The ideal gas law

Why does popcorn pop, do souffles shrink after baking and does choux pastry rise during baking? These are all questions we’ll be trying to answer by applying the ideal gas law to food.

As you probably know if you’ve been on my website before, I love food and science and enjoy it most to combine the two of them. This post is a typical sciency post, but I really felt like I had to write it, since it’ll make my more food focussed posts a lot easier to write. If you’ve been referred to this page through another post, continue reading, it’ll explain to you why gas expands at higher temperature and it’ll help you understand some basic phenomena in food.

Solid – liquid – gas

Let’s start with the basics, the three phases a material (thus also a food) can be in: solid, liquid & gas. The difference between these three states is determined by the way molecules can move.

As you might know, all components in food are made up of molecules. Let’s take water as an example. Pure water is simply a collection of a lot of H2O molecules, nothing else. It’s these molecules that make up your ice, water or water vapour. The difference between the phases is quite clear to see.

In ice (the solid phase of water) the molecules are fixed in a lattice. This means that the solid material will hold its own shape (an ice cube will stay as it is when placed on a table, until it starts melting). Do not be tricked though, even in ice the H2O molecules are moving, be it in such a way that you don’t see. Molecules always move as longas they are above the absolute minimum temperature (but in your kitchen you won’t be able to make it that cold, luckily).

When the ice melts into water (the liquid) the molecules get free of their lattice and they can move around more freely. A liquid will take the shape of a container (imagine placing water on a table, it will flatten out and not stand up like an ice cube).

Upon evaporation of the water (making the gas phase) the molecules will be able to move even more and they’ll be more free in their movements as well. The molecules might jump and escpae and go everywhere. Characteristic for a gas is that it will distribute itself around a certain space. So if you’d place water vapour in a closed container, there will be water vapour all throughout the container.

A bowl full of pingpong balls

In this post we’re mainly interested in the gas phase in order to explain and apply the ideal gas law. As the name says, the ideal gas law is a law that applies to ideal gases. In reality, not a lot of gases actually behave ideally, but the principles do not change too much.

An ideal gas is a gas of which the individual molecules do not interact. They will not stick to each other, or be attracted by one another for instance. This is why an ideal gas is often explained by ping pong balls. Imagine all gas molecules being ping pong balls just pingponging around in a space. They will bump into one another, but not interact otherwise.

The ideal gas law

So here we go, the ideal gas law. This law describes how such an ideal gas behaves when temperature or pressure changes, or when the volume changes. It’ll help us make sense of those food phenomena mentioned at the start as well.

The law is as follows:

pV = nRT

Of course, this needs a little more analysis. Let’s start by explaining what all letters stand for:

  • p = pressure (in case you’re interested, the unit is Pa)
  • V = volume (unit = m3)
  • n = number of molecules (expressed in the unit moles)
  • R = gas constant, this is a fixed number that’ll always be the same (8,314 J/molK)
  • T = temperature (unit = Kelvin)

What does this law actually say? I’ll try to illustrate that using an example.

Imagine a vessel with an imaginary pressure of 5 and a volume of 2 (I will leave out units for simplicity). Multiplying these will give you a value of 10. As the formula says, p x V should be the same value as n x R x T . So in this case the values of n and T are such that the multiplication of n, R and T also gives the number 10.

As long as the temperature and the number of molecules (n and T) stay the same, this will mean the value of p x V will also have to stay the same. It is possible though that one of the two changes. For example, if the pressure decreases from 5 to 2, the volume will have to increase to make sure the multiplication still gives us a number 10. For that to happen, the volume will have to increase, to value 5.

Got this example? In short it says that if any one variable in this formula changes, it could be temperature, pressure, volume or the number of molecules, at least one other variable will have to change as well to make sure that the formula still holds.

freshly popped popcorn
Freshly popped popcorn, can be explained using the principles of the ideal gas law.

Practical case: popcorn

As you could have read in my popcorn science post, popcorn pops because the pressure inside the corn kernel builds up when heating the kernel. Why the pressure increases is a phenomenon that can be explained using this ideal gas law.

In a popcorn kernel moisture evaporates and becomes a gas. When heating the popcorn kernel more and more, moisture will evaporate and the temperature of the kernel will continue rising. If we take a look at the formula, we see the following:

p x V = n (this value is increasing, more water evaporates) x R x T (this increases as well)

So, we see that the right hand side of the formula is increasing in quite a big pace. That will have to mean that somehow the part p x V will also have to increase.

As we read in the popcorn post, a corn kernel is very strong and not flexible at all. Therefore, it cannot expand, thus the volume (V) inside the kernel stays the same. As a result, the pressure has to build up. The law simply states so.

In the end, the pressure becomes to high and the kernel won’t be able to withstand the pressure. As a result, the kernel breaks and all build up pressure is lost, but the volume will expand. In its expansion, the gas will also blow up some of the starches.

Practical case: souffles

Another example of applying the ideal gas law would be souffles. Souffles are very delicate treats, which can be both sweet or savoury. Their basis consists of whipped egg whites with some sort of sauce.

This whipped egg white with sauce is placed into the oven. In this oven several processes take place. But for sake of simplicity, we will not zoom in on all of them, since you can read more on eggs and heat here for instance.

One of the things that happens though is that water evaporates. This water is caught within the whipped egg white with sauce and cannot escape the souffle. So let’s look at our formula:

p x V = n (this value increases) x R x T (since the soufle is in the oven, the temperature will increase as well)

So again, p x V will have to increase. However, unlike the popcorn, the shell of a souffle is not that tough. As a result high pressures cannot be built up (a souffle won’t explode easily). To compensate for the increase in temperature and number of molecules, the structure simply has to expand and increase in volume.

One great challenge with souffles is always to make sure they do not collapse again after you take them out of the oven. Unfortunately, this is practically impossible. A souffle has a very delicate structure, it will become a little more strudy during baking, but it will remain flexible. As soon as you take the souffle out of the oven the temperature of the souffle will decrease and part of the water vapour will condensate again. So the volume simply has to decrease again. A slightly firmer souffle can limit shrinking, but in the end, just about all souffles sink to a certain extent.

Practical case: choux pastry

I’ve already written a long detailed post on choux pastry. I expect that by reading that post and the two examples above, you’ll be able to explain exactly what happens when making these nice little puffs!

Non-ideal gases

As mentioned before, not all gases around us behave ideally. However, the principles explained above can be used to explain a lot of kitchen phenomena. Scientists did come up with ways on how to deal with non-ideal gases to a certain extent, but don’t worry, I will leave it at this. Have fun with recognizing all different phenomena in which the idea gas law plays a role!

Leave a Reply

Your email address will not be published. Required fields are marked *