WEBVTT

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There's a concept that's crucial
to chemistry and physics.

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It helps explain why physical processes
go one way and not the other-

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why ice melts,

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why cream spreads in coffee,

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why air leaks out of a punctured tire.

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It's entropy, and it's notoriously
difficult to wrap our heads around.

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Entropy is often described as
a measurement of disorder.

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That's a convenient image,
but it's unfortunately misleading.

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For example, which is more disordered -

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a cup of crushed ice or a glass
of room temperature water?

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Most people would say the ice,

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but that actually has lower entropy.

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So here's another way of thinking
about it through probability.

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This may be trickier to understand,
but take the time to internalize it

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and you'll have a much better 
understanding of entropy.

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Consider two small solids

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which are comprised 
of six atomic bonds each.

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In this model, the energy in each solid
is stored in the bonds.

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Those can be thought of 
as simple containers,

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which can hold indivisible units of energy
known as quanta.

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The more energy a solid has,
the hotter it is.

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It turns out that there are numerous
ways that the energy can be distributed

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in the two solids

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and still have the same 
total energy in each.

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Each of these options 
is called a microstate.

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For six quanta of energy in Solid A
and two in Solid B,

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there are 9,702 microstates.

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Of course, there are other ways our eight
quanta of energy can be arranged.

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For example, all of the energy
could be in Solid A and none in B,

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or half in A and half in B.

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If we assume that each microstate
is equally likely,

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we can see that some of the energy
configurations

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have a higher probability of occurring
than others.

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That's due to their greater number
of microstates.

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Entropy is a direct measure of each
energy configuration's probability.

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What we see is that the energy
configuration

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in which the energy
is most spread out between the solids

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has the highest entropy.

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So in a general sense,

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entropy can though of as a measurement
of this energy spread.

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Low entropy means 
the energy is concentrated.

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High entropy means it's spread out.

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To see why entropy is useful for
explaining spontaneous processes,

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like hot objects cooling down,

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we need to look at a dynamic system
where the energy moves.

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In reality, energy doesn't stay put.

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It continuously moves between 
neighboring bonds.

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As the energy moves,

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the energy configuration can change.

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Because of the distribution 
of microstates,

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there's 21% chance that the system
will later be in the configuration

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in which the energy is maximally 
spread out,

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there's a 13% chance that it will
return to its starting point,

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and an 8% chance that A will actually
gain energy.

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Again, we see that because there are
more ways to have dispersed energy

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and high entropy than concentrated energy,

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the energy tends to spread out.

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That's why if you put a hot object
next to a cold one,

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the cold one will warm up
and the hot one will cool down.

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But even in that example,

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there is an 8% chance that the hot object
would get hotter.

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Why doesn't this ever happen
in real life?

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It's all about the size of the system.

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Our hypothetical solids only had
six bonds each.

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Let's scale the solids up to 6,000 bonds
and 8,000 units of energy,

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and again start the system with
three-quarters of the energy in A

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and one-quarter in B.

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Now we find that chance of A
spontaneously acquiring more energy

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is this tiny number.

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Familiar, everyday objects have many, many
times more particles than this.

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The chance of a hot object 
in the real world getting hotter

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is so absurdly small,

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it just never happens.

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Ice melts,

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cream mixes in,

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and tires deflate

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because these states have more
dispersed energy than the originals.

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There's no mysterious force
nudging the system towards higher entropy.

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It's just that higher entropy is always
statistically more likely.

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That's why entropy has been called
time's arrow.

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If energy has the opportunity
to spread out, it will.