In this screencast, I'm going to introduce
a few properties of ideal gases,
and one way of determining if something is an ideal gas
is if it behaves the ideal gas law.
Now this can be written a couple ways.
Common way is
PV is nRT,
where this is the total volume,
this is absolute pressure,
and very important, this is absolute temperature.
For example, Kelvin.
And of course R is the gas constant.
However, it's also fairly common to write it this way,
where this is a specific volume.
So what we mean by that,
this might be liters per mole, for example.
Because there are three variables in this equation,
we have to be careful what we conclude.
For example, if I were to raise the temperature,
that doesn't necessarily mean the pressure goes up.
It could be the volume goes up.
It could be both pressure and volume change.
Depends on our system.
So if I were in a piston cylinder,
and I raised the temperature,
temperature goes up, then the volume would also increase.
If I were in a fixed volume container,
well, now the volume can't change,
so when the temperature goes up, the pressure goes up.
Well, one important property of an ideal gas
is we can write a change in enthalpy
in terms of heat capacity and a temperature change.
So I'm writing this for constant values of heat capacity.
We also, for internal energy,
so this is called the constant pressure heat capacity,
and this is called the constant volume heat capacity,
but these equations are good for ideal gases at all times.
And this is true because the H and U
are independent of pressure for an ideal gas.
So one other aspect of the values for CP and CV
results because H is U plus PV,
Just the definition of enthalpy.
So delta H is delta U plus delta PV.
Keep in mind the notation here,
all of these terms are per mole.
And from our ideal gas law, that means I can write
this as delta U plus delta RT.
I can write delta H as CP, CP delta T
I can write delta U as CV delta T.
And the right side, since R is a constant,
becomes R delta T.
Now you can see, I can cross out delta T,
and this says that constant pressure heat capacity
is the constant volume heat capacity
plus the ideal gas constant.
Another aspect of ideal gases
is if we look at gas mixtures.
For example, let's say we just have two components.
Then the total pressure in our system
would be the partial pressure of A
plus the partial pressure of B.
Where, for example, if we just started out
with A in a fixed volume container,
we exert a certain pressure.
If we now added B to that same fixed volume container,
it would exert pressure.
The pressure of A would not change,
because ideal gases, molecules A,
if you like, don't even know molecules B are there.
And of course, the mole fraction of A, then,
is the pressure of A over the total pressure.
So these are important aspects of ideal gases
that we should keep in mind
when we're doing calculations on ideal gases.