Hi. It’s Mr. Andersen and this AP Physics essentials video 131. It is on the ideal gas
law which is sometimes expressed as PV, pressure volume, equals nRT which is the number of
moles times the gas constant times the temperature. And now the temperature is measured in Kelvin.
And so at 0 Kelvin the molecules are not moving. How cold is that? That would be around negative
273 degrees celsius. Have we achieved that in the universe? Well close. In the boomerang
nebula that is around 1 or 2 Kelvin. And in laboratories we have gotten within fractions
of fractions of degree Kelvin by bombarding the matter with lasers on all sides to stop
molecular motions. It starts to form a new state of matter. But with a gas we have these
molecules that are bouncing around and there are a number of macroscopic characteristics
that we can measure in the laboratory. So we have the pressure, the pressure exerted
by the molecules on the container. We will use P to represent that. We have volume. That
is going to be the area in which the gas is contained. We have the amount and we will
measure that in n which is going to be the moles of the material. And then finally we
have temperature. Temperature is going to be in Kelvin. And so we can think of this
like a scale. And so you can think of it as people sitting on a teeter totter. And so
what would happen if we increase the pressure? Well to keep it balanced we would have to
decrease the volume. What happens if we increase the pressure, if we are changing the temperature,
then we would have to increase the temperature. Now it does not work exactly like this. We
have a constant called the gas constant that makes it all equal. And in chemistry you would
have to do a lot of calculations for this. But in physics you just have to know qualitatively
what is going on. And so if we start with a balloon, and you could measure this in the
laboratory, you could actually measure absolute zero. So what you do is take the balloon and
you measure the volume of the balloon. So you could wrap a string around it and measure
its circumference and therefore its volume. And you can plot that at a very cold temperature.
Maybe in a freezer. You could then move to a warmer area, a warmer area and then you
could move to a colder area. So you can gather a bunch of different temperatures and then
the volume of the balloon. And when it is colder it is going to be smaller. When it
is warmer it is going to start to expand. And what you can do is you can extrapolate
from that. So if you play it backwards what would its temperature be when the volume is
zero? It is going to be absolute zero or around negative 273. And so we are going to use a
PHET simulation to do this. R is the gas constant, but what is neat about this simulation is
you could measure the volume. That is how big the container is. The temperature, we
have a thermometer. We have a pressure gauge on the side. And then finally we have n which
is going to be the number of molecules that we are at. And so here is the relationship.
P V equals n R T. And so let’s look at pressure and volume and the relationship between those
two. So what happens as we increase pressure? If we are keeping the other ones constant,
think of that teeter totter again, if you increase the pressure we have to decrease
the volume. And this was studied by scientists. It is known as Boyle’s Law. But let’s
use a PHET simulation to measure it. So what we are going to do is try to keep the temperature
constant and we are going to look at the pressure and then the volume is going to be how big
this container is. So what I did is I decreased the volume. Now what happened? The temperature
went up right away but we are using ice to cool that back down to where it was. And so
what happened is as I decreased that volume, what happened to the pressure gauge? Now the
temperature is back to where it was. You see we saw a great increase in that pressure.
Now I am going to increase the volume, watch what happens to the pressure as I increase
that volume. We are going to see a decrease in that pressure. And so there is a relationship
between the pressure and the volume, keeping the temperature exactly the same. If we were
to graph it, it would look like this. And so what we have is if we increase the volume,
so I am going in this direction, what happened to our pressure? Our pressure decreases. What
happens as we decrease the volume? What happens to our pressure? Our pressure is going to
increase. Now why do we have a number of different lines here? Each of these are going to represent
different temperatures of the gas, as long as we keep those temperatures constant. Now
let’s look at the relationship between the volume and temperature. So if we keep all
the other ones the same, so what is going to happen? Well imagine they are on either
sides of the teeter totter. If I keep the pressure and the number of molecules the same,
as I heat it up, as I increase the temperature, we are going to increase the volume to keep
it balanced. And so why is that? Increase in the temperature increases the average kinetic
energy of the molecules. There is movement around faster. If we keep the pressure the
same, so that change in momentum as they collide with the container, as we increase temperature
volume goes up. As we decrease temperature watch what is happening. The volume is going
down. Now this is a direct relationship. So if we were to graph this, that is that absolute
value calculation I showed you just a second ago. As we increase temperature, bigger volume.
Decrease temperature, lower volume. If we play this out and extrapolate it, absolute
zero. And so did you learn to extrapolate from a volume versus temperature graph to
figure out absolute zero? Do you understand how you could design an experiment to play
around with these using the PHET simulation? Remember you want to keep some of them constant
and then just change one at a time. And then finally, could you analyze a relationship
between pressure and volume? So we are going to get these curves. Each of those represents
a different temperature. And I hope that was helpful.