I told you that the two most important things you should
know in thermodynamics that will get you most of your way
through most exams is that the pressure times the volume is
equal to a constant, and that the pressure times the volume
divided by the temperatures is equal to a constant.
They all change such that the initial pressure times the
volume divided by the initial temperature is equal to the
final pressure times volume divided by the final
temperature.
Assuming that you're not changing the energy of the
system, and we'll do more on that later.
The other thing you should remember is that pressure
times volume is equal to n, where n is
the number of moles.
Mole is a number like dozen, but mole is a huge number-- 6
times 10 to the 23 times R.
R was the universal gas constant-- that's 8.31 joules
per mole Kelvin times the temperature.
Remember, just to be safe, always convert to Kelvin
first.
Let's see if we can do a problem that I can make up on
the fly of this situation.
Let's say I have a balloon, and the volume of the balloon
is 1 meter cubed, so this is a big balloon.
That's fairly large, if you imagine a cubic meter.
The volume is a cubic meter, and let's say the pressure is
equal to 5 pascals, and that's newtons per meter squared.
And let's say we're at a reasonably warm temperature,
so temperature is equal to 20 degrees Celsius, and let's say
that balloon is filled helium.
My question to you is, how many molecules of helium do I
have in the balloon?
Let's just substitute into the equation.
We have pressure, which is 5-- and I'll actually write the
units, I never do it, but you should, and you should always
do it on an exam-- 5 newtons per meter
squared times the volume.
1 meter cubed is equal to my number of moles, n, times the
universal gas constant, 8.31 joules per mole Kelvin, times
temperature.
Remember, and I can't repeat this enough, always convert
the temperature to Kelvin-- so whatever our Celsius
temperature is, add 273.
Add 273 to that, and you get 293 Kelvin.
So I get 5 times 1, and meters square, meters cubed cancels
out and just becomes a meter.
Newton meter is joules.
5 joules is equal to n moles times 8.31
joules per mole Kelvin.
This Kelvin and this Kelvin cancel out, so 8.31 times 293
is equal to 2,434.83 joules per mole.
To get to the number of moles, we just divide both sides of
this equation by that.
And the units should work out, so you get 5.
So n is equal to 5 joules times 1 over 2,434.83.
Since we're dividing by this, this flips; moles per joule.
This joule cancels out with this joule, so we just have to
divide 5 by this, and we'll get the number of moles.
Let's take the inverse of what I had there times 5, and so I
get 0.002 moles.
So this equals 0.0021 moles.
That might seem like a small number to you, but let's
figure out how many molecules that is.
Let me make some space free, so I can write Avogadro's
number down.
Did I even say what Avogadro's number is?
Avogadro's number is the number of molecules per mole--
it's that number.
So, number Avogadro is equal to 6.022 times 10 to the 23
molecules per mole.
The top is molecules, and the bottom is moles-- I know you
can't read that.
I have 0.0021 moles, so how many molecules do I have?
I just multiply that 0.0021 times how many moles per
molecule-- because this is moles-- times Avogadro's
number, which is molecules per mole.
That's molecules, this is moles-- maybe I should write
the whole thing-- so then the moles cancel out, and
Avogadro's number is 6.022 times 10 to the 23-- let's
just remember that-- and let's just
multiply that times 0.0021.
It equals 0.0126 times 10 to the 23 molecules.
This is 0.0126.
That's the same thing as 1.26 times 0.01, and then of course
times 10 to the 23.
What's 0.01?
That's 10 to the negative 2-- 10 to the negative 1 is 0.1,
so this 10 to the negative 2.
Then we get 1.26-- 10 to the negative 2, times 10 to the
negative 3, and we add the exponents times 10 to the 21.
It's roughly 1.26, and then another 19 zeroes-- or roughly
1 followed by 21 zeroes-- is how many molecules of, in this
case, helium we had in the balloon.
It's not too difficult.
The hard part is really just remembering Avogadro's number,
remembering the universal gas constant is 8.31 joules per
mole Kelvin, remembering to always convert your
temperature to Kelvin, and then just making sure all your
units match up.
Sometimes that might be tricky: they might give volume
in liters, and you have to-- especially in this case--
convert it to meters cubed before you do it.
They might give pressure, atmospheres, or bars, and you
should know the conversion, and convert it to pascals or
newtons per meter squared.
Other than that, it's just substituting and just doing
the hairy math and the scientific notation.
Hopefully, that was vaguely clarifying.
See you in the next video.