Program 26 - "Kinetic Theory"

 

Music(Instructor playing pool.)I'm just here today practicing my kinetic theory.Come on.Pretty good, eh?MusicSilico: "We are back with Science 122, The Nature of Physical Science.This is the telecourse that puts your molecules in motion.This is Program 26, Lesson 4.4, Kinetic Theory."Before we're done with this program we will have definedpressure, volume and temperature, and introduced the conceptof air pressure, before we study the gas laws of Boyleand Charles and put them together to state the ideal gas law.Then we will look at Boyle's explanation for the gas lawsas an introduction to the kinetic theory of gasesand the kinetic behavior of matter.Finally, we will show how Brownian motion was usedto convince the skeptics of the existence of atoms.

 

Here are the objectives for today's lesson.These objectives are also in the Study Guide at the beginning of the lesson.Before you begin to study the lesson, take a few minutesto read the objectives and the study questions for this lesson.Look for key words and ideas as you read.Use the Study Guide and follow it as you watch the program.Be sure to read these objectivesin the Study Guide and refer to them as you study the lesson.Focussing on the learning objectives will help youto study and help you to understand the important concepts.Compare the objectives with the study questions for the lessonto be sure you have the concepts under control.The pool table is one of the best models for visualizing thekinetic theory of gases, and in fact, it's one of the physicist's best friends.There is one important imperfection which is...Silico: "You are supposed to strike the white ball first with the cue stick."We were demonstrating, not playing the game, and please don't interrupt, OK?Anyway this important imperfection is friction whichcauses the balls on the table to slow down.

 

I'll try to convince you before this program on kinetic theoryis over that molecules inside this room or inside any container,if they're in the gaseous state, simply don't do that,and this is a little bit difficult for us to accept,but we'll have to work our way up to it.So, molecules are a lot different than real life things like cueballs and basketballs and pendulums and things like thatin the fact that they don't seem to be affectedby friction in the same kind of way.One of the things that, that tells us is that friction,itself, is a molecular phenomenon.And if that doesn't make sense yet, we'll, I hope, have goneinto that before the program's over today, as well.So, here in this program we'll see where atoms and moleculesactually join the Newtonian paradigm.That is, we figure out a way to study atoms and moleculesin terms of forces and heat and temperature linking to motionand actually sort of connecting Newtonianmechanics with chemistry.And you may remember that was one of the big problemswith chemistry is how to explain the forcesof chemistry in terms of Newtonian terms.So, here we'll get into now the conservation of energy, the gaslaws, the atomic theory, and even, yes, statistics.

 

Now this will set the stage for our final programs which willhelp us understand entropy and nonreversible reactions.And it also will help us to understand the electromagnetictheory of light when we get there in the next two programs.So, what we really have here now is Newton's laws appliedto understanding matter at the atomic level.And this, of course, requires a theory of atoms, which we'vejust, I hope, proven in the last three or four programs.Before we actually get into studying the kinetic theory,we want to look at the, what can be called thequantities of state, or the variables for a gas.These are volume, temperature, and pressure.

 

Volume is something we're all aware of.It's simply a measure of the occupied space.Usually measured in some sort of units of volume like meterscubed or liters which are equivalent ways just likecentimeters and inches are equivalent,even though they're both in the metric system.We also know what temperature is becausewe've spent a couple of lessons studying temperature.We do want to note here that in studying gasesor in describing gases, we have to talk about temperatureand absolute temperature or Kelvins.And we'll see why later when we get into the details of the kinetic theory.The most complicated of these three state variables is pressure.

 

Pressure is simply defined as force per unit area.We can also think of this mathematically as simply "F" divided by "A."The units for pressure are some units of force divided by someunits of area, usually Newtons per square meter in the metricsystem, or pounds per square inch in the English system.It's important not to describe these...not to confuse thiswith force, because force is not just another word for pressureanymore than velocity is another word for distance.So, our concern here is actually with the pressure exerted by gases.But it will help first to compare this with pressures in a liquid.So, let's look at the pressures in a liquid first.The pressures in a liquid are exerted by the weightof the liquid and they're equal in all directions.

 

Now, a change in any temperature at any one point in a liquid isaccompanied by a corresponding change at any other point in a liquid.This is something called Pascal's principle and the pressureincreases downward as you move down in the liquid.This is due to the weight of the liquid above a given surface.Now, this is also true for gases, but in a much different way.Here in the liquid we can see, for example, that the shapeof the container makes no difference in the height to which the water rises.In fact, if we were to start here at the surface, in any of thesecontainers, and work our way downward, we would find thesame corresponding pressure increase.And, in fact, at any level in any of the containers,we would find the pressure to be equal.Now this is kind of surprising because there's obviously agreater volume of water above a point in thisfunnel than there is in this funnel.So, it's not just due to the weight of the water, itself, it's dueto the pressure of the water or the force per unit area.

 

OK.This is now also true for gases.But gases work a little bit differently.The reason why gases work differently is becausethey're much less dense than a liquid.In ordinary sized containers like the gas inside a glass sittingon the sink, the difference in pressure between the topand the bottom is negligible, if it's not immeasurable at all.But if the gas or liquid is packaged under externalpressure in a sealed container, the externalpressure, we found to be the same throughout the gas.So, in a, for example, a can of compressed air used for diving,even though the pressure inside is much greater than it is outside,the pressure is still fairly even all the way through.But, where the quantity of gas is large, such as, for example,in the earth's atmosphere, gravitational forces causea significant difference in density and alsoin pressure between the top and the bottom.This is why we find that the atmospheric pressure gets lessas we go to higher and higher altitudes.And we'll come back and look at the conceptof air pressure in the next section.

 

Concept of air pressure is one that we take for granted.In fact, we take it for granted so much that it was very difficult to discover.The reason for this is that we don't feel air pressurebecause it's equal in all directions.So that even though the air is pressing down on uswith a pressure of about almost 15 pounds per square inch,it's pressing down and out in every direction, so we don't notice it.It's another one of those cases of trying to imagine a fish learning about water.The fact that we know about air pressure at all has a lot to do with Galileo's work.You remember Galileo, our first scientist.Here's the background on this.It was known since early in the 16th century that water wouldrise in a tube with one end submerged in water,if the air were drawn out of the tube; sort of like sucking on a straw.Their pumps have been designed to do this.In fact, people had learned to use ground water by pumping waterout of a well using, basically, a suction pump which does thesame thing as sucking out of a straw.

 

 

Scholastic Physics explained this in terms of Aristotle's conceptof nature's abhorrence of a vacuum.The idea that when you suck the air out of the tube, it creates a vacuum.Nature abhors a vacuum, and so the water naturally rushes in to fill the space.This is the basis, as I said before, of all ground water pumps.Well, Galileo, you remember Galileo, he was a smart sortof guy, was told by a workman who was a well digger, actually,that the pump would work only if the pipe was less than 34 feet long.In other words, if you have a straw that's longer than 34 feetlong, you simply won't be able to suck a liquid upthrough the straw--no matter what you do.Galileo being a smart sort of guy wondered why nature'sabhorrence of a vacuum stops at precisely 34 feet.Why 34 feet?Now you may remember that Newton had considered later,this same sort of continuity question with the apple.Galileo, before Newton's time, this didn't seem to make senseto him, that this would stop at 34 feet.If it was just simply the vacuum.So, Galileo reasoned it this way:That the rise of water in the pipe is due to the air pushingon the surface of the water, not from the pulling of the water from the top.

 

Now, this is kind of hard to explain, but it's not really.Because what's happening is that in Galileo's hypothesis, which isessentially our modern hypothesis as well, before the pump suckedthe air out of the pipe, the push of the water was balancedby the downward force of the air in the pipe.So, removing the air, removes the downward force so the waterrises in the tube until its downward force balances thedownward force of the air pressure outside the tube.In other words, the air pressure pushes down on the surfaceof the water, the water exerts a pressure which will balance theweight of air inside the straw until you remove that air,in which case the water rises inside the straw to balancethat force exerted by the air pressure outside.So, Galileo reasoned that the pressure of the air shouldbe about equal to the weight of a column of water 34feet long and one square inch in area.This turns out to be, he weighed this verysuccessfully, about 14.7 pounds per square inch.The pressure, remember, inside the tube equals the pressure outside the tube.

 

Well, in Galileo's time people were not convinced by this.It seemed that they just didn't offer any better explanationfor it than Aristotle's explanation of nature's abhorrence of a vacuum.One of Galileo's students, actually two of Galileo's students,one was named Toricelli; one was named Pascal, decided youshould be able to measure air pressure, changes in airpressure with elevation by using a water tube inverted and seeif as you rise higher in the atmosphere, if the air pressure diminishes.Of course, it's kind of inconvenient to carry a 34 footlong tube of water up a mountain with you.So, Toricelli and Pascal together, actually, reasoned that sincemercury is almost 14 times as dense as water, 13.6 timesto be precise, then the height of a mercury column should beabout 34 feet divided by 13.6, which is about 2 1/2 feet or about 30 inches.So, this particular measure of atmospheric pressure is still used in weather.Actually it's only used in the United States, and it's actually29.96 inches of mercury, not 30 inches of mercury.So, this also equals the standard atmospherewhich is 14.7 pounds per square inch.So, what Toricelli did was simply to fill a tube, which closedon one end, with mercury and invert the whole thing in a dish above the mercury.So what happens now is that the vacuum exerts, as it gets abovethe mercury, and the weight of the air outside pushes the mercuryup until it balances the weight of the air outside.

 

I should also point out that Toricelli and Pascal actually diduse this to measure air pressure and they basically took oneof their barometers up a mountain and watched the barometer fallas you encountered lower and lower air pressure.Interestingly enough Toricelli was a good enough scientistto recognize that the changes in air pressure might be dueto something else, so he also left a second observer at the baseof the mountain with an identical barometer to record the airpressure changes at the base, so he could be sure that the airpressure hadn't changed everywhere while he was up on top of the mountain.So, we can see in summary of this idea of air pressure that theanalogy between the depth of water and the depth of airor pressure in the sea and pressure in the atmosphere isnot really a good one because pressure in water increasesrapidly with depth with no appreciable change in density.On the other hand, the pressure of the air decreases rapidlyin altitude, but there is a corresponding change in density.So, on one hand, the pressure is due to weight, and the other,the pressure is due to weight and something else.

 

So, what we can say here is that the numerical magnitudeof the pressure of the atmosphere exactly equals the weightof a column of air one square inch in cross section.But, as we'll see in a minute, this is not the same as saying thatthe pressure of the air is caused simply by the weight of the air.The proof of Galileo's hypothesis had to waitfor Robert Boyle to invent the vacuum pump.Boyle's pump was a rather ingenious device and verymuch like the pumps we use today.It consisted of a chamberfilled, in this case it wasglass, with a stopper on the top.It also had a stopper on the bottom.And all that happened was there was a piston in the movablecylinder which was driven up and down by a handle connected with gears.So, as the handle was depressed, the piston moved down.That caused a partial vacuum inside the tube.The stop cock was then closed.The piston lifted back up and then the stop cock openedand the whole thing repeated several times.In our modern vacuum pumps we have a two way valve insteadof having to turn the stop cock off and on.So, the use of Boyle's vacuum pump enabled people now,not only to visualize the concept of air pressure,but also to do some other things with it.For example, one of the first things that Boyle did was to putToricelli's barometer in an air tight container and pumped the air out of it.

 

Now what does this prove?Well, it proves that before you start pumping the air out,that the pressure inside the container equals the pressureoutside because simply putting the container over the topof this doesn't change the air pressure.But, now, the weight of the air above the dish could not hold itup because there's not very much weight of air above the dish.Right?There's only this much air above the dish yet the pressure insidethe tube still holds the mercury up.Now, you can now take the vacuum pump and pump that little bitof air out through the stop cock and see that as you pump thatsmall amount of air out of the tube, I should say,out of the container, that the level of the mercuryfalls as you pump the air out.So there's something going on here besides just the weight of the air.The air exerts pressure, but not simply due to its weight.The other thing that came out of Boyle's vacuum pump was atraveling show called the Magdeburg Hemispheres.

 

A count in Germany built a set of hemispheres which he usedto go around various towns in Europe and make betswith people about this concept of air pressure.Only he wouldn't explain to them what air pressure was.What he would do was to, first of all, the hemisphere is simply atwo piece sphere, which has a stop cock on it which you cansuck the air out of with Boyle's vacuum pump.It has a washer that fits between the two spheres.You put the two spheres together and pump the air out of it.And Magdeburg would do this using Boyle's vacuum pump,showing that the pump doesn't really require much of any effort.And then he would tie teams of horses to the two sidesof the sphere and bet the villagers whether or notthe horses would be able to pull it apart.And, I think, you can probably guess that he always won.

 

Now, I have a pair of Magdeburg hemispheres or something likethis that I can show you right here.So, first of all, I have a version of Boyle's vacuum pump.This is a little more modern.This one has the handle does the same thing.There's a little piston inside here, but it's got a two-way valve.It also has a vacuum gauge on it which tells us the pressure.We're not concerned so much at what the pressure is.

 

OK.Here I have two halves.These are not spherical like the Magdeburg spheres,but they're two pieces of steel which are basically emptyinside, and there's a valve here with a stop cock.So what I want to do is to put the tube on this and pump the airout of the small space between there.And I want you to notice here that the spacebetween the two halves is very small.It's only that deep.So there's not much air being taken out of here.So, you'll notice that it still wants to fall apart.But as soon as I pump the pump a couple of times,it's already enough to hold the weight of the other half of the sphere.Now I'm going to pump this out.I don't know if you can see the, I don't think you can see,the pressure gauge, but notice how effortless it is for me to pump this.I'm putting very little effort into it, and now comes the test.Can I pull these things apart?Now I'm not as strong as a team of horses, I'm only as strong as maybe one horse.Ah, ha, ha.So, here goes.

 

Now we're really going to get physical here.I'm going to pull this apart.Grrr, umm, uhh.Nothing I can do can pull it apart.In fact, the thing is...I can't even twist the things.So, listen when I take this apart, you'll hear the little hiss of aircoming out, or I should say going back into the spaces.Not very much air, listen.(Soft hiss.)Now look.So what we've got here is the fact that it's not the amount of airinside that's important, it's the pressure of the air on this surface outside.The surface here is somewhere on the order of 10 square incheswhich means there is a minimum of a force of 150 pounds pulling the thing.

 

Now, I wasn't pulling probably with a forceof150 pounds, but that's quite a bit.There have also been cases, by the way, where shipswere grounded by storms and you try to pull the ship outand you have 45 teams of horses, enough to movethe ship, but the ship simply won't come out of the sand.Can you figure out an explanation for this in terms of what you've just seen?Having a little bit of background now in the concepts of pressure,temperature and volume, we can turn our attention to the gas laws.These gas laws are relationships between temperature, pressureand the volume of gases that were discovered in steps.They're now expressed as what we call the "ideal gas law,"but we want to look at the stages of this, because it helpsto illuminate and illustrate what's going on.The first of these was called Boyle's law.

 

Boyle's law was first put forth in about 1662.Everyone's familiar with Boyle's law because we'veseen it in action all the time.For example, when we pop a balloon.If I squeeze on the balloon, the pressure inside increases(Pop!)until eventually the balloon pops.Right?So, decreasing the volume of the balloon increases the pressureand the pressure eventually causes the balloon to pop.So Boyle's law basically simply looks at the relationshipbetween pressure and volume when the temperature is constant.And we can state it this way: that the pressure times the volume is constant.So, here on the screen we see how this works.Here we have a container which has a movable side.This is a sort of an idealized way to think of this.We have a container with a movable side, like a piston.And I set a weight on top of that.

 

So, the pressure exerted by this weight is equal to its weight,which is force, divided by the area of the top of the piston.So, inside we can measure the volume of the container.We know how to do that.If it's a square container, it's length times depth times height.And then we double the force, simply by putting on an additional weight.So doubling the force also doubles the pressure.All right.We have the same amount of force divided by the sameamount of area, so the pressure is doubled.What we find now is that the volume is reduced to one half.So it's not just a qualitative relationship, it's a quantitative relationship.That pressure times the volume is constant, so if the pressure isdoubled, the volume must be reduced by one half.Right?One increases by a factor of 2, the other decreases by a factor of 2.

 

Now, Boyle didn't have an accurate thermometer to measuretemperature change, so he had to do this at a constant temperature.He also did not have an accurate pressure gauge, so he measuredpressure by using a modified version of Toricelli's barometer.And what he did was simply take Toricelli's barometerand bend it into a "J" shape.So that he observed that when the level of mercury is the samein two sides of the "J" tube, that must mean that thepressure is equal on both sides.In other words, the pressure inside the enclosed portionmust equal the pressure outside the tube.And think about this in terms of Newton's laws.Right.So the downward force on this section of the tube equalsthe downward force on the section of the tube,there's a zero net force, so that no movement takes place.

 

So, now if you add mercury to this side of the tube to a heightof 30 inches, why do you suppose he used 30 inches?Because it's one atmosphere of pressure.And as a result of adding the extra atmosphere of pressure,the volume inside reduces by a factor of 2.So, here you see he's using Toricelli's barometer becausehe knows from that, that the doubling the atmosphericpressure would be adding another 30 inches of mercurySo this is very clever.By the way, you might want to take a guess as to howmany inches of mercury would he have to addto make this go to one forth of this original volume.You can think about that when you get back to me on that.So, I actually have a demo of a little bit more modern versionof Boyle's law which we can see, I think, on the ELMO quite clearly.So, here's a apparatus which has on this side a, basicallya syringe with a piston inside, and it's connectedto a pressure gauge, over here.So you can see, I think, where the end of this is.There's kind of a little glare from the lights, but as I move thisyou can see how the piston moves up and down.You'll also notice that at the same time that the lightor the pressure gauge is also moving.So, we don't want to try to do this perfectlyquantitatively, but we can get a sense here.For example, now the pressure is, the volumeis about 5, the pressure is about 17.So, at a volume of 5, the pressure is about 17.

 

Now, Boyle's law tells us that if we take half of the volume,the pressure should change by some factor.Right?What factor is it?Well, let's see.If we increase the volume, we should decrease the pressure.Is that right?Increase the volume, decreases the pressure?Well, let's see.Here we're at 10 on the chart where the pressure were about...Oh, look at that.About 8 1/2.So, the volume is 10, the pressure is about 8 1/2.I don't know if I can get this all the way up to 20.Let's see what happens.If I take it up to 20, what's the pressure?Oh, the pressure is now down to about...Oh, look at that, 5.So, at a volume of 20, the pressure is down to about 5.So, you notice the relationship here.Let me zoom in on the numbers.As far as the numbers go, look what happened here.We doubled the pressure from 5 to 10.I'm sorry doubled the volume from 5 to 10, the pressure falls off by a factor of 2.Increase the volume by a factor of 2 to decrease the pressure by a factor of 2.Here we've increased the volume by a factor of 4.Well, we didn't quite get the 1/4 of 17.Part of the reason for that is that when the system,this particular system, gets too pressured, a little of the air leaks in.But I think you can see this illustrates the principle very nicely.

 

The second of these gas laws has come to beknown as the law of Charles and Gay-Lussac.This is because it was invented or discoveredjointly by Charles andGay-Lussac.You remember Gay-Lussac.He's the one who came up with the law of combining volumes.Well, he was able to do that partly because of this law which hediscovered, but also because of the inventionof the thermometer which allowed the measurement of pressureto be fairly accurately known, I'm sorry,temperature to be fairly accurately known.So, the law of Charlesand Gay-Lussac simply relatesthe volume to the temperature of a gas, and we find another proportion.But this time it's a direct proportion.

 

 

 

Noting that volume divided by temperature is a constant.So what this means is that if you start out with one liter of gasat 300 degrees Kelvin, notice the use of absolutetemperature, and you double the temperature to600 Kelvins, the volume goes to 2 liters.In other words, doubling the temperature also doubles the volume.The way Gay-Lussac actually did this was to use the fixed points of water.He took a small glass tube which was closed at the bottomand open at the top so that a little droplet of mercury would riseto a level which would balance the pressure below with the weightof the mercury and the pressure above.And as the water heats, goes colder, I should say, the levelof mercury falls indicating that the pressure inside the tube hasalso "falled," and once again, also "falled."Well, this is not an English class, sorry, also "fallen."You can also see that the volume and, therefore, the pressureinside is proportional to the temperature.

 

So, now it's time for us to combine these laws into the ideal gas law.The ideal gas law really is a combination of the lawsof Boyle, and Charlesand Gay-Lussac.So, let's go to the ELMO and I'll show you how to derive this.What we have here is two different laws.On one hand we have Boyle's law that says that pressureis proportional to the inverse of volume.Right.This little symbol, you may remember, means proportion.And at the same time, we have the law of Charles and Gay-Lussac,which notes that volume is directly proportional to temperature.So, how is it that we combine these together?Well, you may remember that one way to turn a proportioninto an equal sign is to add a constant of proportion.So, let's do some mathematical wizardry here and see what happens.So, what does this really say?That pressure is proportional to one over volume?Well, it says that pressure times volume is proportional to some constant, right?

 

Now, the constant might be one, it might be some other number.But, we can write that then as pressure times volume is equalto some constant number which...I'll just use "K" here...it's a nice German mnemonic for constant.So, if pressure times volume equals constant, what about volume and temperature?Well, we already saw in the definition of the law of Charlesand Gay-Lussac that volume divided by temperature is a constant.Right?So, how can we put these things together?It's very similar to what Newton did with his law of gravitation.Right?Just...can you see how this works?If volume is proportional to temperature and pressure timesvolume is a constant, then doesn't it follow that pressure timesvolume, divided by temperature is also equal to some constant.I'm using the same "K" here, the number representedby the constant may not be the same number.But still, if pressure times volume is constant,and volume is divided by temperature is constant,then it must be true that the combination of the three of them is a constant.This is what we call the ideal gas law.Why is it called the ideal gas law, do you suppose?What is ideal about it?Well, it's ideal because gases, ideal gases,or under ideal conditions will behave this way.Now this is such a simple statement, but I might note herethat if we rewrite this, this way, "PV = KT,"we see something else here that didn't show up before.What we see here is that pressure times volume is equivalent to temperature.

 

Now, this is an interesting statement.Pressure times volume is somehow equivalentto temperature and we'll take a look at this ideaof pressure and volume here in a minute.But first, we want to take a look at Daniel Bernoulli and Bernoulli's principle.There were actually several explanations given for the gas laws.One of these was by Boyle.The other was by a man named Daniel Bernoulliwho we'll take a look at in a minute.Boyle looked at the idea of gases as somehow being due to particles.Remember that Boyle was a contemporary of Newtonand that Newton and the members of the Royal Society all thoughtthat matter was made out of small contiguous particleslike today we would call molecules.This was long before the atomic theory, so there was some question.Boyle believed that gases were caused by static contiguousparticles at rest, contiguous meaning touching.

 

Now, in order for them to do this, exert pressure this way,several things had to be true of the molecules or the corpusclesas they were called in Newton's time.One of them was that the particles themselves had to be compressible.So, Boyle's static model sort of envisioned these atomsor molecules being like pieces of wool that you stuff inside a box.So if you stuff them inside the box and close the lid of the box,the box will hold them in, but if you open the box, they come out.Boyle went on to note that if these things are not touching,if the molecules are not touching each other,then they either have to be variable in size to beexpanded, or they must be in motion.

 

Newton, you may remember, favored a motionexplanation for heat and kinetic energy.So, the problem with this is that the static idea,this idea of static expansion, does not account for the abilityof these gases to expand to fill in a container.And this is one of the properties of gases, right?So, then to figure out what causes them to expand, you must saysomething about the fact that the particles are self repulsive.So that you can think of them inside the box, not touchingeach other, but repelling each other, sort of like the similar poles of a magnet.This, now, is very nicely consistent with caloric theorywhich Boyle was a firm believer in.Because with caloric theory, remember, the warmersomething was, the more it expanded and so the caloric was self repulsive.So in Boyle's time, this all worked out very nicely.The other suggestion, now, comes from a man named Daniel Bernoulli.

 

Bernoulli put this forth in 1738.Bernoulli is another one of these guys who was so far ahead of his time.In fact, he deduced Boyle's law using Newtonian mechanics.And anticipated this kinetic theory of gases that we'retalking about now by about a hundred years.His views were far too advanced for his time, and most peoplesimply didn't understand what he was talking about.In fact, it was about three generations too soon.His idea at the time died for lack of attention.But, even so, he made two important contributions to scientific thought.The first one was to recognize the equivalence of heatand mechanical energy through particle motion.And it was the ideas of Bernoulli that Joule revived later onin his own development of the idea of conservation of energy.

 

The second thing was that Bernoulli conceivedof the possibility--this is the important one--he conceivedof the possibility that a quantitative relationship,like Boyle's law, could be induced from the chaoticpicture of randomly moving molecules.In other words, it was his idea that really showed thatthere's a possibility to derive complicated things like the gaslaws from looking at atoms as Newtonian particles.Now at last we're ready to examine the kinetic theory of gases.The kinetic theory was actually postulated by one of John Dalton's students.Remember John Dalton who came up with the atomic theory?The student of John Dalton is someone we've met already.He was James Joule.Remember James Joule?Conservation of energy, mechanical heat?Joule was a student of Dalton and was very impressedwith the concept of the atomic theory of matter.The kinetic theory of gases was actually postulatedfirst by Joule to explain the gas laws.What he really did was that he resurrected Bernoulli's workin a series of lectures and papers for a decade, from 1847 to 1857.So it was actually Joule, a student of Dalton, who's responsiblefor bringing Bernoulli's ideas about the gas laws back into vogue.

 

Joule sharpened the concepts a little bit and fortified itwith convincing arguments and also many calculations.And, using the gas laws, Joule was the first person to give meaningto the concept of absolute zero, which we'll get into later in this program.Joule also took the concept of the kinetic theory of gasesand refined it and extended it to other phenomenon.So that by the end of the 19th century other physicistswith names like Helmholtz and Maxwell and Boltzmannand Gibbs had made great inroads in this, and finally wound uplinking the kinetic theory and the Newtonian paradigm.This is really the connection between the two.It still, however, does not explain chemical bonding.So we have to come back in a later program and deal with chemical bonding.But, what we can say about atoms and molecules is that atomsand molecules are Newtonian particles.That means that they have mass, they obey theNewton's laws, and they do other things.And if we keep this in mind, the kinetic theorybecomes actually very easy to understand.So, let's look at the postulates of kinetic theory.

 

Now here I use the word, postulates, simply as that.A postulate is something, it's a straw man.You say, let's make these postulates and see if it makessense in line with what we know about the gas laws,and what we know about the properties of matter.So what we're doing here is saying we know the gas laws are true,we know what Newtonian particles do and how theybehave, so now we want to see if we can come up with somepostulates which will allow these things to link together.In other words, we're taking an inductive approach to this.So, let's look at the postulates first, and then we'll come backand examine them to see if they make any sense.So, these are the fundamental postulates of kinetic theory,basically as Joule put them forth in 1857.The first one is that gases consist of molecules.

 

OK.That seems like a reasonable one, but again, we'll come backand look at these in somewhat more detail.The second thing is that the molecules are in constant, yet, random motion.Constant and random motion.We'll come back and define what we mean by random here in a minute.The third thing is that molecules are far apart compared to their size.The fifth thing is that molecules exert no forces on each otherexcept during collisions with other molecules of gasand with the walls of the container, and when thesecollisions do take place, the collisions are perfectly elastic.

 

Now we understood a little bit from the concept of kineticenergy what we mean by elastic collisions.So, let's go back and see now if these postulates make senseboth in terms of the gas laws and in termsof the Newtonian properties of matter.So, the first one is that gases consist of molecules.This one is probably the easiest of all to stomach becausewe would expect that gases consist of molecules,because, after all, gases are substances, and from the atomictheory, we understand that substances do consist of molecules.And we also know that changes of state arephysical changes which involve no new substances.So, how can we put that all together?Simply to note that gases consist of the same kind of moleculesas the solid forms, so that water and ice and steam, all contain water molecules.They're just in a different physical state.As far as the constant random motion, we have some prettygood evidence that this takes place as well.For example, gases will diffuse through space to fill the available volume.How many times have you been in a room where somebody'speeling an orange, and within a few minutes, you can smellthe orange all the way across the room.We also know that if you allow gas to expand, it will expandspontaneously to fill the entire space.So, we can say here that it makes sense, then, that pressure isexerted on the walls of the gas containers by the forces of molecular collisions.In other words, what causes pressure is the forces exertedby the molecules as they bombard and impact, not onlywith themselves, but with the walls of the container.I'll sure you in a little bit later how we can actuallyderive this using Bernoulli's method.

 

The next thing is that molecules are far apart compared to their size.This makes sense when we consider that gases are greatlycompressible, and in fact, tremendously compressible.For example, steam occupies a volume of about 2000 timesthat of water at the same temperature.So there's a tremendous amount of compression going on.And we also know that gases are much less dense thantheir solid or liquid counterparts.Steam is much less dense than water, and so are other gases.How about this one?Molecules exert no forces except during collisions.Well, let's see.

 

Gravitational forces are extremely small.In fact, if you calculate the gravitational force between twoatoms, even when they're touching each other, the gravitationalforce is too small to have any impact at all on the atoms and molecules.So, besides gravity, what other kinds of forces are there?The only other kinds of forces we know about besides gravity areelectrical forces, which we haven't considered here yet,but we will, and the forces of impact.And we've already dealt with those by saying thatthis is the cause of pressure.How about this last one?This one might be the hardest one to swallow of all.The collisions are perfectly elastic meaning thatkinetic energy is completely conserved.One way to think of this is to compare the movementof the gas molecules to a room full of bouncing balls,or if you prefer a two dimensional model,think of the balls rolling on the pool table.

 

Now what's the difference between the room fullof bouncing balls or the balls on the pool table, and a container full of gases?Well, imagine that you're on a handball court and you take abunch of super balls and you throw them into the handball court,and they're bouncing around everywhere, bouncing off thewalls, of the ceiling, bouncing off each other.What's going to happen if you close the door and come back tomorrow?Well, the balls will be on the floor, right?They will have lost all their energy because it's inelastic collisions.Does this happen with a container of gas?In other words, if you take a jar and fill it with air and putthe lid on it, when you come back, are all the molecules in the bottom?No, of course, they're not.So, the balls in a container of gas, or I should say, the moleculesin a container of gas do not lose energy and the moleculesdo not collect in the bottom of the container, they keep on bouncing around.

 

Now, this one is a little bit hard to stomach.But, maybe I can say it this way: that if the otherpostulates makes sense, then so does this one.In fact, if the other ones don't make sense,then this was doesn't, but if the other ones make sense,then this one almost has to be true as well.So now we can see how kinetic theory can be extendedto explain not only gases, but also the other states of matter.Let's look at these in order.We've already seen the properties of the gas,but let's review these very quickly.A gas has no fixed shape and no fixed volume and exertspressure on the containers that it's in.So what we know from the kinetic theory is that the gases areat constant, the molecules are in constant random motion,that their molecules are far apart compared to their size,that they're easily compressible, and thatthey have the least restrictions in their motion.The models are balls on a billiard table or super balls bounding around a room.

 

OK?Gases are mostly empty space so they're easily compressed,their motion is constant and rapid, and they exert pressure by collisions.You might imagine that they have many, many collisions, and don'treally move very far, so that there's a short average distancebetween the collisions, and over all, there's no net movement of gas.Think of balls bouncing around inside a railroad car, for example.

 

OK.The next state of matter is the liquid.The liquid, we know, has a fixed volume, but no fixed shape.And it's really the most complicated of all the states.It's sort of intermediate between a gas and a solid.And I want to point out here, if I haven't done so already,that most substances have only a very limited region of liquidstability, things like water and carbon dioxide.So with a liquid, the molecules are closer together than a gasbecause the liquid still maintains its volume but they're freeto move in a limited way so that the liquid can flow.Here we have weak forces between moleculesdue to physical bonds called van der waals bonds that we'llget back to a little bit later, or hydrogen bonds.You can think of this as sort of clusters of solid structuresmixing with a gaseous state in a sliding motion.And a good model for this is a little jar full of magnetic spheres.So here we have the magnetic spheres which sort of sticktogether and you can see that they have kind of the propertiesof a liquid, too, that they flow to fill the container, but they don'tfall apart like the gas molecules because they do exert forces on each other.

 

OK.The third state is the solid.The solid we know has a fixed shape and a fixed volume.Here the molecules are free to move, but only around fixed positions.Here's a model of sphalerite that I brought out before.The molecules are locked in position relative to one anotherso that they might be able to vibrate or they might be ableto rotate, but they can't move around and slide likethe molecules in the liquid do.The best model for understanding the solid would be to imaginethese balls stuck together with very tiny springs.So if I shake the model like this, the individual balls could sortof bounce around, and if I shake them very hard, then they couldfly loose to become more like the model of the loose balls in the liquid state.Using kinetic theory we can also understand how it is that gases exert pressure.The pressure's exerted as molecules exert forceson the walls of their container.This is sort of like throwing a ball at the wall.Remember that when we consider momentum we saw that whenthe ball hits the wall, they exert forces on each other.So the ball exerts a force on the wall, and the wall exerts a force on the ball.This causes the ball to change direction.So, if you have a whole lot of these things going on, all thesedifferent forces, all the different balls bouncing,then the pressure can be seen as the sum totalof all these forces acting on the wall.

 

Now, you can say that, well, with a few molecules as I bouncethe balls like this, you hear the individual thumps,and the pressure's a continuous thing, but the more thumps youhave, the less you hear the individual thumps.It's sort of like listening to rain on a tin roof or on a roof at night.When there's only a few raindrops, you hear, tap,tap, tap, tap, the individual raindrops.But as the rain gets harder and harder and harder, you no longerhear individual raindrops, what you hear is a constant roarwhich stays pretty much constant as long as the rain keeps falling at that rate.So, this is our model.In this model we can see that work, kinetic energy,and the temperature are seen to be different forms of the same thing.But I think we need to come back to that to understandthe concept of temperature and heat a little bit later on.We need to talk very briefly about the ideal gas lawand the difference ideal gases and real gases.What exactly is an ideal gas?An ideal gas is any gas which obeys the ideal gas law.In other words, an ideal gas is a gas which,for which pressure, volume and temperature arealways equal to a constant, "PV over T" is equal to a constant.What do we mean by real gases?Well, let's look at it this way.All gases exert pressure due to molecular collisions.Real gases deviate from the gas laws at lowtemperatures and high pressures.What happens to gases at low temperatures and high pressures?Well, gases will eventually condense into liquids.

 

Steam does this around 100 degrees Celsius at one atmospheric pressure.So, we can think of it this way.Ideal gas, as we said before, exert forces on each other only during collisions.And this can be forces exerted on the walls of the container,or forces exerted on other molecules.And as we saw in the last section, pressure is the resultof the collision or the sum of the collision of all these molecules.So, keep in mind that the gas molecules are Newtonian particles.And they exchange energy and momentum during collisions,just like any other kinds of Newtonian particles.

 

The important difference is that the collisions are perfectly elastic.Or, maybe I should say that the collisionstheoretically in the ideal case are perfectly elastic.Which means, of course, that energy is conservedin the collisions and we saw earlier that we can justify thisby noting that air does not settle to the bottom of the room.What does happen with real gases is that there aresmall attractive forces between the molecules.Those same forces which made the magnetic balls stick togethercan cause the gas to condense to liquid at certain temperaturesby having slightly inelastic collisions.It works sort of like this.These are two molecules and if they come togetherwith a perfectly elastic collision, that means that their energiesbefore and after are both the same.But, what if these were covered with a contact cement or with a glue?Then as they come together in a collision, the glue will tendto remove some of the elasticity from the collision which meansthat there's a loss of energy as work is done to fight against the glue.

 

I think you can also see that if the glue is very strong, that theharder I throw the balls together, the less likely the glue isto hold it, and in fact, if the balls are moving slowly when theycollide, then they're much more likely to stick together.This is exactly what happens with gas molecules.If the molecules are moving slow, then they're likely to stick together.And if they do stick together, then we have a little clumpof molecules, and that clump of molecules is what distinguishesthe liquid state from the gaseous state.In fact, if we were to look at water we would find thatthere are many more clumps of molecules at coolertemperatures than there are at warmer temperatures.So, different gases will liquify at different temperature and pressure.As we've already seem with carbon dioxide in the liquidnitrogen that we used in an earlier program.We can also use the kinetic theory to understand now, for the firsttime, what's the difference between heat and temperatureand how they're both related to energy.Suppose we define it this way and simply note that heat is thetotal energy contained by a collection of molecules.

 

Molecules are moving around, right, so they have kinetic energy.So if you look at the kinetic energy of all the molecules,each molecule, I should say, look at its kinetic energy at anygiven time, add up the total for all the molecules,you will have what we call, heat.Heat is energy which can be transferred, remember.And we saw from the swinging balls example that energy canbe transferred by these molecular collisions.This gets a little bit complicated, and we'renot going to go into great detail with this.But, we can think of it this way.That in a collection of gases, the motion is relatively random,meaning that there's a distribution of energies.It's sort of like if you were to take the sample of how muchmoney is in the pocket of the people in the room where youare now, you'd find that people have different amounts of money.So we can look at the average kinetic energy of the collectionof molecules, and how's that different from the total?Well, suppose it was money again.The average is a measure of the kinetic energy perperson, I should say the money per person.In the case of molecules, it's an average of the kinetic energy per molecule.

 

So, now we're ready to define temperature.Temperature is the average kinetic energy per molecule asopposed to heat which is the total amount of energy of all the molecules.Now don't get me wrong.This is not the only energy that these molecules possessbecause remember that they do stick together some.You may remember in Avagadro's explanationof the law combining volumes that Avagadrotalked about molecules coming in diatomic pairs.There are other gas molecules that consist of more than one atom.And we can look specifically at the types of energyinvolved in these molecules.Here, for example, is a diatomic molecule.It's not really, it's two super balls.But if the balls are stuck together this way, then several thingscan happen which can contribute to their kinetic energy.One thing is that the molecules first of all are stuck togetherby some sort of electrical force which amounts to a type of potential energy.So, to move the balls away like this, would be like pulling them,if they were attached by a string.

 

So, if the molecules are vibrating back and forth like this,they are converting kinetic energy into potentialenergy much like the pendulum does.So, the molecules vibrating like this is one form of kineticenergy which is involved in the concept of heat,but not involved in the concept of temperature.In other words, if we're going to try to extract this energy,we have to somehow break the springs that are holding the balls together.The other thing that can happen is that each ballor each molecule can be rotating.Like this....within it's bond.And the molecule as a whole can be rotating like this.

 

OK.So the molecule can be flying around, moving around,vibrating like this, at the same time that it's spinning.The third thing that can happen, of course, is whatwe call translational kinetic energy.Translational kinetic energy is simply the energy of the balls' motion.That's the energy where the ball actually moves from one place to another.So, the type of kinetic energy that we're talking about thatincorporates temperature is the translational kinetic energy.We can also use the kinetic theory to understand now,finally, what specific and latent heat really are.Both of these are actually forms of potential energy.And they both depend on intermolecular forces,which are electrical in nature.Remember the postulate that said that the balls exertforces on each other only during collisions?Well, in fact, they don't.That all molecules exert a small amount of forces on them,but in general, this does not cause liquification.So we can think of it this way.

 

Specific heat is stored in these intermolecular forces, so thatwhen water is absorbing energy, for example, only part of it isgoing into making the water molecules move faster,the rest of it is going into breaking these physical bonds.So we can think of latent heat in the same sort of way.The latent heat is the energy required to break physical bonds between molecules.So, what's the difference between specific heat and latent heat?They both have to do with potential energy of breaking bonds between molecules.One of them is simply the energy that's great enoughto completely destroy the organized structure of the liquid or the gas.The other is simply enough to rip apart some of the moleculesin the clusters during the heating of a liquid.We can also use the kinetic theory to follow Joule's lineof reasoning to find the magnitude or the value of absolute zero.This is a pretty amazing thing to be able to do since no substancecan be actually cooled to absolute zero.The way it works is really very simple.That fractional...when you look at gases, you notice that if youchange the temperature of the gas, that a fractional changeof one degree Celsius, reduces the volume of the gas by a factor of 1/273.One over 273.What a magic number.So, what this means is that if you look at graphs of the differentgases, the different volumes, different numbers of pressures,that all the gases reduce their volume by the same factor.And when you do this for a whole lot of different gases,you find that all of the graphs which representthese changes, converge on a single point.

 

 

 

Now that single point, of course, is called absolute zero.Which is the basis of the Kelvin temperature scale.And we learned before that zero Kelvin is about minus273 Celsius, or about minus 54 Fahrenheit.So, we can do this in the laboratory actually, and we cansimply plot a graph of the changes of temperature and pressureor temperatures of volume and pressure, any of the threevariables in the gas law in the range where a gas likeair behaves as an ideal gas.And for air, that's anywhere around, between zero and 100degrees certainly, because air doesn't freeze until, I shouldsay solidify, until it gets down to minus 190,and anyway, air behaves as an ideal gas,So we can take those temperatures and pressures,draw a graph, and extrapolate that graph.In other words, send the line down the graph until we findthe place where this line intersects with the vertical axis on our graph.

 

This is the point in this particular graph where the ideal gas wouldhave zero volume, if it remained an ideal gasover that range of temperature and pressure.Of course, gases do not do this, because all gases really changetheir volume and temperature by about this 1/273, which is alittle over a third of a percent for each Celsius degree changein temperature, and all real gases will eventually do what?They'll condense into liquids or freeze into solids.So, what we're saying here with this is that the idealtheoretical minimum that any substance could reach wouldbe the temperature where its gaseous state would disappearif it did not condense or otherwise change state.

 

We can also see from the Kelvin temperature scale that why wehave to use this scale in the gas laws.Because, for example, 200 degrees Celsius is not twice as hot as100 degrees Celsius, because zero is not the lowest temperature.So, if we look at the temperature scales, we see that 200 degreesKelvin is twice as hot as 100 degrees Kelvinbecause zero is the lowest temperature.So, the ideal gas, remember, is theoretical only.And it's a gas which obeys the gas laws under allconditions of temperature and pressure.And we can sort of make a general statement here that any gasclosely approximates the ideal gas under certain conditions,specifically at temperatures which are high compared to itsboiling point and pressures which are low relative to the boiling point.In the 1840's a biologist named Robert Brown was observingpollen grains suspended in water under a microscope and henoticed that the pollen grains were dancing around.He had no explanation for this but it came to be called Brownian motion.Brown went and studied a little bit more and he saw that it alsoapplied, for example, to smoke particles in air.

 

 

The reason I mention this at all is because it was Einstein in 1905who came back and explained Brownian motion in terms of kinetic theory.He did this simply by recognizing that although the molecularmotions are more or less random, that on a very small scale,randomness turns into not completely randomness.In other words, there are patterns and these patterns are causedby the molecules moving slightly in one direction or the other,bumping into the particles and moving them around.The smaller the particle and the higher the temperature, the faster the motion.Einstein did not win a Nobel prize for this, but his explanationwas so elegant and so mathematically sound, and tiedin so well with molecular theory and kinetic theory, that heconvinced almost all the remaining skepticsof the validity of the atomic theory at this point.

 

Well, that's it for this program.Though we've tried to show in this program about kinetic theory,how the theory of the motion of atoms fits in with both physicsand chemistry, and actually forms the link between the two.I would encourage you to take some time with the Study Guideto look up some of these other things that could be explainedby the kinetic theory because all of these things actually tiein with various things in life like the heating and coolingby evaporation, various things like that.So, you might also want to spend some more time at Brownian motion.That would make a very good topic for a paper for the final paper for the class.Well, I believe that's it for this program.So, remember, when it comes to science, get physical.Bye.You've been very quiet again, are you ruminating, or are you just having a bad day?You know, I've been noticing that you....Music