Air Compressor Theory – The Cool Science Behind Compressed Air

Air is freely available everywhere. But compressed air is not. So, what is compressed air and what happens to air when it is compressed?

Read on to learn about the thermodynamics and simple physics of compressing air. We’ll also talk about the reasons for compressing air polytropically instead of isothermally or adiabatically (and don’t worry, we’ll explain those terms too.)


The quantity of air available in our atmosphere is huge and every living thing requires air, which includes oxygen, to survive. However, living beings aren’t the only things that require air.

Engines and machines also require air for their proper and efficient operation. Air plays a vital role in numerous industries, including mobile services, factories, and production plants. But this air is a little different than the air we breathe.

Instead, this air is compressed and then used as a source of energy. Compressed air is an underrecognized power source that can energize tools, machines, and engines—and it does this quite efficiently!

In this article, let’s dive into the theory of compressing air and its various associated laws.

What does “compressed air” mean?

Atmospheric air, which is the air that constantly surrounds us, is made up of many molecules and gas components. The composition looks something like this:

  • 78% Nitrogen molecules
  • 20-21% Oxygen molecules
  • 1-2% water vapor, carbon dioxide & other gas molecules

As gases, these molecules naturally space themselves out, filling up the volume available in free space.

When we compress air, we force those molecules closer together. The same molecules are in the air, but they occupy less space (volume) than they did when the molecules were free. Forcing these gas molecules together has some incredible consequences:

As the number of molecules increases in a given volume, the mass of air also increases. As that mass of air increases, its density also increases. And as the density increases, the pressure of air increases and… voila! We have compressed air.

Basic Theory of Compressing Air

The air we breathe has two major components: nitrogen and oxygen.

Even though air is not a “perfect” or pure gas, the presence of nitrogen and oxygen in major proportion makes it obey very closely to a “perfect” gas. Perfect gases are known to obey a couple of laws:

  • Boyle’s law (PV = k)
  • Charles’s law (V/T = k)


P = Pressure
V = Volume
T = Temperature
k = constant

Boyle’s law and Charles’ law can be combined to form a combination law, which is represented as:

  • PV/T = k

Okay, so what does all this mean?

The combination law can be understood better when we break down Boyle’s law and Charles’s law first.

Understanding Boyle’s Law: PV = k

Boyle’s Law was created by Robert Boyle, a physicist and chemist, in 1662. The law has stood the test of time and explains the relationship between pressure and volume.
PV = k simply means that pressure multiplied by volume will always equal a constant. If the volume decreases, you’ll need more pressure to meet the same constant as before (and vice versa).

What Boyle’s Law tells us is this: as the volume of the space containing air reduces, the pressure increases, if the temperature stays the same. That means that we can increase the pressure of air by forcing it into a smaller space.

Breaking Down Charles’ Law: V/T = k

Now, let’s add in Charles’ Law, which uses the V/T = k formula.

Charles’ Law, which is also called the “law of volumes”, basically tells us what happens to a gas when it’s heated or compressed.

Charles’ Law is a bit newer than Boyle’s, but it’s still quite old. Jacques Charles figured out the relationship between volume and temperature in the 1780’s, and Joseph Louis Gay-Lussac first published the discovery in 1802. (Joseph gave Jacques full credit and decided to name the law after him, which was pretty cool of him.)

Anyway, Charles’ Law tells us that a gas’ volume divided by its temperature equals a constant, which is pressure. When you increase temperature, you also proportionally increase volume to maintain the same pressure.

That’s because the molecules in the gas move away from one another as they are heated, which increases the amount of space the gas takes up.

Putting Boyle’s & Charles’ Laws Together

But what happens when you decrease the volume and force those molecules closer together than they want to be? Hello, combination law!

Boyle’s Law helps us understand pressure and volume, while Charles’ Law teaches us about volume and temperature. But pressure, volume, and temperature all come into play together with that combined formula we mentioned before:

PV/T = k.

Pressure multiplied by volume divided by temperature equals a constant.

The combination law explains what happens to air when it’s compressed into a smaller volume. It tells us that when air is compressed, the pressure and temperature of the air increases, as the volume of the space containing air decreases.

By pushing air into a smaller space, we force it to become hotter and more pressurized. The molecules within the air will try to spread apart, returning to their natural distance, and it’s this constant attempt to move away from one another that causes pressure.

Theoretical Compression Types

Now that we understand what’s happening to air when it becomes compressed, let’s talk about how we compress it. Theoretically, air is compressed in two ways:

  • Isothermal compression
  • Adiabatic compression

Isothermal compression

Isothermal compression may sound intimidating but it’s straightforward, starting with its name. “Iso” means “equal” or “same” and “thermal” means “heat”, so we’re just talking about a form of compression where heat stays the same.

Isothermal compression is the process of compressing air without changing the existing temperature of the system. Now that you’re familiar with combined law, you’re probably thinking, “But wait! How can we possibly increase pressure without increasing the temperature?!”

You can’t. It’s the Law. But that doesn’t mean you have to keep the increased temperature after the air is already compressed.

With isothermal compression, the heat produced during compression is removed at the same rate it’s created, to keep the temperature constant. In theory, the compressor must be designed so that heat generated can also be extracted at an equal rate.

Isothermal compression is represented by the same formula as Boyle’s Law: PV = k.

However, isothermal compression presents real-world limitations: the air needs to be compressed more slowly, the cylinder bore must be small, and the system requires a high standard of cooling. This means the entire system needs to slow down and become a lot less efficient.

Adiabatic Compression

Adiabatic compression, also known as isentropic compression, is the opposite of isothermal compression. With adiabatic compression, the heat generated by compressing air is not removed from the system. Instead, all the heat generated during the act of compression stays in the compressed air.

Theoretically, the adiabatic compression process can be represented as PV^ γ = k, or volume to the power of gamma, multiplied by pressure, equals a constant. To learn more about how this is derived, check out this video from UNSW’s School of Physics:

While adiabatic compression is fine in theory, it also provides real-world limitations. Air that’s too hot is dangerous and can result in both system failure and safety issues. Extremely hot compressed air isn’t desirable for most applications.

Polytropic Compression

With both the isothermal and adiabatic theoretical compression processes, there are huge practical constraints. To overcome these constraints, the real-world air compression process is a hybrid between isothermal and adiabatic compression.

Isothermal compression is the most desirable way to compress air, but it’s not actually possible to achieve. The theory makes sense, but the reality is impossible. Even with the best cooling systems available, the physical components that compress air would need to slow down so much that the air delivery rate would be too slow.

Therefore, we compromise and use a hybrid approach called polytropic compression.

Real-world air compression uses both adiabatic compression and isothermal compression. Compressed air is heated without transferring heat to the cylinder (adiabatic) but it’s cooled down as much as possible (isothermal) without ruining the system flow.

The end-result is efficiently compressed, reasonably cooled air that’s ready to use for countless tasks.