# What are ideal gas laws?

In our previous article, we looked at how continuity can affect engineering problems.  In this article, we’re going to look into what ideal gas laws are and how they can affect engineering problems.

## What are ideal gas laws?

Ideal gas laws are a set of laws and equations that govern the relationship between the pressure, volume, and temperature of a gas.

For an engineer, ideal gas laws are very important in the design of many items.  For example, the pressure of gas inside a tank will have an impact on the design of pressure vessels for transportation, or the working temperature of a gas turbine engine.  We’re going to check out these laws below

### Boyle’s Law

Boyle’s law states that the volume, V, of a fixed mass of gas is inversely proportional to its absolute pressure, p, at constant temperature:

We could rewrite this as:

Where p = pressure (Pa), V = volume of the gas (m³), and k = a constant.

The actual quantity of ‘k’ isn’t important.  It’s important that for a given gas it’s constant, and so the relationship of volume to pressure is inversely proportional for a constant temperature.  Therefore for a change in pressure, say from P1, to P2, you get a corresponding change in volume, from V1, to V2.  As k is a constant, we therefore know that:

### Charles’ Law

In Boyle’s law, we saw the relationship between an ideal gas’s volume and pressure.  Charles’ law gives a similar relationship, but this time it’s between an ideal gas’s temperature and pressure.  Charles’ law states that for a given mass of gas at constant temperature, the volume V is directly proportional to its thermodynamic temperature T:

We can rewrite it to introduce a constant:

Where V = volume (m³), T = temperature (K) and k is again a constant.  V₁ and T₁ are the starting volume (m³) and temperature (K), and V₂ and T₂ are the final temperature and pressure, for a fixed pressure.  This is true for any given pressure, as long as it remains constant.

### Gay-Lussac’s Law

Now we know that for an ideal gas, there is a relationship between volume and pressure (Boyle’s law), and a relationship between volume and temperature (Charles’ law).  So it stands to reason that there must be a relationship between pressure and temperature!

Given the above, this would be easy to derive, and it results in something called the Gay-Lessac’s law.  The pressure p of a fixed mass of gas is directly proportional to its thermodynamic  temperature, T, at a constant volume:

If we do a similar arrangement as we’ve done before, we know this can be rearranged as:

Where P1 and T1 are the starting pressure (Pa) and temperature (K), and P2 and T2 are the final temperature and pressure, for a fixed volume.

### Dalton’s law of partial pressure

The final part of the ideal gas law is called Dalton’s law of partial pressure, and it simply states that the total pressure of a mixture of gases occupying a given volume is equal to the sum of the pressures of each gas, considered separately, at constant temperature.

While it might sound complicated, what it means is that for a container which has a mixture of different gases in it, the total pressure in the container is the sum of each individual gas pressure added up (assuming a constant temperature):

Where P = total pressure, Px is pressure by  gas X, Py is the pressure by gas Y etc.  A partial pressure is the individual pressure of a single gas within that mixture.

Keep an eye out for our next article looking into Bernoulli’s principle and how we can apply it to engineering problems.

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