Now that we have an idea of the heat capacity,
how much energy something has to take in order to raise its temperature.
Let's talk about a deviation that we could have from the ideal gas law
and write down what is called Van der Waal's Equation.
This will be a brief section.
We're just going to introduce a few ideas basically,
add some concepts rather than going into anything quantitative.
But let's go over some things that could cause us to deviate from the ideal gas law.
So unlike the ideal gas law, let's allow a few things.
First of all, let's allow there to be some form of interaction between our molecules.
What this is going to do is change our pressure term in our equation,
because as your particles are moving,
they're also going to be interacting with each other.
And so we can change our pressure equation,
the pressure term in our equation to be slightly modified,
to have a slightly higher pressure of P plus this term
which a ratio of the number of particles to the volume of the container
and then we have a parameter as we call it A,
which is just the parameter to tell us how much this interactions are happening.
So for example, if we said there are no interactions
we can set A equal to zero, to say that there are no interactions.
In that case, this extra added term that we've put in to our pressure,
will just go away and we would be back at our ideal gas behavior.
We can also say, what if our ideal gas particles no longer are ignorably small
but have some actual size to them, some actual volume.
In this case, what we have to do is change the volume term in our equation
to in fact to be slightly smaller
and say instead it is V minus the number of molecules we have
times B, a sort of volume parameter for the molecules.
So why are we subtracting the volume, instead of adding volume
if we're giving volume to our particles?
Well, the reason for this, is this volume term in our equation that we have here,
is measuring the volume of the container that the particles are in,
the volume that they have to move around in,
but if each of these objects get some size
the amount of room that they have to move around is decreased.
Because they are not taking up some size themselves.
So just by putting in a couple of extra parameters,
we can rewrite our ideal gas law, by simply making some substitutions,
substituting this pressure term that we slightly adopted to allow for interactions
and then editing our volume term to allow for some slight change in the volume,
some actual volume of our particles themselves.
In this case, we just rewrite the ideal gas law
again it can just be simple substitution
and arrive what is called the Van der Waal's Equation.
Again, we're not going to do anything quantitative with this equation right now.
We're not going to get into any of the complicated possibilities
because first of all, it's not that common,
and when it use, it's always very clearly laid out,
because it sort of an exceptional case.