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I told you that the two most
important things you should

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know in thermodynamics that will
get you most of your way

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through most exams is that the
pressure times the volume is

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equal to a constant, and that
the pressure times the volume

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divided by the temperatures
is equal to a constant.

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They all change such that the
initial pressure times the

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volume divided by the initial
temperature is equal to the

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final pressure times volume
divided by the final

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temperature.

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Assuming that you're not
changing the energy of the

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system, and we'll do
more on that later.

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The other thing you should
remember is that pressure

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times volume is equal
to n, where n is

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the number of moles.

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Mole is a number like dozen, but
mole is a huge number-- 6

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times 10 to the 23 times R.

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R was the universal gas
constant-- that's 8.31 joules

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per mole Kelvin times
the temperature.

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Remember, just to be safe,
always convert to Kelvin

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first.

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Let's see if we can do a problem
that I can make up on

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the fly of this situation.

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Let's say I have a balloon, and
the volume of the balloon

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is 1 meter cubed, so this
is a big balloon.

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That's fairly large, if you
imagine a cubic meter.

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The volume is a cubic meter, and
let's say the pressure is

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equal to 5 pascals, and that's
newtons per meter squared.

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And let's say we're at a
reasonably warm temperature,

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so temperature is equal to 20
degrees Celsius, and let's say

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that balloon is filled helium.

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My question to you is, how many
molecules of helium do I

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have in the balloon?

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Let's just substitute
into the equation.

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We have pressure, which is 5--
and I'll actually write the

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units, I never do it, but you
should, and you should always

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do it on an exam-- 5
newtons per meter

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squared times the volume.

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1 meter cubed is equal to my
number of moles, n, times the

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universal gas constant, 8.31
joules per mole Kelvin, times

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temperature.

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Remember, and I can't repeat
this enough, always convert

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the temperature to Kelvin--
so whatever our Celsius

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temperature is, add 273.

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Add 273 to that, and
you get 293 Kelvin.

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So I get 5 times 1, and meters
square, meters cubed cancels

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out and just becomes a meter.

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Newton meter is joules.

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5 joules is equal to
n moles times 8.31

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joules per mole Kelvin.

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This Kelvin and this Kelvin
cancel out, so 8.31 times 293

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is equal to 2,434.83
joules per mole.

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To get to the number of moles,
we just divide both sides of

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this equation by that.

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And the units should work
out, so you get 5.

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So n is equal to 5 joules
times 1 over 2,434.83.

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Since we're dividing by this,
this flips; moles per joule.

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This joule cancels out with this
joule, so we just have to

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divide 5 by this, and we'll
get the number of moles.

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Let's take the inverse of what
I had there times 5, and so I

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get 0.002 moles.

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So this equals 0.0021 moles.

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That might seem like a small
number to you, but let's

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figure out how many
molecules that is.

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Let me make some space free,
so I can write Avogadro's

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number down.

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Did I even say what Avogadro's
number is?

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Avogadro's number is the number
of molecules per mole--

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it's that number.

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So, number Avogadro is equal
to 6.022 times 10 to the 23

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molecules per mole.

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The top is molecules, and the
bottom is moles-- I know you

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can't read that.

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I have 0.0021 moles, so how
many molecules do I have?

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I just multiply that 0.0021
times how many moles per

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molecule-- because this is
moles-- times Avogadro's

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number, which is molecules
per mole.

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That's molecules, this is
moles-- maybe I should write

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the whole thing-- so then the
moles cancel out, and

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Avogadro's number is 6.022 times
10 to the 23-- let's

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just remember that--
and let's just

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multiply that times 0.0021.

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It equals 0.0126 times 10
to the 23 molecules.

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This is 0.0126.

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That's the same thing as 1.26
times 0.01, and then of course

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times 10 to the 23.

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What's 0.01?

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That's 10 to the negative 2--
10 to the negative 1 is 0.1,

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so this 10 to the negative 2.

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Then we get 1.26-- 10 to the
negative 2, times 10 to the

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negative 3, and we add the
exponents times 10 to the 21.

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It's roughly 1.26, and then
another 19 zeroes-- or roughly

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1 followed by 21 zeroes-- is how
many molecules of, in this

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case, helium we had
in the balloon.

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It's not too difficult.

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The hard part is really just
remembering Avogadro's number,

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remembering the universal gas
constant is 8.31 joules per

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mole Kelvin, remembering
to always convert your

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temperature to Kelvin, and then
just making sure all your

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units match up.

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Sometimes that might be tricky:
they might give volume

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in liters, and you have to--
especially in this case--

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convert it to meters cubed
before you do it.

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They might give pressure,
atmospheres, or bars, and you

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should know the conversion, and
convert it to pascals or

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newtons per meter squared.

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Other than that, it's just
substituting and just doing

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the hairy math and the
scientific notation.

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Hopefully, that was vaguely
clarifying.

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See you in the next video.

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