The Terror of Knowing What's Inside This Pot

Marika and I recently got an Instant Pot pressure cooker, which we've been enjoying making meals with. Naturally, I was curious about the inner workings of the pot, specifically how the temperature and pressure inside vary with time.

The concept behind a pressure cooker is that when cooking food in water, you typically can't heat it beyond the boiling point: Once the water reaches boiling, any energy you add just goes into making steam. Sometimes you want to cook things at higher temperatures, which is why frying uses oil. That's not very healthy, though, so it would be great to raise the boiling of water. You can do that a little bit by adding salt, which is often suggested for pasta, but that doesn't go quite far enough. Instead, you can put the water under pressure, which raises the boiling point.

A pressure cooker is a sealed container that you add water to, and then heat. As the water evaporates, the pressure builds inside the cooker, raising the boiling point. The pressure depends both on the temperature of the steam, and the number of water molecules that have evaporated:

This is the ideal gas law, with T the temperature in Kelvin, V the volume, R a constant, and n the number of moles of gas molecules. A mole is a way to count very large numbers of things, equal to Avogadro's number, 6.022 * 10^23. My grandfather, a chemist, used to say that he and my grandmother had "Avogadro's Anniversary", because they were married on 10/23.

In order to add molecules to the steam though, we need to boil the water. The temperature that water boils at will change as the pressure increases. Even after we get to boiling, we need to overcome the latent heat to get the water out of the liquid phase and into steam. To accomplish either of these goals, we need to add energy to the system, which translates into temperature through the heat capacity.

Putting all this together with the specs of our model, we can look at the temperature and pressure for two cases: The minimum amount of liquid in the pot, 2 cups, and about half-full, 12 cups.

I was surprised by how quickly the pressure rises once we hit boiling – I kept a constant amount of power throughout the calculation, which causes the pressure to quickly exceed the working range of the pot. You can see the extra energy being used to push more molecules into steam in the sudden change in slope of the temperature plots.

I was hoping that by studying pressure cookers a bit more closely, I'd find them less terrifying to use, but I'm not sure these results are very soothing! I'll just have to keep singing to myself, "Mm ba ba de, Um bum ba de, Um bu bu bum da de..."