We just finished, hopefully, getting intuition for why my
initial pressure times my initial volume divided by my
initial temperature is going to equal-- if I change the
volume, the pressure, the temperature, or some
combination of all of them, it's going to equal my new
pressure times my new volume divided by my new temperature.
And once again, just remember all of this-- pressure times
volume is proportional to the amount of kinetic energy in
the system, and temperature is proportional to the amount of
kinetic energy per molecule.
If we don't change the number of molecules, the amount-- and
since by the conservation of energy, the amount of kinetic
energy isn't going to change unless we do some work, or get
some potential energy-- these quantities and this
relationship won't change.
Watch the last video, and hopefully you'll get some
intuition-- if it's still confusing, I'll make another
video for you guys.
Before I apply this equation-- this is going to get you
pretty far in thermodynamics just knowing this, and even
more just having the intuition of what it means.
I want to clarify something about temperature-- there's a
lot of different ways to measure temperature.
We know that in Fahrenheit, what's freezing of water?
It's 32 degrees Fahrenheit that's freezing, but that's
also 0 degrees Celsius-- actually, that's how the
Celsius scale was determined.
They said, where does water freeze, and then where does
water boil?
100 degrees for Celsius is boiling, and that's
how they rated it.
You could be colder than the freezing of water, and you'd
have to go negative in that situation-- Fahrenheit, I'm
actually not sure.
I need to look that up in Wikipedia, or that might be
something for you to do, and tell me how it came out.
I think the boiling of water in Fahrenheit is 212 degrees,
so it's a little arbitrary.
I think Fahrenheit might be somehow related to human body
temperature, but I'm just guessing.
You can have different scales in this situation, and they
were all kind of a bit arbitrary
when they were designed.
They were just to have some type of relative to scale--
you could say when things are boiling, they're definitely
hotter because they have a higher temperature then when
things are freezing.
You can't divide 100 by zero, but if something is 1 degree,
is it necessarily the case that something that is 100
degrees Celsius is a hundred times hotter, or has a hundred
times the kinetic energy?
Actually, what we'll see is that no, it's actually not the
case-- you don't have 100 times the kinetic energy, so
this is a bit of an arbitrary scale.
The actual interval is arbitrary-- you could pick the
1 degree as being one hundredth of the distance
between zero and 100, but where you start-- at least in
the Celsius scale-- is a bit arbitrary.
They picked the freezing of water.
Later on, people figured out that there is an absolute
point to start at.
And that absolute point to start at is the temperature at
which a molecule or an atom has
absolutely no kinetic energy.
Because we said temperature is equal to the average kinetic
energy of the system, or the total kinetic energy of the
system divided by the number of molecules.
Or we could also say the average
kinetic energy per molecule.
The only way to really say that the temperature is zero--
and this is proportional, because the temperature scales
are still a little bit arbitrary-- the only way to
get to a temperature of zero should be when the kinetic
energy of each and every molecule is zero, or the
average kinetic energy.
So they're not moving, they're not vibrating, they're not
even blinking-- these molecules are stationary.
The point at which that occurs is called absolute zero.
That actually occurs-- absolute zero, which is also
called zero Kelvin, and that is the same thing as minus 273
degrees Celsius.
Nowhere in the universe, at least that I'm aware of, it is
it colder than minus 273 degrees Celsius-- at that
temperature, nothing moves, even at the atomic scale.
I'm talking that the electrons collapse into the nucleus--
everything is completely stationary at zero Kelvin.
It's a theoretical absolute limit-- maybe we'll do a bunch
of videos on how you can get close to that, but in
laboratory environments or maybe in deep space, it gets
really, really close to this.
I'm pretty sure nowhere in the universe do we have absolutely
zero Kelvin, or at least in any place where we actually
have particles, but I might be wrong there-- that's a little
bit out of the scope of what we're talking about.
The true way to measure temperature is in Kelvin.
When you're measuring in Kelvin, if I say-- I have
something that is 1 kelvin versus something that is 5
kelvin, since we nailed down the bottom at a point at which
really do not have kinetic energy, I can make the
statement that this has five times the energy of something
that's at 5 Kelvin versus 1 Kelvin.
That whole long explanation about Kelvin, that was to just
to make the point that whenever we use this formula,
or really any formula in thermodynamics that involves
temperature, we should convert to Kelvin, unless we're just
doing change in temperature.
Then you could you could probably keep it Celsius, but
when you're doing proportionality, or you're
using it for multiplying or dividing by temperature, you
have to use Kelvin.
Hopefully, I made a little bit clear of why that is.
Let's do an example.
You'd be surprised how far this takes you.
Really, the main trick is just to remember to
convert things to Kelvin.
That's the number one reason why people miss questions on
thermodynamics exams-- is that they didn't convert to Kelvin.
This problem is very typical of most of what you'll see--
this is from the Barron's AP physics B on page 226.
It says a confined gas is a temperature of 27 degrees, so
its initial temperature is 27 degrees Celsius.
It has a pressure of 1,000 pascals, or newtons per meter
squared, and the volume is 30 meters.
I think in one of the early videos, I think I said newtons
per meter cubed, but it's newtons per meter squared-- I
just want to make sure I didn't confuse people
previously, so that's the initial volume.
It says the volume is decreased, so then we go to
this date, where my new volume is going to
be 20 meters cubed.
The new temperature is increased, and so the new
temperature is now 50 degrees Celsius.
They want to know what is the new pressure?
Before we just substitute into the equation, and solve for
the new pressure, remember-- if they gave it to you in
Celsius, convert to Kelvin.
If they gave it to you in Fahrenheit, which they seldom
do, then convert into Celsius, and then convert to Kelvin.
We already know that zero Kelvin is equal
to minus 273 Celsius.
Or another way you could say it is x Kelvin is equal to--
essentially, whatever degree you get in Celsius, you just
add 273 to it.
Does that make sense?
Think of it this way: if you're at zero degrees
Celsius, you're already 273 degrees above zero Kelvin.
Think about that, and hopefully that makes sense--
maybe you want to draw a number line just to make sure.
Whatever Celsius degree you have, just add 273 to it, and
you'll get Kelvin.
Add 273 to 27 degrees Celsius, and that's 300 Kelvin, and
then 50 degrees Celsius is-- add 273 to it.
So 50 plus 273 is 323, so now we can
substitute into this formula.
P1, 1,000 pascals times V1 times 30 divided by the first
temperature-- remember to do it in Kelvin--
300, is equal to P2.
We don't know what that is.
P2 times V2 times 20 divided by our new temperature, 323.
We can simplify this: we could take two 0's off of here, take
two 0's off of here, then you could take a 3 out of here,
and then take a 3 out of here, and we're left with 100.
This is equal to 100-- that was 30,000 divided by 300, and
so that's 100 on the left-hand side.
So we have 100 is equal to P times 20 over 323.
I'm running out of time.
If I were to solve for it, 323 times 100 divided by 20
equals-- so my new pressure is 1,615 pascals.
I just solved this equation, and the hard part was
converting to Kelvin.
See you in the next video.