The following content is
provided under a Creative Commons license. Your support will help MIT
OpenCourseWare continue to offer high-quality educational
resources for free. To make a donation or view
additional materials from hundreds of MIT courses, visit
MIT OpenCourseWare at ocw.mit.edu. 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.
He mentions the mathmatigal equation about 15 minutes in, of which I found a Pdf of a paper regarding the laws of thermo dynamics.
The mathematical structure of thermodynamics Peter Salamon1 , Bjarne Andresen2 , James Nulton1 , Andrzej K. Konopka3,1 1 – San Diego State University Department of Mathematics & Statistics San Diego, CA USA 92182-7720 2 – Niels Bohr Institute Universitetsparken 5 DK-2100 Copenhagen Ø Denmark 3 – BioLinguaSM Reasearch, Inc. CASSA Center 10331 Battleridge Place Gaithersburg, MD USA
Which mentions the second law, thermodynamic energy only exists one direction. UNLESS it can be reversed. Which would involve time. I might expand upon this later
On second lecture. Haven't gotten farther in paper but weekend junk and lateness han no consequences. Will communicate further on thoughts regarding triple point of water as a limit. Will extrapolate tomorrow