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## Temperature, kinetic theory, and the ideal gas law

# Thermodynamics part 3: Kelvin scale and Ideal gas law example

## Video transcript

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.