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  • PROFESSOR: Thermodynamics, all right, let's start.

  • Thermodynamics is the science of the flow of heat.

  • So, thermo is heat, and dynamics is

  • the motion of heat.

  • Thermodynamics was developed largely beginning in the

  • 1800's, at the time of the Industrial Revolution.

  • So, taming of steel.

  • The beginning of generating power by burning fossil fuels.

  • The beginning of the problems with CO2 and [NOISE OBSCURES]

  • global warming.

  • In fact, it's interesting to note that the first

  • calculation on the impact of CO2 on climate was done in the

  • late 1800's by Arrhenius.

  • Beginning of a generation of power moving heat from fossil

  • fuels to generating energy, locomotives, etcetera.

  • So, he calculated what would happen to this burning of

  • fossil fuels, and he decided in his calculation, he

  • basically got the calculation right, by the way, but he came

  • out that in 2,000 years from the time that he did the

  • calculations, humans would be in trouble.

  • Well, since his calculation, we've had an exponential

  • growth in the amount of CO2, and if you go through the

  • calculations of -- people have done these calculations

  • throughout times since Arrhenius, the time that we're

  • in trouble, 2,000 years and the calculation, has gone like

  • this, and so now we're really in trouble.

  • That's for a different lecture.

  • So, anyway, thermodynamics dates from the same period as

  • getting fossil fuels out of the ground.

  • It's universal.

  • It turns out everything around us moves energy around in one

  • way or the other.

  • If you're a biological system, you're burning calories,

  • burning ATP.

  • You're creating heat.

  • If you're a warm-blooded animal.

  • You need energy to move your arms around and move around --

  • mechanical systems, obviously, cars, boats, etcetera.

  • And even in astrophysics, when you talk about stars, black

  • holes, etcetera, you're moving energy around.

  • You're moving heat around when you're changing matter through

  • thermodynamics.

  • And the cause of some thermodynamics have even been

  • applied to economics, systems out of equilibrium, like big

  • companies like Enron, you know, completely out of

  • equilibrium, crash and burn.

  • You can apply non-equilibrium thermodynamics to economics.

  • It was developed before people knew

  • about atoms and molecules.

  • So it's a science that's based on macroscopic

  • properties of matter.

  • Since then, since we know about atoms and molecules now,

  • we can rationalize the concepts of thermodynmamics

  • using microscopic properties, and if you are going to take

  • 5.62, that's what you'd learn about.

  • You'd learn about statistical mechanics, and how the

  • atomistic concepts rationalize thermodynamics.

  • It doesn't prove it, but it helps to getting more

  • intuition about the consequences of

  • thermodynamics.

  • So it applies to macroscopic systems that are in

  • equilibrium, and how to go from one equilibrium state to

  • another equilibrium state, and it's entirely empirical in its

  • foundation.

  • People have done experiments through the ages, and they've

  • accumulated the knowledge from these experiments, and they've

  • synthesized these experiments into a few basic empirical

  • rules, empirical laws, which are the laws of

  • thermodynamics.

  • And then they've taken these laws and added a structure of

  • math upon it, to build this edifice, which is a very solid

  • edifice of thermodynamics as a science

  • of equilibrium systems.

  • So these empirical observations then are

  • summarized into four laws.

  • So, these laws are, they're really depillars.

  • They're not proven, but they're not wrong.

  • They're very unlikely to be wrong.

  • Let's just go through these laws, OK, very quickly.

  • There's a zeroth law The zeroth law every one of these

  • laws basically defines the quantity in thermodynamics and

  • then defines the concept.

  • The zeroth law defines temperature.

  • That's a fairly common-sense idea, but it's important to

  • define it, and I call that the common-sense law.

  • So this is the common-sense law.

  • The first law ends up defining energy, which we're going to

  • call u, and the concept of energy conservation, energy

  • can't be lost or gained.

  • And I'm going to call this the you can break even law; you

  • can break even law.

  • You don't lose energy, you can't gain energy.

  • You break even.

  • The second law is going to define entropy, and is going

  • to tell us about the direction of time, something that

  • conceptually we, clearly, understand, but is going to

  • put a mathematical foundation on which way does time go.

  • Clearly, if I take a chalk like this one here, and I

  • throw it on the ground, and it breaks in little pieces, if I

  • run the movie backwards, that doesn't make sense, right?

  • We have a concept of time going forward in

  • a particular way.

  • How does entropy play into that concept of time?

  • And I'm going to call this the you can break even at zero

  • degrees Kelvin law.

  • You can only do it at zero degrees Kelvin.

  • The third law is going to give a numerical value to the

  • entropy, and the third law is going to be the depressing

  • one, and it's going to say, you can't get to zero degrees.

  • These laws are universally valid.

  • They cannot be circumvented.

  • Certainly people have tried to do that, and every year

  • there's a newspaper story, Wall Street Journal, or New

  • York Times about somebody that has invented the device that

  • somehow goes around the second law and makes more energy than

  • it creates, and this is going to be -- well, first of all,

  • for the investors this is going to make them very, very

  • rich, and for the rest of us, it's going to be wonderful.

  • And they go through these arguments, and they find

  • venture money to fund the company, and they get very

  • famous people to endorse them, etcetera.

  • But you guys know, because you have MIT degrees, and you've,

  • later, and you've taken 5.60, that can't be the case, and

  • you're not going to get fooled into investing money into

  • these companies.

  • But it's amazing, that every year you find somebody coming

  • up with a way of going around the second law and somehow

  • convincing people who are very smart that this will work.

  • So, thermo is also a big tease, as you can see from my

  • descriptions of these laws here.

  • It makes you believe, initially, in the feasibility

  • of perfect efficiency.

  • The first law is very upbeat.

  • It talks about the conservation of energy.

  • Energy is conserved in all of its forms.

  • You can take heat energy and convert it to work energy and

  • vice versa, and it doesn't say anything about that you have

  • to waste heat if you're going to transform heat into work.

  • It just says it's energy.

  • It's all the same thing, right?

  • So, you could break even if you were very clever about it,

  • and that's pretty neat.

  • So, in a sense, it says, you know, if you wanted to build a

  • boat that took energy out of the warmth of the air, to sail

  • around the world, you can do that.

  • And then the second law comes in and says well, that's not

  • quite right.

  • The second law says, yes, energy is pretty much the same

  • in all this form, but if you want to convert one form of

  • energy into another, if you want to convert work, heat

  • into work, with 100% efficiency, you've got to go

  • down to zero degrees Kelvin, to absolute zero if you want

  • to do that.

  • Otherwise you're going to waste some of that heat

  • somewhere along the way, some of that energy.

  • All right, so you can't get perfect efficiency, but at

  • least if you were able to go to zero degrees Kelvin, then

  • you'd be all set.

  • You just got to find a good refrigerator on your boat, and

  • then you can still go around the world.

  • And then the third law comes in, and that's the

  • depressing part here.

  • It says, well, it's true.

  • If you could get to zero degrees Kelvin, you'd get

  • perfect efficiency, but you can't get to zero degrees

  • Kelvin, you can't.

  • Even if you have an infinite amount of resources,

  • you can't get there.

  • Any questions so far?

  • So thermodynamics, based on these four laws now, requires

  • an edifice, and it's a very mature science, and it

  • requires that we define things carefully.

  • So we're going to spend a little bit of time making sure

  • we define our concepts and our words, and what you'll find

  • that when you do problem sets, especially at the beginning,

  • understanding the words and the conditions of the problem

  • sets is most of the way into solving the problem.

  • So we're going to talk about things like systems.

  • The system, it's that part of the

  • universe that we're studying.

  • These are going to be fairly common-sense definitions, but

  • they're important, and when you get to a problem set,

  • really nailing down what the system is, not more, nor less,

  • in terms of the amount of stuff, that's part of the

  • system, it's going to be often very crucial.

  • So you've got the system.

  • For instance, it could be a person.

  • I am the system.

  • I could be a system.

  • It could be a hot coffee in a thermos.

  • So the coffee and the milk and whatever else you like in your

  • coffee would be the system.

  • It could be a glass of water with ice in it.

  • That's a fine system.

  • Volume of air in a part of a room.

  • Take four liters on this corner of the room.

  • That's my system.

  • Then, after you define what your system is, whatever is

  • left over of the universe is the surroundings.

  • So, if I'm the system, then everything else is the

  • surroundings.

  • You are my surroundings.

  • Saturn is my surroundings.

  • As far as you can go in the universe, that's part of the

  • surroundings.

  • And then between the system and the

  • surroundings is the boundary.

  • And the boundary is a surface that's real, like the outsides

  • of my skin, or the inner wall of the thermos that has the

  • coffee in it, or it could be an imaginary boundary.

  • For instance, I can imagine that there is a boundary that

  • surrounds the four liters of air that's sitting in the

  • corner there.

  • It doesn't have to be a real container to contain it.

  • It's just an imaginary boundary there.

  • And where you place that boundary becomes important.

  • So, for instance, for the thermos with the coffee in it,

  • if you place the boundary in the inside wall of the glass

  • or the outside wall of the glass and the inside of the

  • thermos, that makes a difference; different heat

  • capacity, etcetera.

  • So this becomes where defining the system and the boundaries,

  • and everything becomes important.

  • You've got to place the boundary at exactly the right

  • place, otherwise you've got a bit too much in your system or

  • a bit too little.

  • More definitions.

  • The system can be an open system, or it can be a closed

  • system, or it can be isolated.

  • The definitions are also important here.

  • An open system, as the name describes, allows mass and

  • energy to freely flow through the boundary.

  • Mass and energy flow through boundary.

  • Mass and energy --

  • I'm an open system, right?

  • Water vapor goes through my skin.

  • I'm hot, compared to the air of the room, or cold if I'm

  • somewhere that's warm.

  • So energy can go back and forth.

  • The thermos, with the lid on top, is not an open system.

  • Hopefully, your coffee is going to stay warm or hot in

  • the thermos.

  • It's not going to get out.

  • So the thermos is not an open system.

  • In fact, the thermos is an isolated system.

  • The isolated system is the opposite of the open system,

  • no mass and no energy can flow through the boundary.

  • The closed system allows energy to transfer through the

  • boundary but not mass.

  • So a closed system would be, for instance, a glass of ice

  • water with an ice cube in it, with the lid on top.

  • The glass is not very insulating.

  • Energy can flow across the glass, but I put a lid on top,

  • and so the water can't get out.

  • And that's the closed system.

  • Energy goes through the boundaries but nothing else.

  • Important definitions, even though they may sound really

  • kind of dumb, but they are really important, because when

  • you get the problem, figuring out whether you have an open,

  • closed, or isolated system, what are the surroundings?

  • What's the boundary?

  • What is the system?

  • That's the first thing to make sure that is clear.

  • If it's not clear, the problem is going to be

  • impossible to solve.

  • And that's also how people find ways to break the second

  • law, because somehow they've messed up on what

  • their system is.

  • And they've included too much or too little in the system,

  • and it looks to them that the second law is broken and

  • they've created more energy than is being brought in.

  • That's usually the case.

  • Questions?

  • Let's keep going.

  • So, now that we've got a system, we've

  • got to describe it.

  • So, let's describe the system now.

  • It turns out that when you're talking about macroscopic

  • properties of matter, you don't need very many variables

  • to describe the system completely thermodynamically.

  • You just need a few macroscopic variables that are

  • very familiar to you, like the pressure, the temperature, the

  • volume, the number of moles of each component, the mass of

  • the system.

  • You've got a magnetic field, maybe even magnetic

  • susceptibility, the electric field.

  • We're not going to worry about these magnetic fields or

  • electric fields in this class.

  • So, pretty much we're going to focus on this set

  • of variables here.

  • You're going to have to know when you describe the system,

  • if your system is homogeneous, like your coffee with milk in

  • it, or heterogeneous, like water with an ice cube in it.

  • So heterogeneous means that you've got different phases in

  • your system.

  • I'm the heterogeneous system, soft stuff, hard

  • stuff, liquid stuff.

  • Coffee is homogeneous, even though it's made up of many

  • components.

  • Many different kinds of molecules make up your coffee.

  • There are the water molecules, the flavor molecules, the milk

  • proteins, etcetera.

  • But it's all mixed up together in a

  • homogeneous, macroscopic fashion.

  • If you drill down at the level of molecules you see that it's

  • not homogeneous.

  • But thermodynamics takes a bird's eye view.

  • It looks pretty, beautiful.

  • So, that's a homogeneous system, one phase.

  • You have to know if your system is an equilibrium

  • system or not.

  • If it's an equilibrium system, then thermodynamics can

  • describe it.

  • If it's not, then you're going to have trouble describing it

  • using thermodynamic properties.

  • Thermodynamics talks about equilibrium systems and how to

  • go from one state of equilibrium to another state

  • of equilibrium.

  • What does equilibrium mean?

  • It means that the properties of the system, the properties

  • that describe the system, don't change

  • in time or in space.

  • If I've got a gas in a container, the pressure of the

  • gas has to be the same everywhere in the container,

  • otherwise it's not equilibrium.

  • If I place my container of gas on the table here, and I come

  • back an hour later, the pressure needs to be the same

  • when I come back.

  • Otherwise it's not equilibrium.

  • So it only talks about equilibrium systems.

  • What else do you need to know?

  • So, you need to know the variables.

  • You need to know it's heterogeneous or homogeneous.

  • You need to know if it's an equilibrium, and you also need

  • to know how many components you have in your system.

  • So, a glass of ice water with an ice cube in it, which is a

  • heterogeneous system, has only one component,

  • which is water, H2O.

  • Two phases, but one component.

  • Latte, which is a homogeneous system, has a very, very large

  • number of components to it.

  • All the components that make up the milk.

  • All the components that make up the coffee, and all the

  • impurities, etcetera. cadmium, heavy metals, arsenic,

  • whatever is in your coffee.

  • OK, any questions?

  • All right, so we've described the system with these

  • properties.

  • Now these properties come in two flavors.

  • You have extensive properties and intensive properties.

  • The extensive properties are the ones that scale with the

  • size of the system.

  • If you double the system, they double in

  • there numerical number.

  • For instance, the volume.

  • If you double the volume, the v doubles.

  • I mean that's obvious.

  • The mass, if you double the amount of stuff

  • the mass will double.

  • Intensive properties don't care about the

  • scale of your system.

  • If you double everything in the system, the temperature is

  • not going to change, it's not going to double.

  • The temperature stays the same.

  • So the temperature is intensive, and you can make

  • intensive properties out of the extensive properties by

  • dividing by the number of moles in the system.

  • So I can make a quantity that I'll call V bar, which is the

  • molar volume, the volume of one mole of a component in my

  • system, and that becomes an intensive quantity.

  • A volume which is an intensive volume.

  • The volumes per mole of that stuff.

  • So, as I mentioned, thermodynamics is the science

  • of equilibrium systems, and it also describes the evolution

  • of one equilibrium to another equilibrium.

  • How do you go from one to the other?

  • And so the set of properties that describes the system --

  • the equilibrium doesn't change.

  • So, these on-changing properties that describe the

  • state of the equilibrium state of the system are

  • called state variables.

  • So the state variables describe the equilibrium's

  • state, and they don't care about how this state got to

  • where it is.

  • They don't care about the history of the state.

  • They just know that's if you have water at zero degrees

  • Celsius with it ice in, that you can define it as a

  • heterogeneous system with a certain density for the water

  • or certain density for the ice, etcetera, etcetera.

  • It doesn't care how you got there.

  • We're going to find other properties that do care about

  • the history of the system, like work, that you put in the

  • system, or heat that you put in the system,

  • or some other variables.

  • But you can't use those to define the equilibrium state.

  • You can only use the state variables,

  • independent of history.

  • And it turns out that for a one component system, one

  • component meaning one kind of molecule in the system, all

  • that you need to know to describe the system is the

  • number of moles for a one component system, and to

  • describe one phase in that system, one component,

  • homogeneous system, you need n and two variables.

  • For instance, the pressure and the temperature, or the volume

  • and the pressure.

  • If you have the number of moles and two intensive

  • variables, then you know everything there is to know

  • about the system.

  • About the equilibrium state of that system.

  • There are hundreds of quantities that you can

  • calculate and measure that are interesting and important

  • properties, and all you need is just a few variables to get

  • everything out, and that's really the power of

  • thermodynamics, is that it takes so little information to

  • get so much information out.

  • So little data to get a lot of predictive information out.

  • As we're going on with our definitions, we can summarize

  • a lot of these definitions into a notation, a chemical

  • notation that that will be very important.

  • So, for instance, if I'm talking about three moles of

  • hydrogen, at one bar 100 degrees Celsius.

  • I'm not going to write, given three moles of hydrogen at one

  • bar and three degrees, blah, blah, blah.

  • I'm going to write it in a compact notation.

  • I'm going to write it like this: three moles of hydrogen

  • which is a gas, one bar 100 degrees Celsius.

  • This notation gives you everything you need to know

  • about the system.

  • It tells you the number of moles.

  • It tells you the phase.

  • It tells you what kind of molecule it is, and gives you

  • two variables that are state variables.

  • You could have the volume and the temperature.

  • You could have the volume and the pressure.

  • But this tells you everything.

  • I don't need to write it down in words.

  • And then if I want to tell you about a change of state, or

  • let's first start with a mixture.

  • Suppose that I give to a mixture like, this is a

  • homogeneous system with two components, like five moles of

  • H2O, which is a liquid, at one bar 25 degrees Celsius, plus

  • five moles of CH3, CH2, OH, which is a liquid, and one bar

  • at 25 degrees Celsius.

  • This describes roughly something that is fairly

  • commonplace, it's 100-proof vodka 1/2 water, 1/2 ethanol

  • -- that describes that macroscopic system.

  • You're missing all the impurities, all the little the

  • flavor molecules that go into it, but basically, that's the

  • homogeneous system we were describing, two component

  • homogeneous systems.

  • Then you can do all sorts of predictive

  • stuff with that system.

  • All right, that's the equilibrium system.

  • Now we want to show a notation, how do we go from

  • one equilibrium state like this describes to another

  • equilibrium state?

  • So, we take our two equilibrium states, and you

  • just put an equal sign between them, and the equal sign means

  • go from one to the other.

  • So, if we took our three moles of hydrogen, which is a gas at

  • five bar and 100 degrees Celsius, and, which is a nice

  • equilibrium state here, and we say now we're going to change

  • the equilibrium state to something new, we're going to

  • do an expansion, let's say.

  • We're going to drop the pressure, the volume

  • is going to go up.

  • I don't need to tell you the volume here, because you've

  • got enough information to calculate the volume.

  • The number of moles stays the same, a closed systems, gas

  • doesn't come out.

  • Stays a gas, but now the pressure is less, the

  • temperature is less.

  • I've done some sort of expansion on this.

  • I've gone from 1 equilibrium state to another equilibrium

  • state, and the equal sign means you go from this state

  • to that state.

  • It's not a chemical reaction.

  • That's why we don't have an arrow here, because we could

  • go back, this way too.

  • We can go back and forth between these

  • two equilibrium states.

  • They're connected.

  • This means they're connected.

  • And when I put this, I have to tell you

  • how they are connected.

  • I have to tell you the path, if you're

  • going to solve a problem.

  • For instance, you want to know how much energy you're going

  • to get out from doing this expansion.

  • How much energy are you going to get out, and how far are

  • you going to be able to drive a car with this expansion,

  • let's say, so that's the problem.

  • So, I need to tell you how you're doing the expansion,

  • because that's going to tell you how much energy you're

  • wasting during that expansion.

  • It goes back to the second law.

  • Nothing is efficient.

  • You're always wasting energy into heat somewhere when you

  • do a change that involves a mechanical change.

  • All right, so I need to tell you the path, when I go from

  • one state to the other.

  • And the path is going to be the sequence, intermediate

  • states going from the initial state the final state.

  • So, for instance, if I draw a graph of pressure on one axis

  • and temperature on the other axis, my initial state is at a

  • temperature of 100 degrees Celsius and five bar.

  • My final stage is 50 degrees Celsius and one bar.

  • So, I could have two steps in my path.

  • I could decide first of all to keep the pressure constant and

  • lower the pressure.

  • When I get to 50 degrees Celsius, I could choose to

  • keep the temperature constant and lower the pressure.

  • I'm sorry, my first step would be to keep the pressure

  • constant and lower the temperature, then I lower the

  • pressure, keeping the temperature constant.

  • So there's my intermediate state there.

  • This is one of many paths.

  • There's an infinite number of paths you could take.

  • You could take a continuous path, where you have an

  • infinite number of equilibrium points in between the two, a

  • smooth path, where you drop the pressure and the

  • temperature simultaneously in little increments.

  • All right, so when you do a problem, the path is going to

  • turn out to be extremely important.

  • How do you get from the initial state

  • to the final state?

  • Define the initial state.

  • Define the final state.

  • Define the path.

  • Get all of these really clear, and you've basically solved

  • the problem.

  • You've got to spend the time to make sure that everything

  • is well defined before you start trying to

  • work out these problem.

  • More about the path.

  • There are a couple ways you could go through that path.

  • If I look at this smooth path here.

  • I could have that path be very slow and steady, so that at

  • every point along the way, my gas is an equilibrium.

  • So I've got, this piston here is compressed, and I slowly,

  • slowly increase the volume, drop the temperature.

  • Then I can go back, the gas is included at every

  • point of the way.

  • That's a reversible path.

  • That can reverse the process.

  • I expand it, and reverse it, no problem.

  • So, I could have a reversible path, or I take my gas, and

  • instead of slowly, slowly raising it, dropping the

  • pressure, I go from five bar to one bar extremely fast.

  • What happens to my gas inside?

  • Well, my gas inside is going to be very unhappy.

  • It's not going stay in equilibrium.

  • Parts of the system are going to be at five bar.

  • Parts of it at one bar.

  • Parts of it may be even at zero bar, if I go really fast.

  • I'm going to create a vacuum.

  • So the system will not be described by a single state

  • variable during the path.

  • If I look at different points in my container during that

  • path, I'm going to have to use a different value of pressure

  • or different value of temperature at different

  • points of the container.

  • That's not an equilibrium state, and that process turns

  • out then to be in irreversible process.

  • Do it very quickly.

  • Now to reverse it and get back to the initial point is going

  • to require some input from outside, like heat or extra

  • work or extra heat or something, because you've done

  • an irreversible process.

  • You've wasted a lot of energy in doing that process.

  • I have to tell you whether the path is reversible or

  • irreversible, and the irreversible path also defines

  • the direction of time.

  • You can only have an irreversible path go one way

  • in time, not the other way.

  • Chalk breaks irreversibly and you can't put it

  • back together so easily.

  • You've got to pretty much take that chalk, and make a slurry

  • out of it, put water, and dry it back up, put in a mold, and

  • then you can have the chalk again, but you can't just glue

  • it back together.

  • That would not be the same state as what

  • you started out with.

  • And then there are a bunch of words that

  • describe these paths.

  • Words like adiabatic, which we'll be very familiar with.

  • Adiabatic means that there's no heat transferred between

  • the system and the surrounding.

  • The boundary is impervious to transfer of

  • heat, like a thermos.

  • Anything that happens inside of the thermos is an adiabatic

  • change because the thermos has no connection in terms of

  • energy to the outside world.

  • There's no heat that can go through the

  • walls of the thermos.

  • Whereas, like isobaric means constant pressure.

  • So, this path right here from this top red path is an

  • isobaric process.

  • Constant temperature means isothermal, so this part means

  • an isothermal process.

  • So then, going from the initial to final states with a

  • red path, you start with an isobaric process and then you

  • end with an isothermal process.

  • And these are words that are very meaningful when you read

  • the text of a problem or of a process.

  • Any questions before we got to the zeroth law?

  • We're pretty much done with our definitions here.

  • Yes.

  • STUDENT: Was adiabatic reversible?

  • PROFESSOR: Adiabatic can be either reversible or not, and

  • we're going to do that probably

  • next time or two times.

  • Any other questions?

  • Yes.

  • STUDENT: Is there a boundary between reversible and

  • irreversible?

  • PROFESSOR: A boundary between reversible and irreversible?

  • Like something is almost reversible and almost

  • irreversible.

  • No, pretty much things are either reversible or

  • irreversible.

  • Now, in practice, it depends on how good

  • your measurement is.

  • And probably also in practice, nothing is truly reversible.

  • So, it depends on your error bar in a sense.

  • It depends on what what you define, exactly what you

  • define in your system.

  • It becomes a gray area, but it should be pretty clear if you

  • can treat something is reversible are irreversible.

  • Other questions, It's a good question.

  • So the zeroth law we're going to go through the laws now.

  • The zeroth law talks about defining temperature and it's

  • the common-sense law.

  • You all know how.

  • When something hot, it's got a higher temperature than when

  • something is cold.

  • But it's important to define that, and define something

  • that's a thermometer.

  • So what do you know?

  • What's the empirical information

  • that everybody knows?

  • Everybody knows that if you take something which is hot

  • and something which is cold, and you bring them together,

  • make them touch, that heat is going to flow from the hot to

  • the cold, and make them touch, and heat

  • flows from hot to cold.

  • That's common sense.

  • This is part of your DNA, And then their final product is an

  • object, a b which ends up at a temperature or a warmness

  • which is in between the hot and the cold.

  • So, this turns out to be warm.

  • You get your new equilibrium state, which is in between

  • what this was, and what a and b were.

  • Then how do you know that it's changed temperature, or that

  • heat has flowed from a to b?

  • Practically speaking, you need some sort of property that's

  • changing as heat is flowing.

  • For instance, if a were metallic, you could measure

  • the connectivity of a or resistivity, and as heat flows

  • out of a into b, the resistivity of a would change.

  • Or you could have something that's color metric that

  • changes color when it's colder, so you could see the

  • heat flowing as a changes color or b changes color as

  • heat flows into b.

  • So, you need some sort of property, something you can

  • see, something you can measure, that tells you that

  • heat has flowed.

  • Now, if you have three objects, if you have a, b, and

  • c, and you bring them together, and a is the

  • hottest, b is the medium one, and c is the coldest, so from

  • hottest to coldest a, b, c, -- if you bring them together and

  • make them touch, you know, intuitively, that heat will

  • not flow like this.

  • You know that's not going to happen.

  • You know that what will happen is that heat will flow from a

  • to b from b to c and from a to c.

  • That's common-sense.

  • You know that.

  • And the other way in the circle will never happen.

  • That would that would give rise to a perpetual motion

  • machine, breaking of the second law.

  • It can't happen.

  • But that's an empirical observation, that heat flows

  • in this direction.

  • And that's the zeroth law thermodynamic.

  • It's pretty simple.

  • The zeroth law says that if a and b -- it doesn't exactly

  • say that, but it implies this.

  • It says that if a and b are in thermal equilibrium, if these

  • two are in thermal equilibrium, meaning that

  • there's no heat flows between them, so that's the definition

  • of thermal equilibrium, that no heat flows between them,

  • and these two are in thermal equilibrium, and these two are

  • in thermal equilibrium, then a and c will be also be in

  • thermal equilibrium.

  • But if there's no heat flowing between these two, and no heat

  • flowing between these two, then you can't have heat

  • flowing between these two.

  • So if I get rid of these arrows, there's no heat

  • flowing because they're in thermal equilibrium, then I

  • can't have an arrow here.

  • That's what the zeroth law says.

  • They're all the same temperature.

  • That's what it says.

  • If two object are in the same temperature, and two other

  • object are in the same temperature, then all three

  • must have the same temperature.

  • It sounds pretty silly, but it's really important because

  • it allows you to define a thermometer and temperature.

  • Because now you can say, all right, well, now b can be my

  • thermometer.

  • I have two objects, I have an object which is in Madagascar

  • and an object which is in Boston, and I want to know,

  • are they the same temperature?

  • So I come out with a third object, b, I go to Madagascar,

  • and put b in contact with a.

  • Then I insulate everything, you know, take it away and see

  • if there's any heat flow.

  • Let's say there's no heat flow.

  • Then I insulate it, get back on the plane to Boston, and go

  • back and touch b with c.

  • If there's no heat flow between the b and c, then I

  • can say all right, a and c were the same temperature.

  • B is my thermometer that tells me that a and c are in the

  • same temperature.

  • And there's a certain property associated with heat flow with

  • b, and it didn't change.

  • And that property could be color.

  • It could be resistivity.

  • It could be a lot of different things.

  • It could be volume.

  • And the temperature then is associated with that property.

  • And if it had changed, then the temperature between those

  • two would have changed in a very particular way.

  • So, zeroth law, then, allows you to define the concept of

  • temperature and the measurement of temperature

  • through a thermometer.

  • Let's very briefly go through stuff that

  • you've learned before.

  • So, now you have this object which is going to tell you

  • whether other things are in thermal equilibrium now.

  • What do you need for that object?

  • You need that object to be a substance, to be something.

  • So, the active part of the thermometer could be water.

  • It could be alcohol, mercury, it could be a piece of metal.

  • You need a substance, and then that substance has to have a

  • property that changes depending on the heat flow,

  • i.e., depending on whether it's sensing that it's the

  • same temperature or different temperature

  • than something else.

  • And that property could be the volume, like if you have a

  • mercury thermometer, the volume of the mercury.

  • It could be temperature.

  • It could be resistivity, if you have a thermocouple.

  • It could be the pressure.

  • All right, so now you have an object.

  • You've got a property that changes,

  • depending on the heat flow.

  • It's going to tell you about the temperature.

  • Now you need to define the temperature scales.

  • So, you need some reference points to be able to tell you,

  • OK, this temperature is 550 degrees Smith, whatever.

  • So, you assign values to very specific states of matter and

  • call those the reference points for your temperature.

  • For instance, freezing of water or boiling of water, the

  • standard ones.

  • And then an interpolation scheme.

  • You need a functional form that connects the value at one

  • state of matter, the freezing point of water, to another

  • phase change, the boiling point of water.

  • You can choose a linear interpolation or quadratic,

  • but you've got to choose it.

  • And it turns out not to be so easy.

  • And if you go back into the 1800's when thermodynamics was

  • starting, there were a zillion different temperatures scales.

  • Everybody had their own favorite temperature scales.

  • The one that we're most familiar with is the

  • centigrade or Celsius scale where mercury was the

  • substance, and the volume of mercury is the property.

  • The reference points are water, freezing or boiling,

  • and the interpolation is linear, and then that morphed

  • into the Kelvin scale, as we're going to see later.

  • The Fahrenheit scale is an interesting scale.

  • It turns out the U.S. and Jamaica are the only two

  • places on Earth now that use the Fahrenheit scale.

  • Mr. Fahrenheit, Daniel Gabriel Fahrenheit was a German

  • instrument maker.

  • The way he came up with his scale was actually he borrowed

  • the Romer scale, which came beforehand.

  • The Romer scale was, Romer was a Dane, and he defined

  • freezing of water at 7.5 degrees Roemer, and 22.5

  • degrees Romer as blood-warm.

  • That was his definition.

  • Two substances, blood and water.

  • Two reference points, freezing and blood-warm, you know, the

  • human body.

  • A linear interpolation between the two, and then some numbers

  • associated with them, 7-1/2 and 22-1/2.

  • Why does he choose 7-1/2 as the freezing point of water?

  • Because he thought that would be big enough that in Denmark,

  • the temperature wouldn't go below zero.

  • That's how he picked 7-1/2.

  • Why not?

  • He didn't want to use negative numbers to measure temperature

  • in Denmark outside.

  • Well, Fahrenheit came along and thought, well, you know,

  • 7-1/2, that's kind of silly; 22-1/2 that's, kind of silly.

  • So let's multiply everything by four.

  • I think it becomes 30 degrees for the freezing of water and

  • 22.5 x 4, which I don't know what it is, 100 or something

  • -- no, it's 90 I think.

  • And then for some reason, that nobody understands, he decided

  • to multiply again by 16/15, and that's how we get 32 for

  • freezing of water and 96 in his words for the temperature

  • in the mouth or underneath the armpit of a

  • living man in good health.

  • What a great temperature scale.

  • It turns out that 96 wasn't quite right.

  • Then he interpolated and found out water boils at 212.

  • But, you know, his experiment wasn't so great, and, you

  • know, maybe had a fever when he did the reference point

  • with 96, whatever.

  • It turns out that it's not 96 to be in good health, it's

  • 98.6 -- whatever.

  • That's how we got to the Fahrenheit scale.

  • All right, next time we're going to talk about a much

  • better scale, which is the ideal gas thermometer and how

  • we get to the Kelvin scale.

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