hang out on the other. This is what causes the bent shape. Electrons have a negative charge, so the water molecule is negative on the free electron side and positive on the hydrogen side. This allows it to loosely bond with itself. The negative part of one water molecule is weakly attracted to the positive part of another water molecule in what is called hydrogen bonding. This extra bond is another mode that can absorb heat! Therefore, any heat that is put in will be divided up into more portions than it would be in other materials because of this extra place it can be stored. So, hydrogen bonding plays an important role in water's high specific heat capacity.

The other contributing factor is not quite as exciting. Some other substances have similar properties, but water is one of the most effective by weight. The water molecule is small and light, so more of them can fit into, say, one gram. This packs even more of each mode into a given weight. Some of the things I've read use this fact to support a claim that water's high specific heat capacity is nothing special. But the truth remains that water's specific heat capacity IS high, which I think is pretty remarkable no matter what.

Let's also briefly consider the cooling of water. It's just the opposite of what I explained above. A lot of heat will have to leave the water before it actually gets cooler. That's why the pool stays warm at night long after the air cools off!

To summarize, water is one of the best materials at absorbing large amounts of heat but undergoing only a small increase in temperature. This is due to both the hydrogen bonding that takes place and the low weight of the water molecule. Water's high specific heat capacity is one of the many unique properties that make it a useful and interesting material!