Now that we've introduced some of the basic quantities
for measuring thermodynamics systems,
we're ready to go on to a few complicated dynamics including chemical reactions.
First, let's take a look at a simple system like this one.
We'll ask, 'How much energy is in this beaker?'
We already introduced the quantity for defining energy,
but now we're going to introduce a new quantity called the enthalpy.
So this will be a slightly different quantity, so let's motivate a little bit
why we need introduce after we have energy and entropy,
a new quantity called enthalpy.
So here's the reason. Again, with the energy in this beaker
we can define some reference energy for ourselves,
and then have a good definition for how this reference energy
begins to change as we evolve our system.
We already said that if we know some reference energy
since we can call the zero energy whatever we would like no matter what it is,
we know how this energy changes
because either heat can be added to or lost from the system,
or the system can do work or have work done on it.
So for these reasons, we have a very good definition
for how the energy changes in the system,
and this quantity we have for energy depends both on the heat.
The heat energy either added to or taken from the system
and the work done by the system or on the system.
So for example, to make this very concrete,
if we had something like this system here,
if heat was added to the system
the energy goes up the internal energy of your system
or if the system does work and pushes maybe on a piston
and causes it to go up as you can see in this picture,
that means that the system did work
and that work will be equal to the pressure of whatever gas was in this piston
times the change in the volume as it lifted the piston up.
We can also reverse this process.
So for example, if I decided to start pushing down on this piston
or maybe as they did often historically in order to measure very quantitative changes,
put little weights on the system,
and I knew exactly how heavy these weights were,
I could press the system down.
What this would do is instead work on the system rather than by the system,
and this is because the change in the volume is now negative --
So if we have a negative change in the volume, that's a negative work done.
And so you can see in our equation for the change in energy
we would have the change in energy would be minus
this negative work done that we just put into the system.
So those two minuses together would make a plus sign,
just meaning we've added energy to the system
by pushing on it and doing work on the system.
So this energy is very well defined,
and the reason is that is a state variable as we already discussed.
So that a diagram like this one, no matter what path we take
as we change the volume and the pressure,
we could do all sorts of things to our system
which will be represented by paths and our pressure-volume diagram.
As long we go back to this point U1
where I've labeled the energy of the system at different points along this path
by U1 or U2 or U3,
no matter what path I take to go away from U1 and go back to U1,
this original energy that we had, initially U1
is always going to be the same
as long we'll come back around to the same point on our diagram.
And again this is because energy is a state variable for our system.
On the other hand, we could ask ourselves the question, and this brings us to the enthalpy.
What if instead of measuring the internal energy,
I wanted to measure the internal heat energy of my system?
The problem is, we can't just use Q
and we can't use Q, the heat energy that's added to or taken from our system
for the reasons we already described.
The Q is not a state variable.
In other words, if I showed up to a system that you are already dealing with
and I wanted to find out how much energy, the heat energy
that you've added to or taken from the system,
there would be no way for me to know this
because Q is not a state variable.
So this motivates us to define a new quantity which is called the enthalpy.
So this quantity H, we're going to discuss a little bit.
It might seem arbitrary just to throw it here right now,
so we'll put it up so we know what it looks like,
and then we'll discuss some of the nice properties of it
to motivate why would we introduce this new variable.
So first of all, one of the great properties of this enthalpy
which is the internal energy plus the pressure times the volume of your system
is that this H, this enthalpy, is a state variable.
We know it's a state variable because it's simply the sum of other state variables.
The internal energy is a state variable.
The pressure and the volume are both state variables.
So just by our very definition of the enthalpy,
it's also a state variable, which we said is nice
because again if I just showed up at some point
I can measure the enthalpy without needing to know
what had been done to the system previously.
The other nice thing about this
is that it includes -- or a way of thinking about it
rather before we get to one of the other great properties
and the reason we define it as it is,
a way to think about this is that it includes not only the internal energy
that your system has right now, U,
but it also includes this extra term which is the pressure that your system currently has
times the volume that your system currently has.
One way to think about this pressure times volume term
is that it's the energy required or the work that you would have to do
to sort of create your system in whatever condition it currently is in.
Because the pressure times the current volume that your system is in
would define, by definition, the amount of work you would have to do
to increase the volume of your system from not existing to be whenever it is,
maybe displacing the air around it since the air has pressure.
And so you can think of this again
as sort of the energy of creating your system
of even having your system be in the environment that it is
where all these other things like the atmosphere are trying to push on your system.
So you don't necessarily need to have this way of thinking about the enthalpy
but sometimes it can be helpful when you're trying to remember the expression for enthalpy --
that it includes two types of energy of your system not only
the energy, the internal energy that your system has right now,
but also sort of the pressure and the volume of your system as it exists,
sort of the pressure it took or the energy it took to create the system where it is.
So this is a way to think about what enthalpy is.
But again, why in the world did we introduce this enthalpy?
Well, let's look what happens if we talk about changes in the enthalpy.
So first, on both sides of this equation, the left and right-hand sides,
I can talk about the change.
So we have delta H, the change in the enthalpy is equal to
delta U, the change in the internal energy
plus the change in pressure times volume as an entire term.
So we can simplify this slightly
because we already have an expression for the change in the internal energy
which we already said is equal to the heat added Q minus the work done by your system W,
and so the change in the enthalpy is now equal
to this slightly changed expression, this new expression.
Going a little bit further, we know what a work done is.
we already have an expression for the work done.
The work is the pressure times the change in volume.
So now we can rewrite this one for time.
We have the change in the enthalpy is equal to the heat.
And then a couple of other terms
the minus pressure times the change in volume
plus the change in the pressure times the volume.
So you can see where we're going with this.
If the pressure is constant,
and this is the reason that this enthalpy is so useful,
that in most chemical reactions in your lab,
your chemicals are open to the atmosphere;
they're just reacting in the presence of some atmospheric normal pressure
without us trying to close in or press on our systems.
And so this is a very common situation that your pressure is constant
because you're just open to the atmospheric pressure, for example.
And if that's the case, then the equation for the enthalpy,
the lowest one that we have here,
the PDV and the delta PV will just be the same term because the pressure isn't changing.
In other words, if the pressure isn't changing,
the right-most term in this last derivation for the change in enthalpy,
we'll just have that constant pressure term pulled on the other side of the delta.
In other words, it would just be a pressure times a change in volume
which is the exact opposite sign of the first term we have here,
which is a minus pressure times the change in volume.
In this case, again, if the pressure of your pressure is constant,
then the change in the enthalpy of your system is simply equal to the heat energy
that was added to or taken from your system.
So the enthalpy has these two nice properties.
On the one hand it's a good way measuring the amount of heat change in your system.
So this is something that we would like to measure
without having to measure the heat change itself which was not a state variable.
And so the enthalpy give us both at once;
it's a way of thinking about the heat energy of our system
while also being a state variable
that will not depend on what path or the past history that our system took.