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7.02 Introduction to Thermodynamics
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Chemistry
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Week 7
In this unit, we will learn about thermochemistry, which is the study of the thermal energy transfer (heat) in chemical reactions. We will learn how these measurements of heat are made via calorimetry. Then, learn to calculate heat transfer using various methods.
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Dr. Allison SoultLecturer
Chemistry
Dr. Kim WoodrumSr. Lecturer
Chemistry
Thermal chemistry is a sub-topic of thermodynamics.
So we need a little introduction to thermodynamics.
If you continue on to the next chemistry class,
which we've called advanced chemistry, we will study thermodynamics in lot more
detail, but let's define thermodynamics here.
Thermodynamics is the scientific study of the interconversion of heat and
other kinds of energy.
So we know that thermochemistry deals with heat.
In thermal dynamics we will talk about other types of energy,
like Gibbs free energy, for example.
But we will focus here on, as I said, on this chapter on just the heat portion.
As we study thermodynamics, we need to find something called a state function,
or the state of the system.
The state of the system is all of the values of all the r,
relevant macroscopic properties.
So, what temperature is it?
That would be part of the state of a system.
What is in pressure if it is a gas?
What state is it in?
Is it a solid, liquid, or gas?
That is the state of a system.
So this would consist of its composition.
What is it made of?
How much energy is in it?
What is its temperature?
What is its pressure as I've mentioned, maybe what's its volume?
How much do you have volume wise?
Now as we talk about the state of the system and we define these things
that give you the relevant, relevant macroscopic properties of that system.
Some of those are called state functions.
These would be the properties that are determined by the state of the system,
regardless of how you achieved that condition.
Let's see what I mean by that with an example.
If I have a an object and I say that it's 6 ounces.
Okay, let's say volume amount.
Well it's going to be 6 ounces regardless of how you got there.
Here in the United States we have Cokes and
they come in twelve ounce cans or beverages of various kinds.
Come in a twelve ounce can.
Now if I had drank half of it, it would be 6 ounces.
If it were an empty can and
at the factory they only put 6 ounces in, it would be 6 ounces.
So it wouldn't matter how you got there.
6 ounces is 6 ounces regardless of how you achieve that.
So the magnitude of change when you have a state
function only depends upon the initial and the final value.
We call this path independent.
So with our example of our soft drink,
did it get 6 ounces because it was full and I drank half?
Okay, so final minus initial would be 6 ounces, minus the 12 I started with and
I had a change of 6 ounces.
Or, did I drink 9 ounces and then spit three back in.
All right, that would, that wouldn't matter.
It'd be the change overall of 6 ounces.
So, for a change in volume, we always will talk about final minus initial.
We'll see this often.
So, a change is always the final value minus initial value.
And it doesn't matter anything else in between, just where you ended and
where you started.
When we use letters for
our state functions, we use capital letters, instead of lower case letters,
whenever there state functions, so that's it's a capital V and not a lower case v.
Here's some other examples of state functions.
We could talk about energy.
It wouldn't matter whether it was total internal energy, kinetic energy,
potential energy.
Energy is a state function is abbreviated with an E.
Capitol E we might use KE for
kinetic energy in which case we use a capitol K and a capitol E, and so forth.
Temperature, temperature is a state function, if we
have a change in temperature it final minus initial and we use a capitol T.
Pressure, that's another one where it is going to
be a capital P where we have a change in pressure, we only care what the final and
initial, it won't make a difference.
So we say that state functions are path independent.
So these two people climbed up the hill.
Some things are path dependent and somethings are path independent.
The altitude would be path independent.
It's change, where those people are standing, they are at the same at,
the altitude.
Where they started and
where they finished, it doesn't matter what path they took.
The change in amplitude would be exactly the same.
Another one would be the amount of energy by virtue of the people's position.
Where are they now?
If they were to roll down the hill,
there would be the same amount of potential to do work.
Now what is very different is the work it took to get to
the top of the mountain, okay?
Somebody had to take a very, very long and convoluted path.
It took 'em a lot longer to get there.
They were up and down and up and down and finally got to the top.
That might be very different than somebody who started at the bottom and
was able to find a very direct path.
Maybe there was a rope attached that they could utilize to pull them up,
what have you, it matters how they got there.
So work is not a state function.
Now we made a statement of Law of Conversation of Energy, and
this is actually the First Law of Thermodynamics.
Energy cannot, can be converted from one form to another, but
it cannot be created or destroyed.
What's not possible, and what was assumed with this statement is if
the total amount of the energy in the universe is a constant.
It's not possible to know the total amount of energy in the universe.
There's way too many complicating factors, down to the atomic level and
the electrons moving about having energy associated with them.
Molecules flying through the air, having energy associated with that.
A car driving down the street having energy associated with that.
It's not possible to know the total amount of energy in the universe, but
we can determine the change in energy as a process takes place.
Now it's not the change in the energy of the universe because that's not changing.
But when a process takes place, we could study that system and
we can know its change of energy, which is abbreviated delta E.
Okay, so the total amount of energy change with any process in the universe is
gotta be 0, because the amount of energy in the universe is a constant.
But whatever the system is doing,
the surroundings has to be doing just the opposite.
So if the system is losing, let's say 10 Joules of heat,
the surroundings must be gaining 10 Joules of heat.
Whatever the one is doing, the other's doing just the opposite.
So if it's losing, it's going down.
If it's gaining, it's a positive value, but overall the universe is not changing.
The other way I like to think of this equation, and
more commonly I think of it this way, is that whatever the delta E,
the change in energy of the system is, that would have to be
equal in magnitude but opposite in sign of the delta E of the surroundings.
So I usually think of it this way, so
this is been stated exactly the same with this equation here.
So let us focus on the delta E of a system,
the change in internal energy of a system.
There are two ways that energy can leave a system.
Or interest system, for that matter, and that is by way of heat or by way of work.
Because those are the only two ways that heat can, or energy can get in or
out of a system, if we go back to the first law of thermodynamics,
we can restate it with a very simple equation.
The delta E, the change in energy of the universe is assumed constant.
You are not going to create or destroy energy, it's just being transferred,
then the transfer of energy is going to be equal to the heat and the work.
So that little equation is one that we need to keep track of.
q stands for heat, w stands for
work, and you will notice that those two things are lowercase letters.
They are not state functions.
They are path dependent.
It matters how you undergo the change.
But overall, E, internal energy, is not a state function.
Now there's a sign convention associated with q and
w that we need to get familiar with.
Now, eventually we'll understand the negative and positive of heat, and
the negative and positive of work, as we work on calculations, but
for now let's just get us familiar with them.
If a reaction is exothermic, or a process is giving off heat,
okay thermal energy is being transferred out of the system in to the surroundings,
the sign for heat is negative.
Okay? So, exothermic is negative.
If on the other hand, a system is gaining thermal energy,
it is an endothermic process and it has a positive sign for endothermic processes.
Now, for work.
Work is negative when the work is done by the system on the surroundings.
So, if the system is pushing out on the surroundings it's
doing work on the surroundings, then that is a negative work.
If the work is done by the surroundings on to the systems, so
it's pushing in on the system maybe,
as a way of thinking of that, squashing in on it, then that is a positive value.
So, if you've got a system in which heat is leaving the system and
work is being done on by the system on the surroundings.
Those are ways that energy is leaving the system.
Both of those are negative discussions that I just had.
And we would have a total change in energy that's negative.
Okay?
If, on the other hand, we have a system.
And here's the system.
And heat is entering the system.
And we're doing work on the system by the surroundings, then both of these would be
positive, and we would have a positive change in energy of that system.
Now let's think about work.
When a gas expands it does work, so
we have a gas that is starting out with this amount of volume, okay.
And it is expanding, and when it expands it is pushing out on the surroundings.
It is going to change in volume by a certain amount.
And that would be represented by final, that's the whole thing, minus the initial,
that's over here, and what I have shaded a little bit there is the change in volume.
So as a gas expands, it is pushing out on the surroundings.
It is doing work on the surroundings.
And that would be a negative.
When a system does work, [SOUND] pushes out.
If the system is doing work on the surroundings,
then that is a negative value.
Now you probably, in terms of work,
have seen in some past classes that work is force times distance.
If you push an object with a certain amount of force over certain distance,
that is one way to calculate work.
But when we're talking about gases we're going to define work this way.
It is a negative of the pressure times the change in volume.
Now, the gas expanding, okay, which is what we saw in the previous picture.
You can look back at it.
If it's expanding, this number is positive.
It is getting bigger.
Well, pressure is always positive.
You can either have no pressure or
you can have a positive pressure, and then we change the sign here.
And so when, if we're expanding a gas, [SOUND] then work is negative.
Now let's see if that makes sense.
If the gas is expanding it is doing work on it's surroundings and
our sign convention says that is a negative value.
So you need to know that equation.
Now when you use this equation to obtain work,
you're going to have units of that are kind of weird.
And let me, [SOUND] now this kind of work is called PV work.
Whenever a gas is expanding or compressing you can calculate work using this
equation, and we will not be using the one you see up here at the top, okay, for
problems that we have in this chapter.
The pressure in the equation is whatever external pressures opposing the change
in volume.
And the change in volume, of course,
would be how the gas is changing it's volume in the container.
When using this equation, if you were to put, you,
if you were to put a pressure and you were to put a volume, a change in volume in,
and you obtain work, what would be the units of that work?
Well, if we use pressure in terms of atmospheres and volume in terms of liters,
the unit that we have, we define as liter atmosphere.
Now it's reversed of what we see up there, but we never call it an atmosphere liter.
The unit is called a liter atmosphere.
Now liter atmosphere doesn't look much like a work unit to us.
But there is a very easy conversion between leader atmospheres in
Joules that you'll need to know and this is it.
If there's 101.3 J, that's your typically energy unit, in 1 liter atmosphere.
So let's consider this problem.
We have got a gas that has a volume change from o.5 liters
to 2.5 liters and is pushing out on an external pressure of 0 atmospheres,
the questions is how much work is done?
Well work is equal minus P delta V.
The P is zero atmospheres, so I don't care what that volume is doing.
It's pushing against 0 atmosphere and so there is no work.
We can go ahead and plug our numbers in for
the change in volume though just to practice.
That would be 2.5 liters as a final, minus 0.5 liters, that's the initial and
that would give us a work of 0 liter atmospheres, or 0, pick any unit you want.
So if you're pushing against an external pressure, you're not doing any work.
I don't care how much the gas is expanding.
So changing a gas's volume doesn't necessarily do work,
unless you're pushing out against an external pressure.
But let's have you do the work for this gas.
It is starting at, and I'm sorry about the break in the line there.
It's starting at 0.5 liters, we'll put it up there, all right?
And it's expanding to 2.5 liters.
It's pushing against an external pressure of 1 atmosphere.
Work the problem and select your answer.
Well, if you picked a negative 200 Joules to one significant figure,
that would be the correct answer.
Now some of you might have forgot to convert to liter atmospheres, so
make sure you do that.
When you determine work as a negative, there is the 1 atmosphere, the final,
which is 2.5 liters, minus initial of 0.5 liters.
It's going to give you 2, or a negative 2 liter atmospheres.
But don't forget that you need to convert that liter atmospheres to Joules because
that's what's being asked for in this problem.
And it's 101.3 Joules per liter atmosphere and
that's why to one significant figure you'll have a negative 200 joules.
Now let's consider this.
We have an exothermic reaction that produces a net increase in
the gas when reacting.
So we have a reaction takes place that you're going to make a gas.
So if the reaction happens, you're producing a gas inside the chamber.
So I want you to think about the sign of q and w.
Well, if you are creating a gas, and let's just put
a container in here, in which we have this little reaction happening, and
gases are being produced as a reaction happens.
Okay?
Those gases are going to make the container expand.
And it's going to push up against that external pressure and we're going to be
able to move the volume, not where we see in this picture right now,
but we will expand it, and let's erase the thing right there.
And let us take it up to maybe, here.
So as the gas is being generating, the volume will expand.
So you're going to select the right answer.
Well did you say they would both be negative?
If you said that, you are correct.
Now how I know it's a negative q?
Because we have the term exothermic, it is giving off heat.
Whenever a gas is expanding, okay, we have got a negative work.
If you forget that, we know that work is a negative P delta V.
If its expanding that's positive, this is always positive,
then the we change the sign and we have a negative work.
Well we know that delta E equals q plus w.
From that previous example that we just talked about,
an exothermic reaction that is producing gas, can we know the sign of delta E?
Is it positive, is it negative, or
we can't know unless we know the value of w and q.
Well, you should have said it's negative, because it's exothermic, that's negative.
Because it's expanding, that's negative.
And if you take a negative number and
add a negative number, this is going to be negative.
If both of these are positive, then this will always be positive.
The only time you don't know is, is if one is positive and
the other is negative, okay?
So these are the two for which you would not know the size of the or
the sign of E delta E, but for both of 'em being negative or
both being positive, you certainly can know.
So this is the end of learning objective number 2,
which we have looked at, kind of the beginnings of thermodynamics.
You will see a lot more about thermodynamics in advanced chemistry.
But for now, that's all we really need to examine, the sign convention of heat,
the sign convention of work and
the idea that those two things are the way we get energy in and out of a system.
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