That's the basic kinetic theory of gases.
It just something to keep in mind
especially in terms of understanding the assumptions that were made
and where those assumptions breakdown,
because assumption will be use more and more as we get into some of these laws
that we're going to derive about ideal gases.
So now that we've discuss that, let's go into some of these laws themselves.
The way that these laws are, are basically derived is that in a physical system,
like the one here, maybe you have a piston or you have a certain amount of gas in it
and you can control what this gas is doing by heating it up or compressing,
other gas that you have.
What happen is that we take some measurable property
about our system and we hold those properties constant
and we make sure all those properties are constant,
but we only vary one other property and see how it react.
So for example, in this system what we might do
is take the temperature to be constant,
so we don't heat it up or cool it down
and we also have a closed container
so that the number of molecules is also a constant.
And so in this piston that you see here,
the number of molecules has to stay the same in this piston
because it can't leave or come in.
And then what we do is we vary some parameter.
We vary some physical property of the system.
So for example, we might vary the volume,
by moving our piston up and down and seeing what happens
as we change the volume that the gas has to occupy.
While we change the volume,
we can measure the only other property that we're not holding constant.
In this case, it will be the pressure.
When we do that you can see in a graph like this,
that the pressure decreases in a slope way, as the volume increases.
So if we give our gas more volume we lift the piston.
We would have a lot less pressure,
whereas if we compress the piston and decrease the volume that the gas can occupy,
the pressure goes up and this is called Boyle's law.
We can follow the exact same kind of procedure
except pick different things to keep constant.
So for example, we can keep the pressure constant
by instead of holding the piston at a particular place
allowing the piston to move up and down on its own.
If this is the case then the piston will stop moving
when the pressure is equilibrated at a particular weight,
specifically whatever pressure it needs to hold up the weight of the piston.
And we can also keep the number constant by again,
assuming a close system like this one.
When we do this and maybe change the temperature
by heating up or cooling down our system,
we get what's called Charles' law
which says the volume that the gas will occupy
that it will long to occupy by lifting the piston
is proportional to the temperature that our system is at.
Finally, we could also hold the pressure in a temperature of a system constant.
In other words, not letting the interesting variables change
in terms of the gas expanding or contracting.
And ask ourselves how the volume of our system depends on
how many particles are in our system.
When we do this we get Avogadro's law
which says that the volume of a system is directly proportional
to how many particles we have in our system.
So for example, if we double the number of particles,
the volume would also double.
This one is somewhat counter intuitive because it seems overly intuitive,
so we want to be careful here.
It might seem too obvious that when we double the number,
the volume also doubles.
So it's important to understand what this law is saying.
It's saying that, at equal volumes of gases,
that are at equal pressure and temperature
there would be the same number of molecules in that system,
which does not mean the same number of atoms in the system.
So for example if we had a case where we had nitrogen molecules
which is N2 which has two atoms per molecule, as you can see on the left here.
And we compare that to a system that has all the exact same other properties,
the pressure and the temperature and the volume.
Then at the same volume, even though the hydrogen molecules only have one atom each,
there will be the same volume in the system.
Even though again, we have a different number of atoms.
We're counting the molecules with Avogadro's law.