Now that we've introduced gases
and how we can measure different properties of gases.
We'll go into some last and farther properties of gases
that we can measure and talk about.
So again, we started with just the basic theory
and now we're going to go into some specific properties of gases and real systems.
We'll start with something called the heat capacity.
And then go into some deviations from the ideal gas law.
We talked about how an ideal gas followed many very particular sets of requirements,
so we're going to allow ourselves to deviate a little bit from those requirements
and see what happens to our ideal gas law in that case.
We finally end with the discussion on what partial pressure is
and what Dalton's law says about partial pressures.
We'll start with the heat capacity.
We'll introduce this with a question.
What is the relationship between energy and temperature?
It's often very attempting to think that this might be just be the same thing,
if the temperature is something changes its energy changes,
and it really does on the same way.
But we're going to dig in into the nuance of this
about the different between energy and temperature.
We'll do that with a question.
As suppose on a very cold day,
I ask you whether you would rather going to a park and sit on a freezing metal chair
or on a freezing wooden chair.
And I think most of us would answer that we would prefer not to sit on a very cold metal object
that would feel extremely cold, even if both of these objects being outside,
where at exactly the same temperature,
because we know everything comes into thermal equilibrium.
So both of these are at the same very cold temperature.
Why is it that we would prefer not to touch the metal object,
even if the wooden object is just as cold?
So let's look into this and ask ourselves the question.
Again, asking about the difference between energy and temperature.
And suppose I add 10 joules of energy to two objects.
First, I add 10 joules of energy to the metal bench
which started at zero degrees freezing, zero degree Celsius,
and then as temperature goes up because I've just added some energy to it.
So now, its new temperature is maybe 2 degrees.
So its temperature went up a little bit because I added some energy to the metal bench.
If I do the same thing and add the same 10 joules to the wooden bench,
which also started that freezing cold at zero degree.
Its temperature it turns out would go up by a lot more.
And this is the counter intuitive idea,
that if you add the same amount of energy to two different objects
that their temperature could respond very differently
to that change in energy that's being added to the systems.
So in summary, metal takes the energy and changes its temperature only a little bit.
Whereas the wooden bench, takes the same energy
and changes its temperature very quickly.
Let's tie this a little better to why we would want to touch one and not touch the other.
Suppose instead of adding a given amount of energy.
I'm talking about the temperature of these objects going up to a specific value.
So for example, if both of these benches are freezing cold initially
and then you touch them, and they want to get to something closer to body temperature,
like 35 degrees.
How much energy would have to be added to each objects
before it comes up to that body temperature?
And just following the same logic what we can see
is that in fact the metal bench has to take much, much more energy from your body
if it wants to get up to that high temperature,
whereas the wooden bench will not take much energy much from your body as you touch it,
to get to the same temperature because wood does not hold, we say as much energy.
So in summary, the metal, so there's one actual last caveat,
before we get into the heat capacity which what we're talking about here.
Which is that if you look up what I've just described on line,
you might find that actually metal is said to take less energy
to raise its temperature of too high value than wood.
Which seems exactly opposite of what I just said if you look this up in a table or something.
So there's one last caveat here which is that for the same amount of volume,
which is what these two benches have since they're the same shape presumably.
For the same amount of volume, metal has a lot more mass,
there's just a lot more substance actually there in a given amount of volume,
because metal is far more dense.
And so for that reason, it's not really an apples to apples comparison,
it's not really a fair comparison between these two benches
because that given volume of metal might be 10 grams of actual material
whereas that same volume of wood would be much lighter and much more sparse
and might just be one gram of material.