What is a Pure Substance ? A pure substance is comprised of a single chemical element or compound.

Ch2, Lesson A, Page 1 - What is a Pure Substance ?

What is a pure substance ? That seems like an easy question, doesn’t it ?

A pure substance is any chunk of matter that has the same composition throughout.

That means that all of the molecules or atoms in the chunk of matter must be the same species.

If a beaker contains ONLY water molecules, then it contains a pure substance.

We have to be careful and not look at any chunk of matter smaller than about 100 mm. If we look much closer than that, we may start to notice the properties of individual molecules and atoms.

For example, we might notice that the oxygen in a water molecule doesn’t have the same properties as one of the hydrogen atoms.

So, we are really talking about a macroscopic piece of matter. This is called the continuum scale.

When Can a Mixture be Treated as a Pure Substance ? Combining two substances...

A Homogeneous (uniform) Mixture can often be treated as if it were a Pure

Substance.

A Heterogeneous (or non-uniform) Mixture cannot be treated as a Pure

Substance.

Ch2, Lesson A, Page 2 - When Can a Mixture be Treated as a Pure Substance ?

Consider the Heterogeneous Mixture shown here. The composition near the top of the vessel is very different from the composition near the bottom of the vessel.

Therefore, this system cannot be considered a pure substance.

What about the homogeneous mixture shown on the left ? It is not a pure substance because it contains different types of molecules. But, can it ever be treated as a pure substance anyway ?

Yes, sometimes it can.

Because the mixture is homogeneous or uniform, the composition is the same throughout.

As long as the composition remains constant and uniform throughout, this mixture can be treated as a pure substance. We call this a pseudo-component.

Air is made up of approximately 79 % nitrogen molecules and 21 % oxygen molecules and yet we often consider it to be a pure substance or pseudo-component.

If, for example, a chemical reaction involving only one of the species in a mixture occurs, then the composition will change. Therefore, it would not be useful or accurate to treat the system as a pure substance.

What if More Than One Phase is Present ? Is Ice Water a Pure Substance ?

Ch2, Lesson A, Page 3 - What if More Than One Phase is Present ?

Consider the glass of ice water shown here. If we consider only the water and not the air above the ice water, is this a pure substance ?

Yes, because everywhere in the system, all of the molecules are water. The phase does not matter.

What if we included the gas above the ice water ? Would the system contain a pure substance ?

Well, that depends. The gas above the ice water might be pure water vapor…no air. In that case the matter would be a pure substance.

However, if there were AIR in the container then the composition of the gas phase would not be pure water like the liquid and solid phases. Thus the matter in the container could NOT be considered to be a pure substance.

Now, let’s take a little closer look at the whole concept of a “phase.

What Are Gas, Liquid and Solid Phases ? Molecules move randomly with three different types of motion: vibration, rotation and

translation. Molecules are separated by large distances and travel a long way between collisions.

Gas Phase

Liquid Phase Molecules move randomly with all three types of motion, but they are much closer together and cannot travel very far between collisions.

Solid Phase

Atoms or molecules have all three types of motion, but they are very close together. As a result, they cannot travel far at all before they collide.

Each molecule moves about within a small space and does not tend to wander.

Solid phase

Ch2, Lesson A, Page 4 - What Are Gas, Liquid and Solid Phases ?

What’s the difference between a gas, a liquid and a solid ?

The first things that come to mind usually have to do with measurable properties of each phase such as density.

But at a molecular level, we could see some more fundamental differences.

In all phases, all the molecules or atoms are in motion. They can move in a variety of ways, but the different types of motion are categorized as vibrational, rotational or translational motion.

Vibrational energies are related to changes in the length, and angle of the bonds within the molecule. There can be many modes in which a molecule can be vibrating at the same time.

Rotational energy is the kinetic energy stored in a molecule because it is spinning.

Translational energy is the kinetic energy in a molecule because it has linear velocity.

The total energy stored in molecules in these forms is called the internal energy and we use the symbol U for the total internal energy of a piece of mater.

The higher the temperature of a given pure substance, the higher its internal energy.

We’ll learn more about internal energy in the next chapter.

The first thing you might notice if you could view the 3 phases on a molecular scale is the average distance between molecules.

In a gas phase the molecules are far apart, while in liquids and solids they are very close together. As a result, gases are often called dispersed phases while liquids and solids are called condensed phases.

Molecules in a gas phase have lots of vibrational, rotational and translational energy and therefore have higher internal energies than when they are in the liquid or solid phases.

Similarly, molecules in the liquid phase tend to have higher internal energies than the same molecules in the solid phase.

It’s not as simple to compare internal energies of DIFFERENT molecules.

Now, solids have relatively rigid structure. But, the molecules or atoms in the lattice still vibrate, rotate and translate. They just tend to stay within a small volume between the neighboring molecules or atoms. They don’t wander about too much.

OK, so what happens to molecules or atoms when a phase change such as boiling or melting occurs ?

We’ll get to that in a minute, but first, can you think of any other phases besides the 3 principal phases shown here ?

Are there Really Only Three Phases ? Click here to animate the graphite structure. Click here to animate the diamond structure. Even a pure substance can exist in more than one phase .

Diamond Structure of Carbon

Graphite Structure of Carbon

Ch2, Lesson A, Page 5 - Are there Really Only Three Phases ?

Are there really only 3 phases ?

No ! There are an unlimited number of phases !

Diamond and graphite are both pure carbon, but they are entirely different phases with different properties and price tags.

Diamond exhibits perfect 3-dimensional symmetry around each and every carbon atom.

Graphite on the other hand has planes or sheets of carbon atoms with the carbon atoms in adjacent sheets lined up directly above and below each other.

This subtle difference in structure makes all the difference in the world in properties as well as price.

Don’t be fooled. Graphite and diamond ARE different phases !

Multiple Liquid Phases: Miscibility

A system can have multiple liquid phases when the substances do not dissolve in each other. Such substances are called immiscible.

For example, oil is not miscible in water. Thus, when oil and water are mixed, two layers, or liquid phases, will exist.

When a system has multiple liquid components that completely dissolve in each other,they are said to be miscible.

The resulting mixture can be considered apure substance if neither liquid participates in a chemical reaction.

Multiple Solid Phases Mixing iron and carbon under proper conditions will produce a uniform mixturecalled an alloy, in this case, steel.

Ch2, Lesson A, Page 7 - Multiple Solid Phases

Under certain circumstances, a solid phase can be both a pure mixture and a single phase.

Steel is a mixture of iron and carbon that can be considered to be a pure substance.

However, steel may or may not be a single solid phase.

You may recall from general chemistry that many solids form crystal lattices.

You may also recall that there are different types of lattices such as face-centered cubic and body-centered cubic. There are many, many geometric arrangements that atoms and molecules can take in a solid.

In fact, uniform crystals are difficult to make and most solids are what we call “amorphous solids.”

The arrangement of the atoms within the solid plays a vital role in determining many of the physical, chemical and mechanical properties of the solid.

There is a limit to how much carbon you can mix with iron in order to obtain a single phase when the mixture solidifies.

There is also a limit to how much iron you can add to carbon and still obtain a single phase when the mixture solidifies.

This sounds a lot like what we discussed regarding the miscibility of liquid phases on the previous page.

When iron and carbon are mixed in a certain ratio and cooled or quenched in a certain manner, one type of structure forms at the molecular level. This is one type of phase or one type of steel.

If the ratio of carbon to iron changes or perhaps even the manner in which the mixture is quenched, the result may be a different type of steel. Both its composition and molecular structure may be different.

The bottom line is that these are indeed different solid phases, just as carbon and graphite are different solid phases.

Phase Changes Principle Phases: solid (ice), liquid (water), and gas (water vapor).

Ch2, Lesson A, Page 8 - Phase Changes

Now let’s take a look at what happens as molecules move from one phase to another.

Consider an ice cube sitting out in the sun on a warm day.

Energy from the sunlight causes water molecules to leave the solid phase and enter the liquid phase. That is, the ice cube begins to melt.

Energy from the sunlight also causes water molecules to leave the liquid phase and enter the gas phase. That is, the water begins to evaporate.

Eventually the ice cube is gone and sometime later even the liquid water is gone. All the water has entered the gas phase and you could say it is gone with the wind. Sorry.

No big surprises here.

But now let’s consider a slightly different system.

Phase Equilibrium Consider a glass of ice water placed inside a sealed, perfectly insulated container. Initially, the ice begins tomelt and the water begins to evaporate.

Eventually, the ice stops melting and the water stops evaporating.

The system has reached phase equilibrium.

Ch2, Lesson A, Page 9 - Phase Equilibrium

Let’s take a look at what happens when we place a glass of ice water into a closed, perfectly insulated container.

Perfectly insulated containers are hard to find, but lets just pretend we have one.

At first, the ice cubes may begin to melt. The liquid water also begins to vaporize.

But eventually the mass of the ice cubes becomes stable. The mass of the liquid water will also become constant.

If the pressure is 1 atm and we wait long enough, all three phases reach 0oC.

We have reached phase EQUILIBRIUM.

Phase Equilibrium is characterized by uniform temperature throughout the system and by no NET changes in the mass or composition of any phases.

Phase equilibrium turns out to be a central concept in this course.

Let’s take a look at one more system that is a glimpse of the type of process that we will study in great detail later in this course.

ch2, Lesson A, Page 10 - Phase Changes in a Closed System

The system shown here is a cylinder containing water with a fitted piston that seals the water inside and the surrounding air out. There is NO air inside the cylinder.

The weight shown on top of the piston is just to remind you that the surrounding atmosphere is pushing down on the piston.

For this problem we will use a special mass-less piston. As a result, the pressure on the water within the cylinder is kept constant at 1 atm.

In this process, heat is steadily added to the water in the cylinder.

Initially, the temperature rises from T1 until it reaches T2 = 100oC, the boiling point at 1 atm.

Then, the first tiny bubble of water vapor forms.

In state 3, much of the liquid water has been vaporized, but the temperature remains constant. All of the energy that was added was used to move the water molecules from the liquid phase into the vapor phase.

Finally, at state 4, the last drop of liquid water vaporizes.

As we add more energy to our system, the temperature once again begins to rise.

We will study this process and related processes throughout this course. I’ll fill in more of the details for you as we move along.

I just wanted to give you a look at where we are going in the course.

Lesson Summary Chapter 2, Lesson A - Introduction to Pure Substances

In this lesson we learned some fundamental ideas about the nature of matter and the phases in which it can be found. First we studied the concept of a pure substance. Then, we complicated matters by introducing the idea that a homogeneous mixture can sometimes be considered a pseudo-component and treated like a pure substance. The fact that multiple phases are present does not influence whether a substance is pure or not.

This brought us to a general discussion of the nature of phases. We discussed solids, liquids and gasesand the differences between them. This gave us a chance to introduce the concepts of vibrational, rotationaland translational energies. Before you studied this lesson you probably thought there were only three phases. Now, you know that there can be many different solid phases, such as diamond and graphite, as well as multiple immiscible liquid phases, such as oil and water.

Once we understood the nature of a phase, we introduced the concept of phase equilibrium. We learned that gases and multiple liquid and solid phases can ALL be in equilibrium with each other. We empasizedvapor-liquid equilirium (VLE) because it is crucial to this course.

In the next lesson, we will study the relationship between pressure, volume and temperature. This is really the heart of classical thermodynamics. In Lesson 2E, we will learn much more about VLE.

What is a Phase Diagram ? Phase diagrams depict how the primary phases (solid, liquid, gas) of a substance change as the pressure, volume and temperature of the system change. Phase diagrams are constructed by plotting the following :

1. Temperature as a function of the molar volume (T- )

2. Pressure as a function of the molar volume (P- )

3. Pressure as a function of temperature (P-T)

Note : The molar volume, , is the volume per mole :

The specific volume, , is the volume per unit mass :

Ch2, Lesson B, Page 1 - What is a Phase Diagram ?

A phase diagram shows you the phase in which a material exists at a given state.

This allows you to pack an enormous amount of information about boiling, melting and other phase changes into a nice compact form.

We will only consider phase diagrams for pure substances in this chapter.

With a little practice, I think you will find that phase diagrams will help you gain a much deeper understanding of phases and phase changes.

There are an amazingly large number of different types of phase diagrams. But, we’re going to start out with the big three: T-V, P-V and P-T Diagrams.

It makes sense to start with these three phase diagrams because you are already familiar with the concepts of temperature, pressure and volume.

But what does the wiggly line over the V mean ? Well, the wiggly line means that we are referring to the MOLAR volume.

The molar volume is the volume per mole or just the total volume of the system divided by the number of moles in the system.

The specific volume is represented by a V with a carat, or “hat,” over it. It is just the volume per unit MASS of the system.

So, why bother with molar and specific volume ? Why not just use plain old volume ?

If we used ordinary volume, then we would need one phase diagram for a system that contained 2 kg of water and another for a system that contains 0.2 kg of water.

Why ? Consider a system with a volume of 2 liters that contained 2 kg of water. Nothing remarkable about that since the density of liquid water at atmospheric pressure is about 1 kg/L.

But what if this 2L volume contained just 0.2 kg of water also at atmospheric pressure ? Could all of the water be a liquid ? No, the density is too low. Some of the water would be in a different phase…the gas phase !

So, the phase depends on the SIZE of the system ! This is not very convenient or helpful !

This problem is fixed by using either the molar or specific volume instead of the total volume. This way a single phase diagram can be used regardless of the size of the system.

Cool. So, for example, water has just one P-T Diagram.

Ok, so let’s learn a few terms that will make it easier for us to discuss phase diagrams.

Key Terms Associated with Phase Diagrams

Subcooled Liquid : A liquid at a temperature below its boiling point ( T < Tsat ) for the

existing pressure.

Saturated Liquid : A liquid at exactly the temperature ( Tsat ) at which it would boil at

the existing pressure ( P = P* ).

Saturated Mixture :

A mixture of saturated liquid and saturated vapor in equilibrium. The temperature is the

saturation temperature, Tsat ,and the pressure is called the vapor pressure P*= P

Saturated Vapor : A vapor at exactly the temperature ( Tsat ) at which it would

condense at the existing pressure ( P = P* ).

Superheated Vapor:.

A vapor at a temperature above its boiling point ( T > Tsat ) for the existing pressure.

Ch2, Lesson B, Page 2 - Key Terms Associated with Phase Diagrams

We’re going to start by focusing on vapor-liquid equilibrium, VLE for short. The concept of saturation is the key to understanding VLE. We all know that at 1 atm water boils at 100oC, right ? This tells us two very important things.

1 – The saturation temperature, Tsat of water at 1 atm is 100oC.

2 – The vapor pressure of water at 100oC, P*(100oC) is 1 atm.

The idea of a saturation temperature is pretty intuitive, but vapor pressure can be confusing.

Vapor pressure is the pressure that a liquid COULD overcome in order to boil. Vapor pressure depends on temperature only.

For example, the vapor pressure of water at 80oC is LESS than 1 atm. Water at 1 atm and 80oC doesn’t boil. We would have to reduce the pressure to less than a half an atm in order to get the water to boil at 80oC.

The vapor pressure of water at 110oC is GREATER than 1 atm. This means that water at 110oC would boil even if the pressure were greater than 1 atm. OK, so now what does saturation mean ?

A sat’d liquid is a liquid that is AT the saturation temperature or boiling point that corresponds to the existing pressure.

So, liquid water at 1 atm and 100oC is a saturated liquid. In this case, Tsat = 100oC and P =

P*(100oC) = 1 atm.

Now, if you put a tiny bit more energy into a sat’d liquid and keep the pressure constant, some of the liquid would BOIL or evaporate and create a vapor phase.

The cool part is that the temperature would not change. The liquid and the vapor would both exist, in equilibrium, at 100oC.

The vapor bubble that forms would be a sat’d vapor at Tsat = 100oC and P = P*(100oC) = 1 atm

A sat’d vapor is a vapor at the saturation temperature that corresponds to the existing pressure.

If you take a tiny bit of energy out of a sat’d vapor, keeping the pressure constant, some of the vapor will condense and create a liquid phase. That liquid phase will be a sat’d liquid.

Do you see ? Sat’d vapor and liquid are phases that ARE or at least COULD be in equilibrium with each other.

So what if we have liquid water at 1 atm and only 25oC ? Is this a sat’d liquid ? NO, because T (25oC) is less than Tsat at 1 atm (100oC). Understand ? This is called a subcooled liquid because

it exists at a temperature BELOW the saturation temperature for that pressure.

Similarly, what if we have water vapor at 1atm and 125oC ? This NOT a sat’d vapor because T > Tsat. This is called a superheated vapor.

More Terms Associated With Phase Diagrams

Saturated Liquid Curve :The curve where only saturated liquid exists.

Saturated Vapor Curve :The curve where only saturated vapor exists.

Critical Point :The point where the saturated liquid curve and the saturated vapor

curve meet. At the critical point, the saturated liquid and saturated vapor phases are the same.

Quality x :In a mixture of saturated vapor and saturated liquid, the quality is the

fraction of the total mass that is in the vapor phase . This is a very important quantity because vapor and liquid have dramatically different thermodynamic properties.

where: mtotal = mliquid + mvapor

Ch2, Lesson B, Page 3 - More Terms Associated With Phase Diagrams

We just need a few more terms to help us discuss and understand VLE.

The sat’d liquid curve is a collection of ALL of the points on a phase diagram that represent sat’d liquids. Each point on the sat’d liquid curve corresponds to a different pressure and the Tsat that is associated with it.

Similarly, the sat’d vapor curve is the collection of ALL of the points that represent sat’d vapors.

The critical point is special. The critical point is the point where the sat’d liquid curve and the sat’d vapor curve MEET. That is to say, the sat’d liquid and sat’d vapor are one and the same. They have identical properties. This seems weird. A liquid and a vapor with the same properties.

We’ll discuss the critical point more thoroughly when we consider a P-T phase diagram.

This is a good time to introduce the concept of quality. When we have a mixture of sat’d vapor and sat’d liquid, quality is used to measure the relative masses of each phase.

Saturated vapor has a quality of 1 because 100% of the mass is in the vapor phase.

Sat’d liquid has a quality of 0 because zero % of the mass is in the vapor phase.

Quality is just the fraction of the total mass that is in the vapor phase.

Ok, so now we have most of the terminology down. Now, let’s take a look at how these different states look on a T-V Diagram.

Building a T-V Phase Diagram

h2, Lesson B, Page 4 - Building a T-V Phase Diagram

Roll your mouse over each point on this diagram as I discuss each state.

In this diagram, we are considering water at a pressure of 1 atm. The curve that we plot is called as isobar …a path of constant pressure.

So, we know that the saturation temperature is 100oC.

Let’s start at point 1 with our system at 20oC. Since T < Tsat, we have a subcooled liquid.

If we add energy to our system, the temperature rises while the pressure remains constant.

At point 2, we reach a temperature of 100oC. T = Tsat. Therefore, this is a sat’d liquid. Since the fraction of the mass of the water that is in the vapor phase is zero, the quality of a sat’d liquid is also zero.

As we continue to add energy to the system, the 1st small bubble of vapor forms and the system moves towards point 3. The quality increases from zero, but the temperature remains constant at Tsat.

When the last small droplet of liquid vaporizes, we have reached point 4, saturated vapor. All of the water is in the vapor phase, so the quality is 1. Notice that the temperature is still at Tsat.

When we add energy to the saturated vapor, the temperature begins to increase again and the systems moves towards state 5.

Since the temperature is above Tsat at 1 atm, this is a superheated vapor. Quality is not defined for superheated vapors.

They say a picture is worth a thousand words, but that is only true if you understand the picture ! Play this clip again if necessary because understanding this picture is very important.

Next we’ll consider a family of isobars at a variety of pressures.

Two-Phase Envelope on a T-V Phase Diagram

Ch2, Lesson B, Page 5 - Two-Phase Envelope on a T-V Phase Diagram

Be sure to roll your mouse over each point on this diagram as I discuss each feature.

The two curves, labeled 1 and 2, are two representative isobars.

Notice that the saturation temperature, or boiling point associated with P1 is higher than the Tsat associated with P2.

We also know that vapor pressure, or the pressure that a liquid can overcome in order to boil, increases with increasing temperature.

Therefore, we can deduce that P1 is greater than P2 !

The curves labeled 3 and 4 on this T-V Diagram are the sat’d liquid and sat’d vapor curves, respectively.

Point 5 is the critical point. This is where the sat’d liquid curve and the sat’s vapor curve meet.

Notice that as Tsat increases towards the critical temperature the values of the molar volume for the sat’d liquid and sat’d vaporbecome more and more similar. Finally at the critical point, the molar volume of the sat’d liquid and the sat’d vapor become equal because the sat’d liquid and the sat’d vapor become the same fluid !

We’ll give more details about the strange behavior of fluids near their critical point when we discuss P-T Phase Diagrams later in this lesson.

The last thing to notice about this phase diagram is that areas or regions on the diagram represent different phases.

To the left of the sat’d liquid curve the pure substance exists as a subcooled liquid.

To the right of the sat’d vapor curve, the substance exists as a superheated vapor, a gas phase.

Under the bell-shaped curve sat’d liquid and sat’d vapor both exist in equilibrium. This is called the 2-phase envelope.

It is VERY important to note that regardless of the quality of the 2-phase mixture, you can always determine the molar volume of the sat’d liquid at a given pressure by reading the molar volume from the sat’d liquid curve at that pressure.

The same is true for the sat’d vapor.

Consider the fact that as the quality increases the total volume of the system also increases. However, the molar volume of the sat’d liquid at a given pressure and the molar volume of the sat’d vapor remains constant. Remember that molar volume has units of volume per mole.

The point is that the properties of sat’d liquids and vapors DO NOT depend on the quality !

The range of temperature and molar volume shown on this phase diagram is most important to this course.

Now, let’s consider a P-V Phase Diagram.

P-V Phase Diagram

Ch2, Lesson B, Page 6 - P-V Phase Diagram

Be sure to roll your mouse over each point on this diagram as I discuss each feature. First, roll the mouse over the number 1. This curve is an isotherm. It represents a path of constant temperature. You’ll notice that the isotherms in the P-V diagram don’t run the same direction that the isobars do in the T-V diagram. Does this make sense ?

Consider a gas in a piston that we can keep at a constant temperature. As we increase the pressure, what happens to the volume of the gas ? It decreases, right ? As a result, as we increase the pressure and move along an isotherm, the molar volume must decrease. So, yes, the general direction of the isotherms in this diagram does make sense.

OK, let’s say we start with a liquid at T1 and a very high pressure inside our piston-and-cylinder device.

As we pull weights off of the piston and reduce the pressure, we slide down the isotherm.

Eventually we reach a pressure exactly equal to the VAPOR PRESSURE of our fluid at a temperature of T1. This means that the liquid in the cylinder is now a sat’d liquid. Roll your mouse over number 2 to see the sat’d liquid curve.

If we now add a tiny bit of energy to the fluid in our cylinder, the pressure remains constant and a tiny bubble of vapor forms.

This vapor is the sat’d vapor that is in equilibrium with the sat’d liquid and it exists at the same temperature, T1, and pressure, P*(T1), but has a larger molar volume.

Roll the mouse over number 3 to see the sat’s vapor curve. The 2-phase envelope may be shaped a bit differently in a P-V diagram, but its meaning doesn’t change. All of the ideas and equations associated with quality apply to P-V diagrams in the same way they did for T-V diagrams.. X = 0 for sat’s liquids and X = 1 for sat’d vapors.

The critical point, number 4, is still located where the sat’d liquid and sat’d vapor curves meet.

Roll the mouse over number 5. The isotherm that passes through the critical point is called the critical isotherm and we represent this temperature with the symbol Tcr. Roll-over the number 6.

Now, we didn’t mention this when we discussed the T-V Diagram, but what happens when the temperature is greater than Tc ?

This is called a super-critical fluid and the isotherm labeled number 6 is a super-critical isotherm.

We will discuss super-critical fluids in more detail when we discuss P-T diagrams in the following pages..

In our P-V diagram, we also expanded the range of pressures and volumes to include regions where solids exist. These regions exist in T-V diagrams as well, but we wanted to break you into all of these ideas slowly.

This P-V diagram represents a substance in which the solid has a smaller molar volume than the liquid. This means the solid is more dense than the liquid. Some substances do not follow this trend. Water is the most common example of a fluid in which the solid is less dense than the liquid. Basically, ice floats. The concept of solid-vapor equilibrium is probably new to you. Click to the next page and I’ll tell you a little more about it.

Key Terms to Describe the P-T Phase Diagram Vaporization :The process in which a liquid changes into the vapor phase.

This process is also called boiling. The reverse process is called condensation.

MeltingThe process in which a solid changes into the liquid phase.

The reverse process is called freezing or fusion.

Sublimation:The process in which a solid evaporates directly into

the vapor phase withoutmelting first. The reverse process is called desublimation.

Critical Point:The point at which the saturated liquid curve and the saturated vapor

curve meet.At the critical point, the saturated liquid and saturated vapor phases are the same.

Triple Point:The point at which solid, liquid and vapor phases can all exist

in equilibrium. All three of the processes listed above can occur. At equlibrium the forward rateequals the reverse rate for each process.

Ch2, Lesson B, Page 7 - Key Terms to Describe the P-T Phase Diagram

Here are a few more definitions that will help us understand P-T Phase Diagrams.

Vaporization should be a pretty familiar concept to you. It is commonly called boiling when the fluid under consideration is a pure substance.

Condensation is the same process going in the opposite direction. A vapor condenses to enter the liquid phase.

Melting is probably also pretty familiar to you. Freezing or fusion is the process by which a pure liquid is converted into the solid phase.

The phase change that is probably new to you is called sublimation.

Sublimation and de-sublimation relate to solid-vapor equilibrium in the same way that vaporization and condensation relate to VLE.

The most common example of sublimation occurs in the ice-cube tray of the freezer in your kitchen.

If you leave the ice cubes in the freezer too long, they shrink ! The cubes no longer fill the slots in the tray.

You see, over a period of time, the ice sublimates and the water molecules move from the solid phase directly into the vapor phase without ever forming a liquid.

The conclusion that we draw is that solids, just like liquids, exert a vapor pressure ! More about this when we look at the P-T Diagram on the next page.

I hope you remember what the critical point means, but the triple point may be new to you.

Recall that in the 2-phase envelope sat’d liquid and sat’d vapor both existed at equilibrium.

Well, at the triple point, sat’d liquid and vapor exist in equilibrium with the solid phase !

Since all 3 phases are in equilibrium, all 3 of the processes I just mentioned are occurring simultaneously.

Equilibrium means that the three reverse processes are also occurring and that the rates of the three forward processes are exactly equal to the rates of the three reverse processes.

Evaporation and condensation are occurring at the same rate.

Melting and freezing are occurring at the same rate.

And sublimation and de-sublimation are occurring at the same rate.

Now, lets see how all these ideas translate into a phase diagram.

P-T Diagram for a Substance That Expands on Freezing

h2, Lesson B, Page 8 - P-T Diagram for a Substance That Expands on Freezing

As I mentioned back on page 6, there are two different types of materials: ones that expand when they freeze and ones that contract when they freeze.

By expanding, the solid phase has a larger molar volume than the liquid with which it is in equilibrium.

This P-T diagram represents a material that expands when it freezes, like water.

How can you tell from this diagram whether the substance expands or contracts when it freezes ?

Well, consider that the 3 red curves represent paths along which two phases exist in equilibrium.

The triple point is the point at which all 3 of these equilibrium curves intersect. All 3 phases are in equilibrium.

First, consider a point on the VLE curve between the triple point and the critical point.

What happens if we raise the pressure on our mixture of sat’d liquid and sat’d vapor while keeping the temperature constant ?

The sat’d vapor condenses to a sat’d liquid and then it becomes a subcooled liquid. So, the region labeled “Liquid” on this diagram actually represents a region of subcooled liquid.

On this diagram it is easy to see why subcooled liquids are sometimes called compressed liquids. Compresses liquids are liquids that exist at pressures ABOVE their vapor pressure at the existing temperature.

Now consider a point on the fusion curve that lies between the solid region and the liquid region.

If we raise the pressure on our ice-water mixture while keeping the temperature constant, what happens ?

The state of the system move straight up from the fusion curve and enters the liquid region. That is to say, the ice melts.

What happens to the volume of the system as the pressure increases and the temperature remains constant ? The volume and the molar volume both decrease. A smaller molar volume corresponds to a LARGER density.

Therefore, liquid water has a greater density than the ice with which it exists in equilibrium. Ice floats and the fusion curve on the P-T Diagram for water has a negative slope !

The 3rd equilibrium curve on this diagram is the sublimation curve.

It represents the collection of temperatures and pressures at which vapor and solid exist at equilibrium.

Now, you may be wondering what happens beyond the critical point in this diagram, as well as the previous 2 diagrams.

Consider a process that begins with a sat’d liquid. Click on the gold point and watch the path as the liquid undergoes the following 4 steps, in order

1. the pressure is increased above the critical pressure…the state moves straight up 2. the temperature is then increased above the critical temperature. … the state moves

horizontally to the right. The fluid is no longer a liquid, but a supercritical fluid. 3. the pressure is now reduced BACK to the original pressure … the state moves straight

down and is now a superheated vapor. 4. finally the temperature is reduced BACK to the saturation temperature. … the state

moves horizontally to the left. The vapor is once again a saturated vapor.

What just happened ? Well, the fluid was transformed from a sat’d liquid into a sat’d vapor WITHOUT EVER BOILING !

Remember that vaporization and condensation only occurs along the red curve connecting the triple point and the critical point.

I told you the behavior of supercritical fluids was a little weird !

Now, let’s take a look at a P-T Diagram for the more common case in which the substance contracts upon freezing

P-T Diagram for Substance That Contracts on Freezing

Ch2, Lesson B, Page 9 - P-T Diagram for Substance That Contracts on Freezing

Not too much new here to see, right ?

The key point is that the freezing curve now has a positive slope !

If we increase the pressure at constant temperature on a liquid-solid mixture, the liquid will freeze.

This indicates that the solid is more dense than the liquid.

The logic behind this is completely analogous to the argument presented on the previous page.

See if you can convince yourself that a substance with a fusion curve that has a positive slope also has a solid that is more dense than the liquid at the same temperature and pressure.

Well, that concludes our discussion of phase diagrams. I hope this gives you a strong foundation to build on in the lessons and chapters to come.

But first, I’d like you to try a couple of example problems and then take a short quiz, just to reinforce what I have presented here

Lesson Summary Chapter 2, Lesson B - P-V-T : Phases and Phase Diagrams

In this lesson, we began by introducing the two important intensive variables and . We used to help us define two of the three key phase diagrams for a pure substance: the T-V Diagram, the P-V Diagram and the P-T Diagram.

We used these three types of diagrams to help explain the nature of subcooled and saturated liquids and saturated and superheated vapors. This led into an explanation of saturation temperature and vapor pressure. We will consider these topics in more detail in lesson 2D. We also learned that the saturated liquid curve and the saturated vapor curve meet at the critical point to form the two-phase envelope on both the T-V Diagram and the P-V Diagram. We took this opportunity to define a supercritical fluid. Next, we briefly discussed solid-liquid equilibriumand solid- vapor equilibrium and how they are represented on a P-V Diagram.

The P-T Diagram looks quite different from the other two phase diagrams. Here we introduced the ideas of sublimation-desublimation, melting-fusion, vaporization-condensation and the dynamic nature of phase equilibrium. We also described the triple point and contrasted substances that contract upon fusion with those that expand upon fusion. Water is the most notable example of a substance that expands when it freezes.

In the next lesson, we will consider how to obtain P-V-T data from tables.

How to Obtain Data From Tables In the previous lesson, we discussed the relationships between pressure, temperature and volume. We focused on understanding the nature of phases and phase changes by studying phase diagrams. Now, we will turn our attention to determining pressure, volume, temperature and other properties from tables of thermodynamic data. In this lesson, we will study all three parts of a typical set of thermodynamic tables.

Saturation Temperature Tables

Saturation Pressure Tables

Subcooled Liquid Tables

Superheated Vapor Tables

We will only consider water in this lesson, but thermodynamic tables for ammoniaand the refrigerant R-134a are also provided in the LT Advantage Bonus Materials.

Ch2, Lesson C, Page 1 - How to Obtain Data From Tables

In the previous lesson, we introduced the concept of phase diagrams.

Phase diagrams are graphical representations of the relationships between pressure, volume and temperature.

As wonderful as phase diagrams are for helping to understand and visualize phases and phase changes, it is not very easy to accurately obtain numerical values from them.

Consequently, vast amounts of thermodynamic data have been compiled in tabular form.

As you might imagine, these tables are very large and take up many pages each.

The goal of this lesson is to learn how to quickly and accurately obtain the values you need from thermodynamic tables.

Now, the catch is that a set of thermodynamic tables for a given substance comes in 4 parts.

The 1st two parts provide the properties of sat’d liquids and sat’d vapors.

So, why are there 2 parts that provide the same information ?

Well, one part contains rows of data evaluated at nice even values of temperature.

The other part has rows of data evaluated at nice even values of pressure.

That’s why the two parts are called the saturation temperature tables and the saturation pressure tables.

The properties of superheated vapors occupy a separate section of their own.

The properties of subcooled liquids also have their own section in a complete set of thermodynamic tables.

That may sound a bit scary, but we’ll work it all out in great detail so that you feel confident about using thermodynamic tables.

In this lesson, we’ll only use the thermodynamic tables for water, ammonia and a refrigerant called R-134a.

The thermodynamic tables for steam are always called the steam tables even though they include the properties of liquid water as well.

You will find the steam tables as well as the thermodynamic tables for two common refrigerants, ammonia and R-134a, in the Ch2 1st Aid Kit.

These 2 refrigerants are popular because they are environmentally friendly and you will lean more about these and other refrigerants in Chapter 9.

But right now, let’s learn about thermodynamic tables.

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Chapter 2, Lesson C - Obtaining Data From Tables

In this lesson, we learned to extract data from thermodynamic tables. We only

considered P, and T, but we will see later in this chapter that all of the methods that we learned in this lesson can be applied to other properties such as internal energy and enthalpy.

We learned that thermodynamic tables contain one section for saturated vapor and saturated liquid, one section for superheated vapor and one section

for subcooled liquid. Each section contains tabular data, including , and other properties. The saturation tables are further divided into two subsections: the Saturation Temperature Table and the Saturation Pressure Table. Use the Saturation Temperature Table when the saturation temperature is known and use the Saturation Pressure Tablewhen the saturation pressure is known.

We learned that Linear Interpolation is an essential skill in extracting numbers from any and all data tables. The key equation for Linear Interpolation was carefully derived and its use was demonstrated in an example problem.

We found that interpolation was almost always required when reading the Subcooled Liquid Tables. Finally, we learned to read the Superheated Vapor Tables. Double interpolation is often required when obtaining data from bothSubcooled Liquid Tables and Superheated Vapor Tables.