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PROFESSOR NELSON: So last time
we just about finished up the

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discussion of thermochemisty,
and we went through a

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description of calorimetry, how
we actually make measurements

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of thermodynamic a quantities.
 

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I should mention, which I
didn't last time, that you know

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a calorimeter, apart from
measuring heats of formation

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also is used to measure
standard thermodynamic

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quantities like
heat capacities.

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You know how much heat does it
take to raise the temperature

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of something by a degree?
 

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Well, you put the material
inside the calorimeter, and you

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have a heater and it's
connected up to current source,

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and you can accurately measure
how much heat you're putting

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in, because you can measure how
much current is going into it,

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and you separately are
measuring the temperature of

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the material, so it's a
straightforward way of

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measuring the heat capacities,
thermodynamic data

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of this sort.
 

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So work on phase
transitions, just ordinary

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properties of material.
 

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Chemical reactions, all the
thermochemistry involved is

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done using constant pressure or
constant volume calorimetry

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in a pretty routine way.
 

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So we talked about how to use
the results of measurements

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like that to calculate reaction
energetics, enthalpies

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of reaction.
 

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And I just want to end the unit
on thermochemistry with a

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real brief discussion of an
approximate way of formulating

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heats of reaction, and that is
in terms of bond energies.

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Now you know you're probably
never going to sit down and do

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a series of thermodynamic
calculations using

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bond energies.
 

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You could always look up heats
of formation of compounds and

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from those determine very
accurately heats of reaction,

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by looking at the heats of
formation of products and the

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heats of formation of the
reactants and subtracting them.

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And since that data is
available for a really wide

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range of materials, that's sort
of the simplest approach and

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the most accurate one to
determine reaction energetics.

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On the other hand, if you just
want to think about molecules,

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you know, you think
about bonds.

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You know if you say I've got
methane or ethane, I'm going

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to use a fuel and burn it
and capture the energy.

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How much energy do
we have in there?

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Well the way you want to be
thinking about that is all

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right, I'm going to take the
starting material, the fuel,

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I'm going to break bonds, and
I'm going to form some final

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product with new bonds.
 

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Roughly what kinds of
energetics are we

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talking about?
 

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In biological systems, it's
also super important.

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You know you think about
ordinary biochemical

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energetics, what's used is fuel
in biology and what are the

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products that are formed?
 

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And again, it's just super
important to be able to think

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sort of semi-quantitatively in
terms of bond energies, because

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you don't want to always
be going and looking up

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everything in tables.
 

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If you need to do an extensive
series of calculations, it's

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very useful to have the tables.
 

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But if you just want to think
about how something is working,

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you know biological or system
or an engine or another

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application, it's very useful
to just be able to think in

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terms of bond energies.
 

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So let's just go
over bond energies.

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And you've seen this in 5.111
and 2, so I'm not going to

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belabor it but they're just a
little bit of examples that I

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want to go through, just so
it's fresh on your mind.

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So the idea, of course, is to
be able to have an idea of how

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much energy is involved in
forming or breaking

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a single bond.
 

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So, if we just do this by
example, we can take methane so

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it's a real simple case because
we know it's just got four

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identical carbon hydrogen
bonds, and we could say OK,

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let's just break them.
 

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So we'll start with methane gas
and go to one atom of carbon in

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the gas phase, plus four atoms
of hydrogen in the gas phase.

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The energetics in this case
aren't given by the usual

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heats of formation.
 

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You'd just say, if I want to
know about methane, I can look

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up its heat of formation from
the elements in their standards

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states. but the difference
here is these elements aren't

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in their standard states.
 

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Carbon in its standard state at
room temperature and pressure

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is graphite, a solid, it's not
carbon atoms in the gas phase,

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and hydrogen in the standard
state is hydrogen molecules

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H2, not individual atoms.
 

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All right, so we'd like
to have this bond energy

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for these things.
 

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So let's just to make a
cycle that will allow

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us to determine this.
 

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So this'll be our first
step in that cycle, or

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one way of getting there.
 

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And this delta H of reaction is
going to be by definition four

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times our bond energy for
a carbon hydrogen bond.

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Now let's go to be elements
that are in their standards

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states at room temperature
and pressure.

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So let's go to
carbon as graphite.

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And let's go to two molecules
of hydrogen gas, so this will

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be step two and this
will be step three.

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And this will allow us to work
because now we're starting in

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standard states, so we can just
use regular heats of formation.

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And that's the key.
 

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So if we look at step one delta
H1 there as we've defined it,

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four times our bond energy.
 

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Two, this is just negative
heat of formation of methane,

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which we can look up.
 

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And three, is similar.
 

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Essentially it's the heat of
formation of carbon in the gas

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phase and hydrogen atoms in the
gas phase, commonly called

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heats of atomization, but these
are also tabulated just like

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heats of formation of
ordinary compounds.

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In fact, in the appendix to
your book that has

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thermodynamic data, you can
find carbon gas phase atoms

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including heat of formation,
and same with individual

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hydrogen atom as opposed to
hydrogen molecules

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in the gas phase.
 

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So those data are available.
 

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So we can write delta Hc
from atomization, and

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two times delta H of H2.
 

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This is the way this is
tabulated and this is molar.

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And of course now we've
written a cycle.

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So we know that to get from
here to here is the same as to

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go through these two steps.
 

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In other words delta H1 is the
sum of delta H2 and delta H3.

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00:07:48 --> 00:08:01
 


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And so this says that our four
times the carbon hydrogen bond

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energy is just given by minus
the heat of formation of

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methane plus the heat of
atomization of carbon, plus the

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two times the heat
of atomization for

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hydrogen molecules.
 

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And if we look up the numbers
that are tabulated, what we

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discover is that our carbon
hydrogen bond energy is

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416.2 kilojoules per mole.
 

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Very useful to have numbers
like that stored in your head.

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To have some basic idea of just
ordinary chemical energetics

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in terms of bond energies.
 

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Hydrogen bonds, you know
roughly 20 kilojoules

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per mole, and so forth.
 

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Just having those kinds of
energetic enables you to think

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in a qualitative way about
what's likely to happen in an

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ordinary chemical or
biochemical situation.

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OK, so this is in a sense the
simplest case, because we've

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talked about the dissociation
of a molecule that consists

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of all identical bonds.
 

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But it's straightforward
to go from there to

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additional bond energies.
 

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So from this we've got a value
for a sort of typical carbon

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hydrogen bond, right.
 

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We can do the same thing now
for ethane, and that's got a

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single carbon carbon bond, as
well as a bunch of carbon

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hydrogen bonds, but now the we
know the carbon hydrogen bond

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energy, we can use that number
plus the relevant heats of

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formation to determine the
carbon carbon bond energy.

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And we can keep going and
extend this to essentially

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tabulate bond energies for
a very large number of

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different sorts of bonds.
 

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So just as an example, ethane,
so now we're going to have --

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this I'll write it all out just
some we can keep proper track

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of all the bonds that we're
going to be breaking.

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So C2H6 goes to two carbon
gas phase atoms, and

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six hydrogen atoms.
 

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So in this case, our, I can
write this again as one delta

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H1 is six times the carbon
hydrogen bond energy plus the

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carbon carbon bond energy
that we'd like to determine.

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And again we can go through
now a similar cycle.

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So again this now can be
equilibrated with carbon

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graphite plus three molecules
of hydrogen in the gas

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phase, just like before.
 

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And so from that we can see
that we'll end up with an

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equality between these, and
negative delta H naught

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formation for C2H6 or ethane,
plus two delta H of carbon

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atomization, plus three
delta H for atomization

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hydrogen molecule.
 

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So we've already seen we could
look up these numbers and this,

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and we've already determined a
carbon hydrogen bond energy.

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So again, if we find all the
relevant values, we can

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determine that our carbon
carbon bond energy

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is 342 kilojoules.
 

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And so on.
 

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So we can keep going and again
build up a bigger and bigger

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inventory of bond energies just
to provide us with the kind of

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intuition that we'd like to
have to be able to think about

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ordinary molecular energetics.
 

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Any questions about
bond energies?

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All right.
 

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Of course, if we know bond
energies, we also could

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make estimates of
heats of formation.

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So if we have some new
compound, we don't know

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its heat of formation,
we know its structure.

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We know what bonds
are involved.

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We could get an estimate for
what we might expect for its

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heat of formation if we know
those, and I think I'll just

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write this out on the board by
example, but not work through

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the numbers explicitly.
 

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You know, let's say we
were going to make, you

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know, n pentane C5H12.
 

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And of course again keeping
proper track of all

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the carbon carbon and
carbon hydrogen bonds.

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But now in principle we know
the carbon carbon bond energies

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and the carbon hydrogen
bond energies.

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So we should be able to figure
out the heat of formation of a

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compound like this, even if we
don't know it from a table.

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And it's again through a
similar sort of cycle so if we

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start with the atoms in the gas
phase, and go to n pentane.

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So this is now the bond
energies which we

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basically know.
 

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And again make our cycle of
involving the elements in their

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stable form at standard
temperature and pressure.

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Then again, here's
our one, two, three.

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Here's our minus delta H of
atomization, and here's

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our heat of formation.
 

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And that's the point, is that
now we can use what we've

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already elaborated for the bond
energies and the known

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enthalpies of atomization, and
we could determine the

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heat of formation.
 

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If we do that, we wind up
with a value of minus

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152.6 kilojoules.
 

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If we measure it.
 

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If we look up in a table what
the actual value is, we

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discover it's minus
146.4 kilojoules.

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So it's a few percent off.
 

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Why is it off?
 

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Why isn't it right?
 

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STUDENT: [UNINTELLIGIBLE]
 

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00:16:11 --> 00:16:12
PROFESSOR NELSON: Yes, exactly.
 

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You know you can't use the C-H
bonds from methane for every

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C-H bond, or the C-C bond in
ethane for every carbon

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carbon single bond.
 

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There'll be variations,
usually of modest

239
00:16:25 --> 00:16:28
magnitude, in the values.
 

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So this isn't going to be an
exact calculation, but

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certainly this is close enough
for allowing us to think

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qualitatively and
semi-quantitatively about

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00:16:37 --> 00:16:39
ordinary energetics.
 

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Another illustration of it is
if we look at neopentane --

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00:16:55 --> 00:16:58
so same chemical formula.
 

246
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Same number of carbon carbon
and carbon hydrogen bonds.

247
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So according to the way we've
done this calculation, we

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00:17:04 --> 00:17:08
should get exactly the same
number, because all we're doing

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00:17:08 --> 00:17:11
is adding up the total number
of bonds, and it's the same.

250
00:17:11 --> 00:17:16
But what we discover is that
for neopentane, delta H of

251
00:17:16 --> 00:17:28
formation, neopentane is
minus 166.1 kilojoules.

252
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So again it's different in this
case in the other direction.

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But certainly close enough that
allows us to think reasonably

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about what might happen
in ordinary situations.

255
00:17:42 --> 00:17:47
Any questions about
bond energies?

256
00:17:47 --> 00:17:55
OK, now we're going to go to a
new topic, and let me say, the

257
00:17:55 --> 00:17:58
topic we're going to start now,
the second law, is really in a

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sense, this is the start of
the whole rest of the term.

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00:18:02 --> 00:18:06
So far, what we've covered
essentially is conservation

260
00:18:06 --> 00:18:11
of energy, how you think
about energetics and what

261
00:18:11 --> 00:18:12
contributes to them.
 

262
00:18:12 --> 00:18:14
That is heat and work.
 

263
00:18:14 --> 00:18:16
How to account for
them all properly.

264
00:18:16 --> 00:18:19
What happens under constant
volume or constant pressure

265
00:18:19 --> 00:18:23
conditions that led us to
the definition of enthalpy

266
00:18:23 --> 00:18:27
right and so forth.
 

267
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And once you get your arms
around these ideas, and it

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00:18:33 --> 00:18:38
takes some work to do that,
but once you do, the actual

269
00:18:38 --> 00:18:42
execution of things can be
pretty straightforward, and

270
00:18:42 --> 00:18:46
some of this can seem like just
you know a lot of accounting.

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00:18:46 --> 00:18:47
It's not.
 

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00:18:47 --> 00:18:50
It takes some effort to become
accustomed to it and familiar

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00:18:50 --> 00:18:53
with how to properly think
about heat and work and

274
00:18:53 --> 00:18:55
how they contribute to
energy and so forth.

275
00:18:55 --> 00:18:59
But given that amount of
effort, a lot of this can

276
00:18:59 --> 00:19:02
be reduced to fairly
straightforward

277
00:19:02 --> 00:19:04
calculational stuff.
 

278
00:19:04 --> 00:19:09
What we're about to start is a
little different from that in

279
00:19:09 --> 00:19:15
some sense, and really in some
ways more difficult because

280
00:19:15 --> 00:19:20
what we're going to try to
understand starting with this

281
00:19:20 --> 00:19:25
next set of topics is what
determines whether something

282
00:19:25 --> 00:19:29
happens spontaneously?
 

283
00:19:29 --> 00:19:32
We haven't really talked
about that in any of this.

284
00:19:32 --> 00:19:35
We've talked about whether
reactions are endothermic

285
00:19:35 --> 00:19:38
or exothermic.
 

286
00:19:38 --> 00:19:41
But as you're going to see
that doesn't determine what

287
00:19:41 --> 00:19:42
happens spontaneously.
 

288
00:19:42 --> 00:19:45
It certainly is one of
the factors, but by no

289
00:19:45 --> 00:19:47
means the only one.
 

290
00:19:47 --> 00:19:51
What determines what
happens just by itself?

291
00:19:51 --> 00:19:54
Or another way of saying that
is, if I have some sort of

292
00:19:54 --> 00:19:56
system, it could be an engine.
 

293
00:19:56 --> 00:19:57
It could be a
chemical reaction.

294
00:19:57 --> 00:20:01
It could be a biochemical
system or some part of it.

295
00:20:01 --> 00:20:07
What determines where the
equilibrium is and the

296
00:20:07 --> 00:20:11
direction that things would
have to go in order to reach

297
00:20:11 --> 00:20:15
or approach the equilibrium?
 

298
00:20:15 --> 00:20:19
What is the equilibrium
state of something?

299
00:20:19 --> 00:20:23
Actually, what we've discussed
so far really doesn't allow us

300
00:20:23 --> 00:20:26
to determine that, and there
are a few easy ways to

301
00:20:26 --> 00:20:29
sort of bring that out.
 

302
00:20:29 --> 00:20:35
One is you can imagine
constructing some kind of

303
00:20:35 --> 00:20:42
cyclic process that you know it
could remove heat like a

304
00:20:42 --> 00:20:49
refrigerator does from a cool
region and export the heat to a

305
00:20:49 --> 00:20:52
hotter region, like the room,
or outside a window if it's

306
00:20:52 --> 00:20:54
an air conditioner or
something like that.

307
00:20:54 --> 00:20:55
Just move the heat.
 

308
00:20:55 --> 00:20:57
That's it.
 

309
00:20:57 --> 00:21:01
Why not?
 

310
00:21:01 --> 00:21:05
I mean you could do that
and not necessarily

311
00:21:05 --> 00:21:08
violate the first law.
 

312
00:21:08 --> 00:21:11
Or what about, here's
a simpler case.

313
00:21:11 --> 00:21:16
What if I just have a chamber
with a divider, and I pump out

314
00:21:16 --> 00:21:22
half of it, and I put gas in
this half, so there's gas and

315
00:21:22 --> 00:21:29
there's vacuum, and then
I remove the divider.

316
00:21:29 --> 00:21:32
So I certainly expect
that what happens is the

317
00:21:32 --> 00:21:34
gas fills the volume.
 

318
00:21:34 --> 00:21:36
Why?
 

319
00:21:36 --> 00:21:40
The first law didn't tell me
that that needs to happen.

320
00:21:40 --> 00:21:43
Why doesn't it go back the
other way, anyway, even

321
00:21:43 --> 00:21:44
without the barrier?
 

322
00:21:44 --> 00:21:49
Why doesn't the gas just by
itself all wind up over here?

323
00:21:49 --> 00:21:53
Let's say it's a pretty dilute
gas, so even if it does all end

324
00:21:53 --> 00:21:56
up in this half, you know
the energy of any sort of

325
00:21:56 --> 00:21:59
unfavorable repulsions between
molecules is negligible.

326
00:21:59 --> 00:22:02
Maybe they even have
weak attractions?

327
00:22:02 --> 00:22:05
Why doesn't that happened?
 

328
00:22:05 --> 00:22:07
It's a good thing for us
that it doesn't happen.

329
00:22:07 --> 00:22:10
Why in this room doesn't the
air all just sort of collect

330
00:22:10 --> 00:22:11
over there somewhere?
 

331
00:22:11 --> 00:22:15
Or just the oxygen
molecules in the air and

332
00:22:15 --> 00:22:17
suffocate all of us.
 

333
00:22:17 --> 00:22:20
The first law doesn't
have anything to say

334
00:22:20 --> 00:22:23
about that actually.
 

335
00:22:23 --> 00:22:26
Whatever the reason it doesn't
happen, we're not going to find

336
00:22:26 --> 00:22:30
the answer to that
in the first law.

337
00:22:30 --> 00:22:34
So that's what the second law
of thermodynamics and the

338
00:22:34 --> 00:22:36
development of entropy
is all about.

339
00:22:36 --> 00:22:40
It's to help us understand
what is the direction

340
00:22:40 --> 00:22:42
of spontaneous change?
 

341
00:22:42 --> 00:22:45
What governs that, and what's
the equilibrium state

342
00:22:45 --> 00:22:51
that is reached when the
spontaneous change occurs?

343
00:22:51 --> 00:22:55
OK?
 

344
00:22:55 --> 00:22:59
So the second law is going to
give us basically a principle

345
00:22:59 --> 00:23:02
that'll tell us the direction
of spontaneous change.

346
00:23:02 --> 00:23:04
One way of thinking about that
is it's going to allow it to

347
00:23:04 --> 00:23:06
sort of determine the
direction of time.

348
00:23:06 --> 00:23:09
You know if we see initial or
if we see one state and we see

349
00:23:09 --> 00:23:12
another state, we'll be able or
know, time must have been going

350
00:23:12 --> 00:23:15
this way, right because the
spontaneous change would

351
00:23:15 --> 00:23:19
happen in this direction.
 

352
00:23:19 --> 00:23:30
So, I'm going to put up a
couple of just statements

353
00:23:30 --> 00:23:34
of the second law
of thermodynamics.

354
00:23:34 --> 00:23:38
I'll start with kind
of an easy one.

355
00:23:38 --> 00:23:56
So maybe I'll start
with that here.

356
00:23:56 --> 00:24:08
Here's a statement by Clausius.
 

357
00:24:08 --> 00:24:13
The first law says that
the energy of the

358
00:24:13 --> 00:24:16
universe is constant.
 

359
00:24:16 --> 00:24:34
We're always conserving
in one way or another.

360
00:24:34 --> 00:24:50
And the second law is
that the entropy of the

361
00:24:50 --> 00:24:58
universe is increasing.
 

362
00:24:58 --> 00:25:03
Now we're going to define
entropy presently.

363
00:25:03 --> 00:25:06
But I'm writing this up just to
give you some foreshadowing of

364
00:25:06 --> 00:25:10
how we're going to try to
guide our thinking about

365
00:25:10 --> 00:25:13
spontaneous processes.
 

366
00:25:13 --> 00:25:17
This tells us about
conservation of energy.

367
00:25:17 --> 00:25:22
This tells us about which
direction things move in

368
00:25:22 --> 00:25:25
spontaneously, namely the
direction that leads to an

369
00:25:25 --> 00:25:33
increase in this soon to be
defined quantity entropy.

370
00:25:33 --> 00:25:38
It's going to turn out to be a
state function, and it'll help

371
00:25:38 --> 00:25:42
us understand the direction
of spontaneous change.

372
00:25:42 --> 00:25:46
You know, like the first law
the second law too was

373
00:25:46 --> 00:25:51
developed before there was a
very well defined understanding

374
00:25:51 --> 00:25:53
of the molecular
nature of matter.

375
00:25:53 --> 00:25:56
We're going to talk about
the second law and entropy

376
00:25:56 --> 00:25:58
in macroscopic terms.
 

377
00:25:58 --> 00:26:01
Later on in the semester
we'll also discuss them

378
00:26:01 --> 00:26:03
in microscopic terms.
 

379
00:26:03 --> 00:26:05
We'll do a little bit of what's
called statistical mechanics,

380
00:26:05 --> 00:26:09
of microscopic, basically
discussing the microscopic

381
00:26:09 --> 00:26:14
origins of entropy in terms
of disorder of molecules.

382
00:26:14 --> 00:26:18
But really, the thermodynamics
of entropy and the second law

383
00:26:18 --> 00:26:22
evolved because people were
trying to build things.

384
00:26:22 --> 00:26:24
It was the Industrial
Revolution. people were trying

385
00:26:24 --> 00:26:28
to build engines, steam
engines, and other kinds of

386
00:26:28 --> 00:26:31
devices, refrigerators
other things.

387
00:26:31 --> 00:26:35
And they couldn't understand --
first of all, why couldn't you

388
00:26:35 --> 00:26:39
make it perfectly efficient?
 

389
00:26:39 --> 00:26:40
You know, you'd have
a steam engine.

390
00:26:40 --> 00:26:43
There'd be a source of heat.
 

391
00:26:43 --> 00:26:46
You could extract work.
 

392
00:26:46 --> 00:26:48
Never seemed like you
could get it all and

393
00:26:48 --> 00:26:52
turn it all into work.
 

394
00:26:52 --> 00:26:55
Why not?
 

395
00:26:55 --> 00:26:57
And if not, what were
the limitations on it?

396
00:26:57 --> 00:27:02
What was the best efficiency
you could achieve?

397
00:27:02 --> 00:27:05
So in a very practical way
people were motivated to

398
00:27:05 --> 00:27:12
think very hard about
these kinds of questions.

399
00:27:12 --> 00:27:17
So let's just look at some of
the things that brought out

400
00:27:17 --> 00:27:21
the need for this kind
of consideration.

401
00:27:21 --> 00:27:38
So let me start by drawing
one of the impossibilities.

402
00:27:38 --> 00:27:40
We could try to build
a heat engine.

403
00:27:40 --> 00:27:49
Where we've got some
temperature T1 which is hot,

404
00:27:49 --> 00:27:54
and some amount of heat, q1
goes into our system, and our

405
00:27:54 --> 00:27:57
system runs as a cycle.
 

406
00:27:57 --> 00:28:00
It goes around and around,
because in any practical

407
00:28:00 --> 00:28:02
situation we're going to
need to keep going and

408
00:28:02 --> 00:28:06
repeating the process.
 

409
00:28:06 --> 00:28:09
Some amount of work comes out.
 

410
00:28:09 --> 00:28:14
We'll call it minus w, because
work is always defined as

411
00:28:14 --> 00:28:18
the work that's done by the
environment on the system.

412
00:28:18 --> 00:28:21
So if I'm drawing the arrow
this way, then I want

413
00:28:21 --> 00:28:27
to write it as minus w.
 

414
00:28:27 --> 00:28:31
Now this would be just swell.
 

415
00:28:31 --> 00:28:32
This is it.
 

416
00:28:32 --> 00:28:34
That's the whole heat engine.
 

417
00:28:34 --> 00:28:37
This is running in a cycle.
 

418
00:28:37 --> 00:28:41
So we know that,
delta u is zero.

419
00:28:41 --> 00:28:45
So that would mean that, you
know, the amount of work out

420
00:28:45 --> 00:28:51
would just equal the heat
in every time around.

421
00:28:51 --> 00:28:54
Never happens.
 

422
00:28:54 --> 00:28:57
Can't make it happen.
 

423
00:28:57 --> 00:29:02
The only way it works
is if instead there's

424
00:29:02 --> 00:29:12
an additional part.
 

425
00:29:12 --> 00:29:27
Somewhere heat is also
lost to a cold reservoir.

426
00:29:27 --> 00:29:30
In other words, you know
I burned some fuel.

427
00:29:30 --> 00:29:35
I consumed something to produce
my hot source, and I'm going to

428
00:29:35 --> 00:29:41
then try to turn it into work,
which I can, but only partly.

429
00:29:41 --> 00:29:45
There's going to be heat loss
somewhere to a colder region,

430
00:29:45 --> 00:29:48
and I can't avoid it.
 

431
00:29:48 --> 00:29:53
And it was discovered that
this was always the case.

432
00:29:53 --> 00:29:59
So this can be built where,
just to be clear on these. q1

433
00:29:59 --> 00:30:02
is a positive number, because
again that's heat going from

434
00:30:02 --> 00:30:04
the environment to the system.
 

435
00:30:04 --> 00:30:19
This is our system
running in a cycle.

436
00:30:19 --> 00:30:26
So q1 is positive, minus w
is positive, that is work

437
00:30:26 --> 00:30:31
is being done on the
environment by the engine.

438
00:30:31 --> 00:30:42
And minus q2 is positive.
 

439
00:30:42 --> 00:30:51
And T1 is greater than T2.
 

440
00:30:51 --> 00:30:55
That I can build.
 

441
00:30:55 --> 00:31:00
Here's another thing
we could try to do.

442
00:31:00 --> 00:31:01
It's sort of the opposite.
 

443
00:31:01 --> 00:31:04
We could try to produce
a refrigerator but not

444
00:31:04 --> 00:31:07
have to do any work.
 

445
00:31:07 --> 00:31:13
So let's go the other way, in
other words, let's go from T2

446
00:31:13 --> 00:31:20
which is cold we're going to go
in this direction now, which

447
00:31:20 --> 00:31:26
means q2 will be a positive
number and here's our

448
00:31:26 --> 00:31:29
system running in a cycle.
 

449
00:31:29 --> 00:31:34
And now here's minus q1 now
is going to be our positive

450
00:31:34 --> 00:31:37
number, and we're going to
remove heat from q2 and move

451
00:31:37 --> 00:31:43
it, or from T2 a cold
region and move it to some

452
00:31:43 --> 00:31:46
place that's hotter.
 

453
00:31:46 --> 00:31:49
Also a pretty nice idea.
 

454
00:31:49 --> 00:31:53
And also obviously impossible.
 

455
00:31:53 --> 00:31:59
It only works if I put work in
there to make it happen, then

456
00:31:59 --> 00:32:04
yes I can take heat out of a
cold body and move it up into a

457
00:32:04 --> 00:32:11
hotter reservoir of some sort.
 

458
00:32:11 --> 00:32:21
So here's a refrigerator.
 

459
00:32:21 --> 00:32:28
Again T1 is greater than
T2, and in this case q2

460
00:32:28 --> 00:32:29
is greater than zero.
 

461
00:32:29 --> 00:32:37
I'm removing heat, minus q1 is
greater than zero, that is

462
00:32:37 --> 00:32:44
heat is going up this way.
 

463
00:32:44 --> 00:32:45
Work is greater than zero.
 

464
00:32:45 --> 00:32:48
Has to be.
 

465
00:32:48 --> 00:32:55
Of course the thing is running
in a cycle. delta u is zero.

466
00:32:55 --> 00:33:09
So that means that work must
be minus q1 plus q2, right?

467
00:33:09 --> 00:33:14
And work is greater than zero,
so that's saying minus q1 right

468
00:33:14 --> 00:33:20
that's a positive number,
must be bigger than q2.

469
00:33:20 --> 00:33:23
In other words, I am taking
some heat away from

470
00:33:23 --> 00:33:25
the cold region.
 

471
00:33:25 --> 00:33:27
The heat I'm dumping into the
hotter region is bigger than

472
00:33:27 --> 00:33:29
the amount that I taking
away here, because it's

473
00:33:29 --> 00:33:33
also got this amount.
 

474
00:33:33 --> 00:33:39
That's why, you know, if it's a
humid or warm summer afternoon

475
00:33:39 --> 00:33:41
and you think oh what I a great
idea, I've got this little

476
00:33:41 --> 00:33:42
fridge in my room.
 

477
00:33:42 --> 00:33:47
I'm going to open it up
and cool the room off.

478
00:33:47 --> 00:33:49
Turns out not to work too well.
 

479
00:33:49 --> 00:33:51
Because of course what
the fridge is doing,

480
00:33:51 --> 00:33:53
it's cold inside.
 

481
00:33:53 --> 00:33:57
So it's a machine that's
removing heat from the inside

482
00:33:57 --> 00:33:58
and dumping it outside.
 

483
00:33:58 --> 00:34:01
There are coils in the back of
the fridge, and if you touch

484
00:34:01 --> 00:34:03
them they're a little
bit warm and so on.

485
00:34:03 --> 00:34:09
The heat is being
lost to the room.

486
00:34:09 --> 00:34:10
How much heat?
 

487
00:34:10 --> 00:34:14
Well, the work that
goes in is also added.

488
00:34:14 --> 00:34:17
So the amount of heat that goes
out into the room is bigger

489
00:34:17 --> 00:34:19
than the amount of heat that
you're taking away

490
00:34:19 --> 00:34:22
from the space.
 

491
00:34:22 --> 00:34:23
That's bad.
 

492
00:34:23 --> 00:34:26
So if you try opening the
refrigerator door to cool off

493
00:34:26 --> 00:34:28
your room at the same time as
you're dumping heat into your

494
00:34:28 --> 00:34:31
room, all you discover is
the net effect is to

495
00:34:31 --> 00:34:35
heat up your room.
 

496
00:34:35 --> 00:34:38
Because you know the amount of
heat that the thing is removing

497
00:34:38 --> 00:34:41
from somewhere on the inside
there and struggling to do that

498
00:34:41 --> 00:34:44
because you've left the door to
the fridge open, right, is not

499
00:34:44 --> 00:34:47
as big as the amount out
heat that's coming out in

500
00:34:47 --> 00:34:49
those coils on the back.
 

501
00:34:49 --> 00:34:52
It's not as big because that
heat has not only the heat that

502
00:34:52 --> 00:34:55
you're removing from the
inside, but also this

503
00:34:55 --> 00:34:57
amount of work.
 

504
00:34:57 --> 00:34:58
It's all conserved
because delta u is zero.

505
00:34:58 --> 00:35:02
The thing is running
in a cycle.

506
00:35:02 --> 00:35:04
Try it sometime.
 

507
00:35:04 --> 00:35:06
You can verify this
experimentally in a

508
00:35:06 --> 00:35:07
very simple way.
 

509
00:35:07 --> 00:35:11
It's not a very effective way
to work, and it wastes a little

510
00:35:11 --> 00:35:14
bit of energy, but could be
worth it in the interest of

511
00:35:14 --> 00:35:18
knowledge and discovery.
 

512
00:35:18 --> 00:35:23
Let me write an alternate
statement of the second

513
00:35:23 --> 00:35:35
law of Clausius.
 

514
00:35:35 --> 00:35:49
All spontaneous processes
are irreversible.

515
00:35:49 --> 00:35:54
When I open that panel in the
container, I've got gas on one

516
00:35:54 --> 00:35:58
side and vacuum in the other
and it expands in there, it

517
00:35:58 --> 00:36:03
happens spontaneously,
and it's irreversible.

518
00:36:03 --> 00:36:11
It's not just going to go back.
 

519
00:36:11 --> 00:36:14
And now let me write a
mathematical statement

520
00:36:14 --> 00:36:28
of the second law.
 

521
00:36:28 --> 00:36:38
And we'll celebrate it's
importance by using this color.

522
00:36:38 --> 00:36:44
Going around in a cycle, if I
integrate the quantity dq

523
00:36:44 --> 00:36:50
reversible over T, I get zero.
 

524
00:36:50 --> 00:36:55
Remember this, this is
our special function.

525
00:36:55 --> 00:36:58
Let me just keep going
a little more though.

526
00:36:58 --> 00:37:02
Let me also write
another version.

527
00:37:02 --> 00:37:09
If I write dq for an
irreversible path over T,

528
00:37:09 --> 00:37:16
right, less than zero.
 

529
00:37:16 --> 00:37:22
It's not the same.
 

530
00:37:22 --> 00:37:28
This is a state function.
 

531
00:37:28 --> 00:37:29
This isn't.
 

532
00:37:29 --> 00:37:32
Remember of course that the
heat that's exchange between

533
00:37:32 --> 00:37:36
the system and the environment
depends on the path.

534
00:37:36 --> 00:37:42
If there is a reversible path,
and you see how much heat was

535
00:37:42 --> 00:37:46
exchange with the environment,
and you look at that divided by

536
00:37:46 --> 00:37:50
temperature integrate over the
whole thing, you discover

537
00:37:50 --> 00:37:56
that as long as the path is
reversible, it only depends on

538
00:37:56 --> 00:37:59
the states at the beginning
and the end of the path.

539
00:37:59 --> 00:38:01
In other words if you have
various ways you can go from

540
00:38:01 --> 00:38:06
state one to two that are
reversible, it's

541
00:38:06 --> 00:38:07
always the same.
 

542
00:38:07 --> 00:38:12
We saw that for just a couple
of examples, a couple

543
00:38:12 --> 00:38:13
lectures back.
 

544
00:38:13 --> 00:38:16
Remember, we looked at these
thermodynamic cycles and just

545
00:38:16 --> 00:38:18
said, well let's just
calculate those.

546
00:38:18 --> 00:38:22
And those were, those all
involved reversible processes.

547
00:38:22 --> 00:38:25
So, in effect, we looked at
different paths to go from

548
00:38:25 --> 00:38:27
one state to another.
 

549
00:38:27 --> 00:38:29
We had a cycle, and one
path went to here, and

550
00:38:29 --> 00:38:31
the other path went back.
 

551
00:38:31 --> 00:38:35
We discovered that, in fact,
this one zero around the cycle

552
00:38:35 --> 00:38:38
or the way we expressed it at
the time is the value of this

553
00:38:38 --> 00:38:42
was the same regardless of the
way we got from one state to

554
00:38:42 --> 00:38:44
the other, whether we took a
straightforward route or a more

555
00:38:44 --> 00:39:09
circuitous route, as long
as they were reversible.

556
00:39:09 --> 00:39:28
We're going to define dS as dq
reversible over T, and since

557
00:39:28 --> 00:39:35
we're dealing with a state
function delta S going from

558
00:39:35 --> 00:39:45
state one to two of dq
reversible over T is S2

559
00:39:45 --> 00:39:52
minus S1 state function.
 

560
00:39:52 --> 00:40:03
And S as state function is the
entropy, and of course the us,

561
00:40:03 --> 00:40:19
it will always be special.
 

562
00:40:19 --> 00:40:27
All right, now, the second law,
you know it's difficult to

563
00:40:27 --> 00:40:31
understand and to get your arms
around, because you know, do

564
00:40:31 --> 00:40:32
I really calculate this?
 

565
00:40:32 --> 00:40:36
I actually have to find a
reversible path in order

566
00:40:36 --> 00:40:39
to do the calculation.
 

567
00:40:39 --> 00:40:43
Normally, you know, when you
calculate delta u and delta h

568
00:40:43 --> 00:40:48
and so forth, you have various
ways to calculate them that can

569
00:40:48 --> 00:40:49
be pretty straightforward.
 

570
00:40:49 --> 00:40:53
But here, you actually have to
determine the heat exchanged

571
00:40:53 --> 00:40:57
between the system and the
environment, and you know

572
00:40:57 --> 00:41:02
that does, in general,
depend on the path.

573
00:41:02 --> 00:41:07
But it turns out that this
quantity, you know, the

574
00:41:07 --> 00:41:13
differential of that heat over
the temperature, also depends

575
00:41:13 --> 00:41:18
on path unless it's
a reversible pass.

576
00:41:18 --> 00:41:21
Any reversible path will
lead to the same results.

577
00:41:21 --> 00:41:26
It doesn't depend on path
among reversible paths.

578
00:41:26 --> 00:41:30
What that means in practice is
if we say OK, start here and

579
00:41:30 --> 00:41:33
end here and calculate the
entropy, you actually have to

580
00:41:33 --> 00:41:36
sort of figure out a reversible
way of getting from here to

581
00:41:36 --> 00:41:41
here so that you can
do that calculation.

582
00:41:41 --> 00:41:44
So it's really very different
from ordinary functions that

583
00:41:44 --> 00:41:50
you've been dealing with.
 

584
00:41:50 --> 00:41:54
A lot of people, you know,
because the second law is

585
00:41:54 --> 00:41:58
difficult to understand,
you know you can easily go

586
00:41:58 --> 00:42:01
online and see thousands of
violations of the second law.

587
00:42:01 --> 00:42:05
It's still easy to look,
to go find claims of

588
00:42:05 --> 00:42:08
perpetual motion machines.
 

589
00:42:08 --> 00:42:10
Some of them cost
a lot of money.

590
00:42:10 --> 00:42:13
You can buy them,
see how they work.

591
00:42:13 --> 00:42:20
But and also, all sorts of
schemes for producing energy.

592
00:42:20 --> 00:42:22
Go online and see, right.
 

593
00:42:22 --> 00:42:25
You're just, they're just
crazy ideas about getting

594
00:42:25 --> 00:42:26
energy from nothing.
 

595
00:42:26 --> 00:42:29
Getting energy from the
heat that's just already

596
00:42:29 --> 00:42:31
present in the air.
 

597
00:42:31 --> 00:42:33
I mean there's heat in the
air, all this motion,

598
00:42:33 --> 00:42:34
it must have energy.
 

599
00:42:34 --> 00:42:40
We should be able to
extract it and use it.

600
00:42:40 --> 00:42:43
Turns out we can't do that.
 

601
00:42:43 --> 00:42:50
It has to look
something like this.

602
00:42:50 --> 00:42:52
OK.
 

603
00:42:52 --> 00:42:55
I want to look at some more
statements of the second law.

604
00:42:55 --> 00:43:00
To do that I just want to
indicate one definition

605
00:43:00 --> 00:43:04
which is just to be clear
what these things mean.

606
00:43:04 --> 00:43:08
These are what I've called
heat reservoirs or

607
00:43:08 --> 00:43:10
hot or cold bodies.
 

608
00:43:10 --> 00:43:14
Here's what I mean to
be more specific.

609
00:43:14 --> 00:43:20
A heat reservoir is basically
a very large thermal mass

610
00:43:20 --> 00:43:21
at the same temperature.
 

611
00:43:21 --> 00:43:25
And the real idea is that you
can bring heat out of it as

612
00:43:25 --> 00:43:30
much as you want and the
temperature won't change.

613
00:43:30 --> 00:43:33
It's an idealization. right If
you have something that's big

614
00:43:33 --> 00:43:36
enough, and it's at a constant
temperature, of course you can

615
00:43:36 --> 00:43:39
take heat away, but it's just
so enormous that you won't

616
00:43:39 --> 00:43:41
measurably change
it's temperature.

617
00:43:41 --> 00:43:47
In practice you might be able
or approach that limit.

618
00:43:47 --> 00:43:58
OK, now let's look at some more
definitions or statements

619
00:43:58 --> 00:44:19
of the second law.
 

620
00:44:19 --> 00:44:27
This is from Kelvin of Kelvin
temperature scale fame.

621
00:44:27 --> 00:44:35
It's impossible to convert
heat into work with a system

622
00:44:35 --> 00:44:37
that operates in a cycle.
 

623
00:44:37 --> 00:44:38
I'm going to write
this all out.

624
00:44:38 --> 00:44:39
I know you've got it in
your notes too, but

625
00:44:39 --> 00:44:41
it's super important.
 

626
00:44:41 --> 00:45:02
To convert heat into work with
a system that operates in a

627
00:45:02 --> 00:45:08
cycle, without at the same time
transferring some heat

628
00:45:08 --> 00:45:31
to a colder reservoir.
 

629
00:45:31 --> 00:45:34
OK, a couple of
things to notice.

630
00:45:34 --> 00:45:37
One is, you know, in some
sense the second law is

631
00:45:37 --> 00:45:39
kind of negative, right?
 

632
00:45:39 --> 00:45:44
Must not have been
done in the new age.

633
00:45:44 --> 00:45:49
It tells us what we can't do.
 

634
00:45:49 --> 00:45:52
And that really is in a
sense what it's all about.

635
00:45:52 --> 00:45:56
It's telling us what are
our limitations of what

636
00:45:56 --> 00:46:00
can be accomplished.
 

637
00:46:00 --> 00:46:09
Very important part of this
statement -- in a cycle.

638
00:46:09 --> 00:46:12
Of course any practical engine
has to keep going, so there's

639
00:46:12 --> 00:46:16
going to be a cycle in some way
or another, but it's important

640
00:46:16 --> 00:46:20
because, you know, there are
some -- if I'm not operating

641
00:46:20 --> 00:46:24
in a cycle, I can convert
heat into work just fine.

642
00:46:24 --> 00:46:34
You know, I could have a heat
source, got a candle, and I've

643
00:46:34 --> 00:46:38
got a piston, maybe I've
got a weight on it.

644
00:46:38 --> 00:46:45
I've got something stopping it.
 

645
00:46:45 --> 00:46:48
And then I remove the stoppers
and let it go, and because of

646
00:46:48 --> 00:46:51
the heat, there's expansion.
 

647
00:46:51 --> 00:47:04
It pushes up, right, and it'll
be up higher somewhere.

648
00:47:04 --> 00:47:05
Worked!
 

649
00:47:05 --> 00:47:08
Heat turned into work.
 

650
00:47:08 --> 00:47:10
I don't have a cold
body somewhere.

651
00:47:10 --> 00:47:12
But I only did this once.
 

652
00:47:12 --> 00:47:14
There was just one
stroke of the piston.

653
00:47:14 --> 00:47:17
If I want to continue it and
run in a cycle, somehow

654
00:47:17 --> 00:47:31
I've got to have a place
where the heat goes.

655
00:47:31 --> 00:47:37
So this sort of diagram
describes effectively the way

656
00:47:37 --> 00:47:41
the Kelvin statement works.
 

657
00:47:41 --> 00:47:44
This works fine and like we
illustrated before, it

658
00:47:44 --> 00:47:50
doesn't work fine if I
don't have this part of it.

659
00:47:50 --> 00:47:53
I won't be able to just take
all the heat and convert it to

660
00:47:53 --> 00:47:58
work, like I, in principle,
could do, if I don't need

661
00:47:58 --> 00:48:13
to run it in a cycle.
 

662
00:48:13 --> 00:48:17
Here is yet another statement
by Clausius And we'll

663
00:48:17 --> 00:48:25
end with that one.
 

664
00:48:25 --> 00:48:29
Maybe I'll just read this one,
so we can not go over the time.

665
00:48:29 --> 00:48:32
So, it's impossible for any
system to operate in a cycle

666
00:48:32 --> 00:48:38
that takes heat from a colder
reservoir, transfers it to a

667
00:48:38 --> 00:48:42
hotter reservoir, without at
the same time converting

668
00:48:42 --> 00:48:45
some work into heat.
 

669
00:48:45 --> 00:48:47
In other words, it's a
statement kind of similar to

670
00:48:47 --> 00:48:51
the Kelvin statement, but
applying to the case of

671
00:48:51 --> 00:48:55
moving heat from a colder
to a hotter region.

672
00:48:55 --> 00:49:00
Can't do it, unless some work
is also converted to the

673
00:49:00 --> 00:49:14
heat that gets released
into the hot region.

674
00:49:14 --> 00:49:15
I think we'll stop there.
 

675
00:49:15 --> 00:49:21
Next time what we'll do is lay
out a very well-defined kind of

676
00:49:21 --> 00:49:25
engine called Carnot cycle that
allows us to very explicitly go

677
00:49:25 --> 00:49:28
through and say OK, let's
just work out the steps of

678
00:49:28 --> 00:49:32
isothermal and adiabatic
expansions and contractions.

679
00:49:32 --> 00:49:35
In other words, how does
the engine really work?

680
00:49:35 --> 00:49:38
And just calculate it going
around in a cycle and

681
00:49:38 --> 00:49:41
see exactly how all
this is born out.

682
00:49:41 --> 00:49:43
And we'll see that next time.
 

683
00:49:43 --> 00:49:43