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# The Ideal Gas Law

The Ideal Gas Law is the following equation:

PV = NkT,

where:
P ≡ pressure of gas (e.g. air) in a room or container,
V ≡ volume (i.e. size) of the container,
N ≡ number of molecules of gas in the container,
T ≡ temperature of the gas, and
k ≡ the Boltzmann constant, discussed in the What is temperature? page in this section.

## What on Earth does it mean?

The Ideal Gas Law describes the way in which so-called ideal gases behave...

### What is an ideal gas?

An ideal gas is a gas in which the molecules that make up the gas have no size, never collide or otherwise interact with each other, and if they hit the walls of the container they're held inside, they rebound off perfectly without having lost any of their speed or energy.

#### That sounds unrealistic. Do such gases actually exist?

No! Ideal gases are also known as perfect gases, and do not (as far as we currently know) exist anywhere in the physical universe. The idea of an ideal gas is purely hypothetical.

#### So why bother having a physical law for something that doesn't even exist?

Well, even though no gas is perfect, most come close enough to make the ideal gas law quite useful in calculating semi-accurate results. For example, look at hydrogen or helium gas - these molecules may not be without size; but in comparison to the volume of the average container in the lab, that size is negligible (think about it - those atoms are tiny). And if the number of molecules in the container is low, then the molecules will meet so rarely that interactions such as collisions between them will be rare enough to have a negligible effect on the results of an experiment.
So while the ideal gas law is not 100% accurate for real gases, it is often a satisfactory approximation.

### What does the Ideal Gas Equation tell us?

• It tells us that if a sealed (so N is constant), rigid (so V is constant) container is heated (increasing T), then the pressure inside the container will increase (and vice versa).
• It tells us that if the container is squeezed or otherwise compressed (reducing V) then the pressure (P) will increase, and if there is a leak in the container, then gas may escape (N may decrease). And vice versa.
• It tells us that there is a compromise between pressure and volume (on the left hand side of the equation).
[So, if the pressure increases inside a container (but, for instance, temperature and number of particles remains constant) then there will actually be a tendency for the volume of the container to increase; thus allowing pressure to decrease (and vice versa). In this way; the whole system automatically chooses the most stable state for itself, as in the case of balloons. Of course, if the container is rigid, then the only way it's volume can change is if it explodes or crumples in on itself. That's why things like spray cans are always reinforced.]
• It tells us that if the pressure increases; then the temperature will increase. That's right - just increase the pressure of the system, and the system heats itself up. For example, if you put a match head inside a sealed gas syringe and squeeze the plunger; the inside of the syringe gets so hot that the match head spontaneously ignites. But you need to slam the plunger down fast! Otherwise, the system cools down to room temperature just as quickly as it heated up; and the pressure instantly drops to a level that balances the container's volume for that amount of gas at room temperature.
Compress the container fast on the other hand; and the heat doesn't have time to escape - so the pressure shoots right up. If you have a suitable container, you can feel this. It's much harder to compress a gas syringe quickly than slowly; owing the the extra pressure you have to work against.

The Kelvin Temperature Scale

What is Temperature

The Ideal Gas Law