Inequality word problems

WEBVTT
Kind: captions
Language: en

00:00:00.710 --> 00:00:03.030
John is making pasta dough.

00:00:03.030 --> 00:00:07.500
To make the dough, he
mixed 3/2 cups wheat flour

00:00:07.500 --> 00:00:11.550
with 3/4 cups regular
flour in some water.

00:00:11.550 --> 00:00:13.960
Write an inequality to
express the relationship

00:00:13.960 --> 00:00:17.040
between the wheat flour
and the regular flour.

00:00:17.040 --> 00:00:19.570
He mixed 3/2 cups
of wheat flour.

00:00:19.570 --> 00:00:23.962
3/2 is the exact same
thing as 1 and 1/2,

00:00:23.962 --> 00:00:25.670
if we were to write
it as a mixed number.

00:00:25.670 --> 00:00:28.030
So it's more than 1
cup of wheat flour.

00:00:28.030 --> 00:00:31.790
And he mixes his that with
3/4 cups of regular flour.

00:00:31.790 --> 00:00:37.880
Well, 3/4 is less than 1, so 3/2
is definitely greater than 3/4.

00:00:37.880 --> 00:00:42.080
And we can just pick greater
than right over there.

00:00:42.080 --> 00:00:45.600
3/2 is greater than 3/4.

00:00:45.600 --> 00:00:48.390
Let's do a couple more of these.

00:00:48.390 --> 00:00:51.010
One of the deepest points
in the Indian Ocean,

00:00:51.010 --> 00:00:55.870
the Diamantina trench, is
at negative 8 kilometers.

00:00:55.870 --> 00:00:57.720
We say it is
negative 8 kilometers

00:00:57.720 --> 00:01:01.370
because it is 8 kilometers
below sea level.

00:01:01.370 --> 00:01:07.850
The deepest part of the Bering
Strait is at negative 5 and 4/9

00:01:07.850 --> 00:01:09.370
kilometers.

00:01:09.370 --> 00:01:12.290
Write an inequality to show the
relationship between these two

00:01:12.290 --> 00:01:15.550
points, and determine
which point is deeper.

00:01:15.550 --> 00:01:16.050
Let's see.

00:01:16.050 --> 00:01:19.030
We have a greater
than sign here.

00:01:19.030 --> 00:01:21.050
So we want to write
whichever quantity

00:01:21.050 --> 00:01:25.090
is greater on the
left-hand side.

00:01:25.090 --> 00:01:26.240
We look right over here.

00:01:26.240 --> 00:01:30.359
This number, negative 5 and
4/9, it is less negative.

00:01:30.359 --> 00:01:32.150
So it's actually going
to be greater value.

00:01:32.150 --> 00:01:34.640
It's not as deep.

00:01:34.640 --> 00:01:41.300
We can write negative
5 and 4/9 kilometers

00:01:41.300 --> 00:01:44.420
is greater than
negative 8 kilometers.

00:01:44.420 --> 00:01:46.680
And so if we're thinking
about which point is deeper,

00:01:46.680 --> 00:01:49.138
it's going to be the one that's
more negative, because that

00:01:49.138 --> 00:01:52.090
tells us how far below
sea level we are.

00:01:52.090 --> 00:01:53.990
So the negative
8 kilometer point

00:01:53.990 --> 00:01:57.570
is further below sea level.

00:01:57.570 --> 00:01:58.110
Let's see.

00:01:58.110 --> 00:01:59.280
Negative 8 kilometers.

00:01:59.280 --> 00:02:06.120
The Diamantina trench
at negative 8 kilometers

00:02:06.120 --> 00:02:07.460
is the deeper point.

00:02:07.460 --> 00:02:08.840
This is fun, because in
some of these questions

00:02:08.840 --> 00:02:09.923
you actually learn things.

00:02:09.923 --> 00:02:13.100
I always thought that the
deepest part of the Bering

00:02:13.100 --> 00:02:14.030
Sea-- well, anyway.

00:02:14.030 --> 00:02:16.430
We can talk about
that another time.

00:02:16.430 --> 00:02:23.185
Negative 8 kilometers, so the
Diamantina trench is deeper.

00:02:23.185 --> 00:02:25.820
Let's do one more.

00:02:25.820 --> 00:02:27.580
John is making noodles.

00:02:27.580 --> 00:02:33.130
To make the batter, he mixes
11/16 cups tapioca flour

00:02:33.130 --> 00:02:36.170
with 3/8 rice flour
and some water.

00:02:36.170 --> 00:02:38.960
Write an inequality to
express the relationship

00:02:38.960 --> 00:02:41.790
between the tapioca
flour and rice flour.

00:02:41.790 --> 00:02:44.180
So we're really comparing
11/16 cups of tapioca

00:02:44.180 --> 00:02:45.990
to 3/8 cups rice flour.

00:02:45.990 --> 00:02:48.370
So we're really comparing
these two fractions.

00:02:48.370 --> 00:02:50.180
And at first it might
seem hard to compare.

00:02:50.180 --> 00:02:51.980
You have different denominators.

00:02:51.980 --> 00:02:56.310
But 3/8 could easily be
converted to a fraction with 16

00:02:56.310 --> 00:02:57.170
as the denominator.

00:02:57.170 --> 00:02:58.300
What would you do?

00:02:58.300 --> 00:03:00.474
Well, if you doubled
both the 3 and the 8--

00:03:00.474 --> 00:03:02.390
you have to do the same
thing to the numerator

00:03:02.390 --> 00:03:04.460
and the denominator--
this fraction

00:03:04.460 --> 00:03:07.975
3/8 is equivalent to 6/16.

00:03:07.975 --> 00:03:09.850
And then you would have
the same denominator.

00:03:09.850 --> 00:03:12.737
You could compare 11/16 to 6/16.

00:03:12.737 --> 00:03:14.320
Well, if you have
the same denominator

00:03:14.320 --> 00:03:16.926
and this numerator is
greater, 11 is greater than 6,

00:03:16.926 --> 00:03:22.720
11/16 is going to be
greater than 6/16,

00:03:22.720 --> 00:03:25.460
which is the same thing as 3/8.

00:03:25.460 --> 00:03:27.450
And we got it right.


Reading bar charts: putting it together with central tendency

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:02.810
In this chart right
here we're given scores

00:00:02.810 --> 00:00:05.430
on midterm and final exams,
where the vertical axis

00:00:05.430 --> 00:00:06.920
is the score in points.

00:00:06.920 --> 00:00:10.280
And then each of these
pairs of bar charts

00:00:10.280 --> 00:00:13.130
give us for an individual, where
the blue bar is, for example,

00:00:13.130 --> 00:00:15.520
how Ishaan did on the
midterm, the yellow is

00:00:15.520 --> 00:00:16.520
how he did on the final.

00:00:16.520 --> 00:00:19.110
For Emily, the blue is how
she did on the midterm,

00:00:19.110 --> 00:00:20.607
yellow is how she
did on the final.

00:00:20.607 --> 00:00:22.690
And we have a bunch of
interesting questions here.

00:00:22.690 --> 00:00:26.730
The first question, what
was the median score

00:00:26.730 --> 00:00:28.429
for the final exam?

00:00:28.429 --> 00:00:29.970
So just as a review,
median literally

00:00:29.970 --> 00:00:31.430
means what was the middle score?

00:00:31.430 --> 00:00:34.570
So really we should list all
the scores for the final exam

00:00:34.570 --> 00:00:36.730
and sort them in order
and then figure out

00:00:36.730 --> 00:00:39.480
what the middle
score actually was.

00:00:39.480 --> 00:00:41.470
So let's look at all the
scores on final exam.

00:00:44.810 --> 00:00:46.020
Sp you have 100 here.

00:00:46.020 --> 00:00:47.700
Ishaan got 100 on
the final exam.

00:00:47.700 --> 00:00:50.430
Remember, this yellow
bar is the final exam.

00:00:50.430 --> 00:00:52.150
So there's 100.

00:00:52.150 --> 00:00:54.510
Emily also got 100
on the final exam.

00:00:54.510 --> 00:00:56.850
It looks like it was
an easy final exam.

00:00:56.850 --> 00:01:00.700
Daniel also got 100
on the final exam.

00:01:00.700 --> 00:01:05.480
And then, let's see, Jessica,
it looks like she got a 75.

00:01:05.480 --> 00:01:07.579
And then William got an 80.

00:01:07.579 --> 00:01:09.120
So if we were to
sort these in order,

00:01:09.120 --> 00:01:10.953
and let's say we did
it in increasing order,

00:01:10.953 --> 00:01:13.500
you could write-- well,
the lowest score was a 75,

00:01:13.500 --> 00:01:17.510
then you have an 80, and then
you have three 100's-- 100,

00:01:17.510 --> 00:01:19.810
another 100, and another 100.

00:01:19.810 --> 00:01:21.700
So there's five scores
right over here,

00:01:21.700 --> 00:01:22.830
so you will have a middle.

00:01:22.830 --> 00:01:24.288
If you had an even
number, then you

00:01:24.288 --> 00:01:28.270
would take the mean of
the two center values.

00:01:28.270 --> 00:01:29.920
But here you have
one center value,

00:01:29.920 --> 00:01:32.400
and when you order it like
this, it's pretty clear

00:01:32.400 --> 00:01:36.880
that your center value,
your middle value, is 100.

00:01:36.880 --> 00:01:40.761
So the median score for
the final exam is 100.

00:01:40.761 --> 00:01:42.760
And that's because you
had so many hundreds here

00:01:42.760 --> 00:01:45.570
that the median, the middle
score, was still 100.

00:01:45.570 --> 00:01:50.340
What is the midrange
of the midterm scores?

00:01:50.340 --> 00:01:52.300
I'll do it in blue
in honor of the color

00:01:52.300 --> 00:01:54.090
of the bars for the midterm.

00:01:54.090 --> 00:01:59.761
So the midrange is the mean of
your highest and lowest scores.

00:01:59.761 --> 00:02:00.760
So let's calculate this.

00:02:00.760 --> 00:02:03.020
So let's go to the midrange.

00:02:03.020 --> 00:02:05.460
The midrange, you could view
it as the arithmetic mean,

00:02:05.460 --> 00:02:08.690
or the average of your
highest and lowest scores,

00:02:08.690 --> 00:02:10.145
so the midrange of midterm.

00:02:14.070 --> 00:02:16.840
So let's see, the
highest midterm score,

00:02:16.840 --> 00:02:19.240
looking at the blue, the
highest one is right here.

00:02:19.240 --> 00:02:21.120
So Jessica got 100
on the midterm,

00:02:21.120 --> 00:02:22.840
so that's your highest score.

00:02:22.840 --> 00:02:25.850
Your lowest score on the midterm
looks like this one right

00:02:25.850 --> 00:02:26.350
over here.

00:02:26.350 --> 00:02:29.490
Daniel got a 60.

00:02:29.490 --> 00:02:32.340
And so the midrange is
going to be the mean,

00:02:32.340 --> 00:02:34.460
the arithmetic mean
of these two numbers.

00:02:34.460 --> 00:02:39.530
So you add 100 plus 60, divide
by 2, you get 160 over 2,

00:02:39.530 --> 00:02:40.880
or 80.

00:02:40.880 --> 00:02:43.960
So this right over
here is going to be 80.

00:02:43.960 --> 00:02:47.335
What was the average student
score for the final exam?

00:02:47.335 --> 00:02:49.100
Well, for, that we
just have to add up

00:02:49.100 --> 00:02:51.600
the scores on the final
exams and then divide

00:02:51.600 --> 00:02:53.407
by the number of scores we have.

00:02:53.407 --> 00:02:55.240
So we might be able to
do that in our heads.

00:02:55.240 --> 00:02:55.800
Let's see.

00:02:55.800 --> 00:02:57.800
Well, we could-- let me
just write it over here.

00:02:57.800 --> 00:03:04.990
So we have 100, plus 100,
plus 100, plus 75, plus 80.

00:03:04.990 --> 00:03:10.349
So all of that divided by 5,
that will give us our average.

00:03:10.349 --> 00:03:12.140
If someone tells you
average without giving

00:03:12.140 --> 00:03:13.556
more information,
they're probably

00:03:13.556 --> 00:03:15.680
talking about the
arithmetic mean.

00:03:15.680 --> 00:03:22.210
So this is going to be
300 plus another 155,

00:03:22.210 --> 00:03:24.535
so it's going to be 455 over 5.

00:03:29.910 --> 00:03:32.200
And let's see, 5,
this is going to be

00:03:32.200 --> 00:03:35.020
equal to-- 5 goes in--
let me write it down here.

00:03:35.020 --> 00:03:40.390
This is equal to-- 5 goes
into 45, or 450 ninety times

00:03:40.390 --> 00:03:41.370
and into 5 once.

00:03:41.370 --> 00:03:43.580
So this is going
to be equal to 91.

00:03:43.580 --> 00:03:48.710
So the average score for
the final exam is a 91.

00:03:48.710 --> 00:03:51.840
What was the mode for
the final exam scores?

00:03:51.840 --> 00:03:54.174
So the mode is the
most common score.

00:03:54.174 --> 00:03:55.840
So once again, we've
listed all of them,

00:03:55.840 --> 00:03:58.470
and it's pretty clear the
most common score here is 100.

00:03:58.470 --> 00:04:01.810
100 shows up three times,
while a 75 only shows up once,

00:04:01.810 --> 00:04:03.760
and an 80 only shows up once.

00:04:03.760 --> 00:04:06.220
So here the most
common score is 100.

00:04:06.220 --> 00:04:08.420
It shows up three times.

00:04:08.420 --> 00:04:10.920
What is the range of
the midterm scores?

00:04:10.920 --> 00:04:12.730
So the range is
literally the difference

00:04:12.730 --> 00:04:15.426
between the highest score
and the lowest score.

00:04:15.426 --> 00:04:17.300
So the highest score,
we already figured out,

00:04:17.300 --> 00:04:20.000
and this is for the midterm.

00:04:20.000 --> 00:04:22.469
So the highest score is 100.

00:04:22.469 --> 00:04:25.010
And we're going to subtract from
that the lowest score, which

00:04:25.010 --> 00:04:27.190
was a 60.

00:04:27.190 --> 00:04:29.580
So the range is equal to 40.

00:04:29.580 --> 00:04:31.670
The midrange was the
average of these two things.

00:04:31.670 --> 00:04:33.920
The range is just the
difference between the two.

00:04:33.920 --> 00:04:38.110
So the range of the
midterm scores is 40.

00:04:38.110 --> 00:04:40.090
And we're done.


Reading bar charts: comparing two sets of data

WEBVTT
Kind: captions
Language: en

00:00:00.510 --> 00:00:02.080
So we have this bar chart here.

00:00:02.080 --> 00:00:04.580
This says Scores on
Midterm and Final Exams.

00:00:04.580 --> 00:00:07.330
So this axis, the vertical
axis, is the scores.

00:00:07.330 --> 00:00:08.890
And then it's by student.

00:00:08.890 --> 00:00:12.160
And the blue bar is the
midterm, and the yellow bar

00:00:12.160 --> 00:00:13.320
is the final.

00:00:13.320 --> 00:00:16.070
And the question they ask
us is by how many points did

00:00:16.070 --> 00:00:20.660
Nadia's score improve from the
mid-term to the final exam?

00:00:20.660 --> 00:00:21.639
So let's look at Nadia.

00:00:21.639 --> 00:00:23.430
So this is who we're
talking about-- Nadia.

00:00:23.430 --> 00:00:25.500
And we care about how
many points did she

00:00:25.500 --> 00:00:27.540
improve from the
midterm to the final.

00:00:27.540 --> 00:00:30.340
Midterm is blue,
final is yellow.

00:00:30.340 --> 00:00:32.460
So on the midterm, it
looks like she scored--

00:00:32.460 --> 00:00:35.980
and if I were to eyeball
it, it looks like 75 points.

00:00:35.980 --> 00:00:39.030
And on the final, it
looks like she scored 80.

00:00:39.030 --> 00:00:41.850
It looks like she
scored 85 points.

00:00:41.850 --> 00:00:45.435
So it looks like her score
improved by 10 points,

00:00:45.435 --> 00:00:47.690
so 10 points.

00:00:47.690 --> 00:00:49.890
Let's try one more.

00:00:49.890 --> 00:00:52.870
How many students improved
their scores from the midterm

00:00:52.870 --> 00:00:54.530
to the final exam?

00:00:54.530 --> 00:00:56.780
So to improve from the
midterm to the final, that

00:00:56.780 --> 00:00:58.830
means that the yellow
bar for a given student,

00:00:58.830 --> 00:01:01.710
which is the final, is going to
be higher than the midterm bar.

00:01:01.710 --> 00:01:03.876
That's the only way you can
improve from the midterm

00:01:03.876 --> 00:01:04.670
to the final.

00:01:04.670 --> 00:01:07.740
So Brandon improved from
the midterm to the final.

00:01:07.740 --> 00:01:10.550
Vanessa improved from
the midterm to the final.

00:01:10.550 --> 00:01:12.720
Daniel improved from the
midterm to the final.

00:01:12.720 --> 00:01:15.180
Kevin improved from the
midterm to the final.

00:01:15.180 --> 00:01:17.850
William got a lower score on
the final than the midterm,

00:01:17.850 --> 00:01:18.784
so he did not improve.

00:01:18.784 --> 00:01:20.950
So the number of students
that improved their scores

00:01:20.950 --> 00:01:25.910
from midterm to final are
one, two, three four students,

00:01:25.910 --> 00:01:28.873
so 4 students.


Creating a bar chart

WEBVTT
Kind: captions
Language: en

00:00:00.920 --> 00:00:04.019
20 teachers were asked
about their favorite course.

00:00:04.019 --> 00:00:05.600
7 teachers said language.

00:00:05.600 --> 00:00:06.950
3 teachers said history.

00:00:06.950 --> 00:00:08.400
9 teachers said geometry.

00:00:08.400 --> 00:00:10.160
1 teacher said chemistry.

00:00:10.160 --> 00:00:12.600
0 teachers said physics.

00:00:12.600 --> 00:00:15.680
Create a bar chart showing
everyone's favorite courses.

00:00:15.680 --> 00:00:18.062
So we've got the bar
chart right over here.

00:00:18.062 --> 00:00:19.520
And let's see what
we need to plot.

00:00:19.520 --> 00:00:22.240
So it said, 0
teachers said physics,

00:00:22.240 --> 00:00:23.940
which is surprising
to me since physics

00:00:23.940 --> 00:00:25.720
is arguably my favorite course.

00:00:25.720 --> 00:00:27.570
But let's plot
what the data has.

00:00:27.570 --> 00:00:29.864
So physics-- so right now
it looks like it's halfway

00:00:29.864 --> 00:00:31.405
between 0 and 1, so
you actually have

00:00:31.405 --> 00:00:33.730
to bring the physics down to 0.

00:00:33.730 --> 00:00:35.990
Let's see, chemistry.

00:00:35.990 --> 00:00:37.600
Let's see, 1 teacher
said chemistry,

00:00:37.600 --> 00:00:40.350
so we got to bring
chemistry up to 1.

00:00:40.350 --> 00:00:43.010
Now, 9 teachers said geometry.

00:00:43.010 --> 00:00:46.350
So geometry, let's
bring that up to nine.

00:00:46.350 --> 00:00:48.510
1 teacher said chemistry.

00:00:48.510 --> 00:00:49.510
Oh, I already read that.

00:00:49.510 --> 00:00:50.360
History.

00:00:50.360 --> 00:00:50.870
History.

00:00:50.870 --> 00:00:55.310
3 teachers said history, so
let's bring history up to 3.

00:00:55.310 --> 00:00:56.070
And then language.

00:00:56.070 --> 00:01:00.810
7 teachers said language,
so let's move this up to 7.

00:01:00.810 --> 00:01:04.099
And I think if I didn't
make any careless mistakes,

00:01:04.099 --> 00:01:04.980
we should be done.

00:01:04.980 --> 00:01:05.480
Yep.

00:01:05.480 --> 00:01:07.050
Very good.


Reading bar charts: basic example

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:03.800
At Hogwarts, there are
four houses-- Gryffindor,

00:00:03.800 --> 00:00:06.460
Hufflepuff, Ravenclaw,
and Slytherin.

00:00:06.460 --> 00:00:09.550
The bar chart below shows
the number of house points

00:00:09.550 --> 00:00:11.320
that each house received today.

00:00:11.320 --> 00:00:14.550
How many house points
did Hufflepuff receive?

00:00:14.550 --> 00:00:17.120
So if we look at
this bar chart, we

00:00:17.120 --> 00:00:20.980
could assume that this column
right over here is Hufflepuff,

00:00:20.980 --> 00:00:22.530
because it's the
only one that starts

00:00:22.530 --> 00:00:25.430
with an H. This will be
Gryffindor, this is Ravenclaw,

00:00:25.430 --> 00:00:26.760
and this must be Slytherin.

00:00:26.760 --> 00:00:28.840
And so, if we look
at Hufflepuff's bar,

00:00:28.840 --> 00:00:33.660
it looks like they have
3 points scored today.

00:00:33.660 --> 00:00:36.160
So let's put 3 points.

00:00:36.160 --> 00:00:37.920
All right, let's try one more.

00:00:37.920 --> 00:00:40.330
So here they're saying,
how many house points

00:00:40.330 --> 00:00:41.830
did Slytherin receive?

00:00:41.830 --> 00:00:43.640
So this is going
to be Slytherin,

00:00:43.640 --> 00:00:49.220
and it looks like they
received 4 points.


Second Law of Thermodynamics

WEBVTT
Kind: captions
Language: en

00:00:00.249 --> 00:00:01.317
- [Voiceover] So I'm going to ask you

00:00:01.317 --> 00:00:03.187
what I think it is an
interesting question.

00:00:03.187 --> 00:00:06.286
Have you ever sat in a
room at room temperature,

00:00:06.286 --> 00:00:08.353
lets say it's around
70 degrees Fahrenheit.

00:00:08.353 --> 00:00:10.814
And watched a glass of liquid water

00:00:10.814 --> 00:00:13.270
spontaneously have ice in the middle?

00:00:13.694 --> 00:00:16.138
And I'm guessing that
you have never seen that.

00:00:16.457 --> 00:00:18.895
Of course you wouldn't see
ice spontaneously form,

00:00:18.895 --> 00:00:22.285
specially if the room is
at 70 degrees Fahrenheit.

00:00:22.285 --> 00:00:24.619
If it's above the freezing
temperature of water.

00:00:24.619 --> 00:00:26.824
But my question to you is, why not?

00:00:26.824 --> 00:00:28.659
Because that does not seem to defy

00:00:28.659 --> 00:00:31.352
any of the laws of physics,
the Newtonian physics.

00:00:31.352 --> 00:00:33.704
Or even the first law of Thermodynamics.

00:00:33.704 --> 00:00:36.194
Lets just think about how
that actually could occur.

00:00:36.194 --> 00:00:38.905
Lets imagine a bunch of water molecules,

00:00:38.957 --> 00:00:40.403
in their liquid state.

00:00:40.826 --> 00:00:44.785
So, I have a bunch of water
molecules in their liquid state.

00:00:44.785 --> 00:00:46.260
I'm gonna do a good number of them.

00:00:46.260 --> 00:00:47.757
And, they have some temperature.

00:00:47.757 --> 00:00:50.451
Remember, temperature's just
about average kinetic energy.

00:00:50.451 --> 00:00:53.725
But, each of these, are gonna
have their own velocities,

00:00:53.725 --> 00:00:55.292
their own momentums.

00:00:55.292 --> 00:00:57.719
So, they're all going
to be bouncing around

00:00:57.719 --> 00:00:59.623
in different ways.

00:00:59.623 --> 00:01:01.527
And, they have their
hydrogen bonds between them.

00:01:01.527 --> 00:01:05.753
That's why water is liquid
state at room temperature,

00:01:05.753 --> 00:01:07.181
as opposed to gas.

00:01:07.181 --> 00:01:09.607
You got some hydrogen bonds between them.

00:01:09.607 --> 00:01:14.234
But I'm not gonna get too
fixated on that just yet.

00:01:14.391 --> 00:01:17.258
Now, you can imagine
they're all bouncing around

00:01:17.258 --> 00:01:18.187
in random ways,

00:01:18.187 --> 00:01:20.950
but there is some probability that they

00:01:20.950 --> 00:01:23.319
interact just in the right way

00:01:23.319 --> 00:01:26.860
that maybe this molecule right over here

00:01:26.860 --> 00:01:29.158
is able to hit this one in the right way.

00:01:29.158 --> 00:01:33.187
So it transfers most of its
momentum to the faster molecule.

00:01:33.187 --> 00:01:35.985
And so this one actually
looses some of its momentum.

00:01:35.985 --> 00:01:37.460
And it slows down.

00:01:37.460 --> 00:01:39.584
And just as that's happening
in the neighborhood of it,

00:01:39.584 --> 00:01:41.349
one of the other molecules is able

00:01:41.349 --> 00:01:44.112
to transfer most of its
momentum to some other molecule.

00:01:44.112 --> 00:01:45.710
So it too slows down.

00:01:45.710 --> 00:01:49.168
So it too slows down.

00:01:49.488 --> 00:01:51.508
So they all have much smaller momentum.

00:01:51.508 --> 00:01:53.586
And then maybe this one,
at the exact same time

00:01:53.586 --> 00:01:54.921
is able to do it.

00:01:54.921 --> 00:01:59.217
So it slows down, so it slows down here.

00:01:59.217 --> 00:02:01.585
And then the other ones that got

00:02:01.585 --> 00:02:03.396
the momentum transferred to them,

00:02:03.396 --> 00:02:04.627
they're all moving faster now.

00:02:04.627 --> 00:02:06.984
So lets say that one got their
momentum transferred to it.

00:02:06.984 --> 00:02:09.050
That one got momentum transferred to it.

00:02:09.050 --> 00:02:11.187
That one got momentum transferred to it.

00:02:11.187 --> 00:02:13.218
That one got momentum transferred to it.

00:02:13.218 --> 00:02:15.552
And, this one got momentum
transferred to it.

00:02:15.552 --> 00:02:18.385
And now, these molecules right over here,

00:02:18.385 --> 00:02:20.091
their momentum is small enough,

00:02:20.091 --> 00:02:21.717
their velocities are small enough,

00:02:21.717 --> 00:02:24.480
that the hydrogen bonds

00:02:24.480 --> 00:02:25.920
really take over and they're able to start

00:02:25.920 --> 00:02:28.752
forming some form of a lattice structure.

00:02:28.752 --> 00:02:30.917
They're getting cold
enough, you could say,

00:02:30.917 --> 00:02:33.001
to actually freeze.

00:02:33.123 --> 00:02:36.635
So these are turning into ice.

00:02:36.861 --> 00:02:38.208
Why can't that happen?

00:02:38.208 --> 00:02:40.251
What I've just described,
I'm just talking about

00:02:40.251 --> 00:02:42.585
things colliding and
transferring their momentum.

00:02:42.585 --> 00:02:45.708
I'm talking about energy not
being created or destroyed.

00:02:45.708 --> 00:02:49.086
So it seems to fit in with the
first law of Thermodynamics.

00:02:49.086 --> 00:02:52.987
So it seems like, theoretically,
maybe it is possible

00:02:52.987 --> 00:02:56.087
for ice to spontaneously form.

00:02:56.087 --> 00:02:57.748
Or maybe another way to think about it,

00:02:57.748 --> 00:03:01.056
maybe it is possible to
start off with a system

00:03:01.056 --> 00:03:02.554
that is fairly uniform.

00:03:02.554 --> 00:03:04.621
It has an average temperature here.

00:03:04.621 --> 00:03:06.618
But maybe a cold pocket could form

00:03:06.618 --> 00:03:08.452
by the rest of it turning hot.

00:03:08.452 --> 00:03:12.905
So, maybe initially, all
of the water is 70 degrees.

00:03:13.061 --> 00:03:14.884
So, everything I'm showing you

00:03:14.884 --> 00:03:17.909
is a neutral 70 degrees Fahrenheit.

00:03:18.053 --> 00:03:20.793
But maybe, there's some
probability that spontaneously,

00:03:20.793 --> 00:03:23.127
I have no creation or loss of energy,

00:03:23.127 --> 00:03:25.019
but some of the energy from the middle

00:03:25.019 --> 00:03:28.067
gets put into the outside, so it warms up.

00:03:28.479 --> 00:03:30.540
So, let me do this in a different color.

00:03:30.743 --> 00:03:32.752
So maybe all of this water outside,

00:03:32.752 --> 00:03:35.050
maybe this is a top-down
view of the water.

00:03:35.050 --> 00:03:37.878
Maybe all of this water heats up.

00:03:38.185 --> 00:03:39.822
Maybe all that water heats up.

00:03:39.822 --> 00:03:41.819
And all the water in
the middle, cools down.

00:03:41.819 --> 00:03:43.758
But they have the same total,

00:03:43.758 --> 00:03:46.091
they have the same total kinetic energy.

00:03:46.091 --> 00:03:48.321
So I haven't created or lost energy,

00:03:48.321 --> 00:03:51.084
it's just happened to
be that, spontaneously,

00:03:51.084 --> 00:03:54.160
I was able to transfer energy
from the middle, outwards.

00:03:54.160 --> 00:03:56.053
And even as the middle
got a little bit colder,

00:03:56.053 --> 00:03:58.154
I was able to transfer
more and more energy

00:03:58.154 --> 00:04:01.092
from the cold, the cold water,

00:04:01.092 --> 00:04:02.821
to the hot water.

00:04:02.821 --> 00:04:05.085
And it gets ordered in this way.

00:04:05.085 --> 00:04:08.220
This is actually, it feels possible,

00:04:08.220 --> 00:04:11.552
due to some of the physics
that we already know.

00:04:11.552 --> 00:04:14.640
But, some thoughtful folks,
like these gentlemen here,

00:04:14.640 --> 00:04:17.659
this is Carnot, considered
the father of Thermodynamics.

00:04:17.659 --> 00:04:19.946
Kelvin, Rudolf Clausius.

00:04:19.946 --> 00:04:22.152
They repeatedly observed,
this doesn't seem to be

00:04:22.152 --> 00:04:23.673
happening in nature.

00:04:23.673 --> 00:04:25.391
Specially when you get
to the characters like

00:04:25.391 --> 00:04:26.552
Kelvin and Clausius.

00:04:26.552 --> 00:04:28.421
They're saying, "hey look,
it doesn't look like we're

00:04:28.421 --> 00:04:31.394
"observing transfer of heat

00:04:31.394 --> 00:04:33.750
"from cold to hot.

00:04:33.750 --> 00:04:36.061
"And, since we're not observing it,

00:04:36.061 --> 00:04:38.754
"lets just add our own Second
Law of Thermodynamics".

00:04:38.754 --> 00:04:40.786
The Second Law of
Thermodynamics is really based

00:04:40.786 --> 00:04:42.853
on empirical observation.

00:04:42.853 --> 00:04:44.385
And the Second Law of Thermodynamics,

00:04:44.385 --> 00:04:45.813
according to Rudolf Clausius,

00:04:45.813 --> 00:04:47.253
and I'm gonna paraphrase this,

00:04:47.253 --> 00:04:49.157
is that we don't see spontaneous,

00:04:49.157 --> 00:04:50.515
let me write this down.

00:04:50.515 --> 00:04:55.169
Second Law of

00:04:55.169 --> 00:05:00.105
Thermodynamics.

00:05:00.227 --> 00:05:02.560
He said, we don't see
a spontaneous transfer

00:05:02.560 --> 00:05:06.519
of heat from cold areas to hot areas.

00:05:06.519 --> 00:05:09.155
So Second Law of Thermodynamics.

00:05:09.155 --> 00:05:13.380
So no transfer, no spontaneous.

00:05:13.392 --> 00:05:15.761
We can use work,

00:05:15.761 --> 00:05:17.693
like things like refrigeration equipment

00:05:17.693 --> 00:05:21.717
to make heat flow

00:05:21.717 --> 00:05:24.190
from cold to hot and cool something down.

00:05:24.190 --> 00:05:26.971
But no spontaneous transfer,

00:05:27.220 --> 00:05:30.256
transfer of heat,

00:05:31.922 --> 00:05:36.922
from cold to hot.

00:05:38.099 --> 00:05:40.455
And maybe I'll underline hot

00:05:40.455 --> 00:05:42.487
in orange right over here.

00:05:42.487 --> 00:05:44.020
And this was just really
based on observation,

00:05:44.020 --> 00:05:45.552
because we don't spontaneously
see this happening,

00:05:45.552 --> 00:05:49.221
we don't see the water
randomly organizing itself

00:05:49.221 --> 00:05:51.415
into a hot region and a cold region,

00:05:51.415 --> 00:05:52.948
and getting so cold that maybe

00:05:52.948 --> 00:05:54.654
some of it will spontaneously freeze.

00:05:54.654 --> 00:05:56.117
What we do observe is that

00:05:56.117 --> 00:05:58.056
if I were to put ice water
in the middle of a room

00:05:58.056 --> 00:05:59.252
at room temperature,

00:05:59.252 --> 00:06:00.157
I'm gonna see the other way.

00:06:00.157 --> 00:06:03.861
I'm gonna see transfer of heat

00:06:03.861 --> 00:06:06.166
from, let me draw a cup here.

00:06:06.427 --> 00:06:08.656
I'm gonna see transfer of heat

00:06:08.656 --> 00:06:11.349
from the warmer regions
to the colder regions.

00:06:11.349 --> 00:06:14.502
So, these are ice cubes right over here.

00:06:14.786 --> 00:06:16.034
And,

00:06:17.723 --> 00:06:19.401
this is the water.

00:06:19.685 --> 00:06:21.770
This is the water right over here.

00:06:21.822 --> 00:06:23.656
We're gonna see the
transferred heat the other way,

00:06:23.656 --> 00:06:27.093
from the cold regions, to the hot regions.

00:06:27.093 --> 00:06:28.846
Now, this was an empirical observation

00:06:28.846 --> 00:06:31.388
and it seemed to hold
up to experimentation.

00:06:31.388 --> 00:06:33.972
But why do we actually see that?

00:06:34.128 --> 00:06:36.648
And it turns out, that there's some

00:06:36.648 --> 00:06:39.991
super, super, duper,
duper, small probability

00:06:39.991 --> 00:06:41.187
that this could actually happen.

00:06:41.187 --> 00:06:42.894
Remember in real systems
that we're talking about.

00:06:42.894 --> 00:06:45.053
And Thermodynamics is
really the study of systems

00:06:45.053 --> 00:06:47.724
more than individual molecules
that we're talking about.

00:06:47.724 --> 00:06:48.710
Any system we're talking about,

00:06:48.710 --> 00:06:51.450
we're talking about way more molecules,

00:06:51.450 --> 00:06:54.051
way more actors than just
three molecules here.

00:06:54.051 --> 00:06:56.077
We could be talking about...

00:06:56.582 --> 00:06:58.451
Well, if you look at
the number of molecules

00:06:58.451 --> 00:06:59.415
in a glass of water,

00:06:59.415 --> 00:07:01.261
you're looking at things with

00:07:01.261 --> 00:07:04.291
20, 24, 25 zeros,

00:07:04.291 --> 00:07:07.008
depending on the size
of your glass of water.

00:07:07.008 --> 00:07:09.388
So you're looking at a huge,
huge number of molecules.

00:07:09.388 --> 00:07:10.955
And so statistically.

00:07:10.955 --> 00:07:12.476
And the didn't think
about things statistically

00:07:12.476 --> 00:07:14.252
until Boltzmann comes along.

00:07:14.252 --> 00:07:17.747
But statistically, the odds
of this happening are so low.

00:07:17.747 --> 00:07:19.187
Specially when you're thinking about,

00:07:19.187 --> 00:07:20.417
I'm not talking about
just three molecules,

00:07:20.417 --> 00:07:21.961
I'm talking about

00:07:21.961 --> 00:07:24.690
way, way more than three molecules

00:07:24.690 --> 00:07:27.865
that you're just never
going to actually see it.

00:07:27.987 --> 00:07:29.461
And you can think about this,

00:07:29.461 --> 00:07:32.637
if we were to allow
ourselves to look at the

00:07:33.060 --> 00:07:34.419
molecular level of things.

00:07:34.419 --> 00:07:36.184
To not just look at the macro level.

00:07:36.184 --> 00:07:37.943
You could see why this is.

00:07:38.088 --> 00:07:39.777
So, if you,

00:07:40.317 --> 00:07:42.865
if you were to have some
type of a container.

00:07:43.347 --> 00:07:44.839
Let me draw a container here.

00:07:45.657 --> 00:07:47.533
If you were to have a container.

00:07:48.119 --> 00:07:51.393
And you have, on the left-hand side,

00:07:51.393 --> 00:07:54.766
lets say you start with a bunch
of molecules that are hot.

00:07:54.980 --> 00:07:57.076
So they have a high kinetic energy.

00:07:57.558 --> 00:07:59.787
So these are, these have

00:07:59.787 --> 00:08:02.707
a high average kinetic energy here.

00:08:03.618 --> 00:08:05.006
These molecules.

00:08:06.242 --> 00:08:07.606
And,

00:08:07.786 --> 00:08:09.585
on the right side of the container,

00:08:09.585 --> 00:08:11.989
you have, maybe some molecules.

00:08:11.989 --> 00:08:13.556
And maybe they're the
same type of molecule,

00:08:13.556 --> 00:08:15.536
but they have low kinetic energy.

00:08:16.041 --> 00:08:17.695
So their temperature,

00:08:17.759 --> 00:08:19.791
on average they have a
lower kinetic energy.

00:08:19.791 --> 00:08:20.986
They might have a few that

00:08:20.986 --> 00:08:22.055
have high kinetic energy.

00:08:22.055 --> 00:08:24.542
But on average, the have
a lower kinetic energy.

00:08:24.992 --> 00:08:28.823
So we see that the, we see,

00:08:28.823 --> 00:08:30.983
that the temperature here is lower.

00:08:30.983 --> 00:08:32.336
So let me write this down.

00:08:32.457 --> 00:08:33.723
Right now where we're starting off,

00:08:33.723 --> 00:08:36.840
this has a lower temperature.

00:08:37.055 --> 00:08:39.992
While the left-hand side
has a higher temperature.

00:08:39.992 --> 00:08:41.490
Now what's going to happen?

00:08:41.490 --> 00:08:43.591
These molecules, they can
interact with each other.

00:08:43.591 --> 00:08:45.054
They're gonna bounce into each other.

00:08:45.054 --> 00:08:47.190
The things with high kinetic energy,

00:08:47.190 --> 00:08:48.491
they're gonna bump into the things

00:08:48.491 --> 00:08:49.593
with low kinetic energy.

00:08:49.593 --> 00:08:50.952
And all of these things are also going

00:08:50.952 --> 00:08:52.461
to get mixed together.

00:08:52.461 --> 00:08:53.924
But even if somehow you weren't mixing it,

00:08:53.924 --> 00:08:55.654
these things would be bumping into these

00:08:55.654 --> 00:08:57.906
and transferring their momentum.

00:08:57.906 --> 00:09:00.925
So, as time goes on you're going to have,

00:09:00.925 --> 00:09:03.706
you're going to have a system
that looks more like this.

00:09:03.851 --> 00:09:05.894
Where all of them are going to have

00:09:05.894 --> 00:09:08.251
more of a medium,

00:09:08.251 --> 00:09:10.190
or on average, a medium kinetic energy.

00:09:10.190 --> 00:09:11.594
There's still gonna be differences

00:09:11.594 --> 00:09:13.150
in their kinetic energies,

00:09:13.150 --> 00:09:15.890
but they're not gonna
be divided in this way

00:09:15.890 --> 00:09:17.638
between left and right.

00:09:17.852 --> 00:09:21.771
So you're gonna see it all mixed in,

00:09:21.823 --> 00:09:25.015
and you're gonna see that,

00:09:25.015 --> 00:09:26.316
neither the left of the right

00:09:26.316 --> 00:09:28.609
is going to have a higher temperature.

00:09:28.789 --> 00:09:31.157
And so what is the net effect?

00:09:31.157 --> 00:09:33.479
Well we had a transfer of energy

00:09:33.479 --> 00:09:36.643
from the hotter molecules
to the colder molecules.

00:09:36.788 --> 00:09:39.354
So, that energy that we're talking about,

00:09:39.354 --> 00:09:40.724
that is heat.

00:09:40.724 --> 00:09:42.734
We use Q to denote the heat.

00:09:42.734 --> 00:09:45.066
We have a transferred
energy from hot to cold.

00:09:45.066 --> 00:09:48.514
It's statistically
unlikely, very unlikely,

00:09:48.514 --> 00:09:50.012
bordering on impossible,

00:09:50.012 --> 00:09:52.821
but there's an infinitely
small chance it happens,

00:09:52.821 --> 00:09:54.319
it's just it wont be observed.

00:09:54.319 --> 00:09:55.294
Then you could go the other way,

00:09:55.294 --> 00:09:56.153
but that's not what we see.

00:09:56.153 --> 00:09:58.972
What we're talking about many, many, many,

00:09:58.972 --> 00:09:59.985
not even millions.

00:09:59.985 --> 00:10:01.958
Millions of millions
of millions of millions

00:10:01.958 --> 00:10:03.386
of molecules.

00:10:03.386 --> 00:10:05.685
You're gonna see the ones
with the higher kinetic energy

00:10:05.685 --> 00:10:08.054
on average mix in and transfer it

00:10:08.054 --> 00:10:10.085
to the ones with lower kinetic energy.

00:10:10.085 --> 00:10:11.490
And so that's why they were able to say

00:10:11.490 --> 00:10:13.313
"hey we don't see any
spontaneous transfer of heat

00:10:13.313 --> 00:10:14.555
"from cold to hot".

00:10:14.555 --> 00:10:16.854
It is always going from,

00:10:16.854 --> 00:10:20.111
It is always going from hot to cold.


Reading stem and leaf plots

WEBVTT
Kind: captions
Language: en

00:00:00.660 --> 00:00:03.380
The government created the
following stem-and-leaf plot

00:00:03.380 --> 00:00:07.200
showing the number of turtles at
each major zoo in the country.

00:00:07.200 --> 00:00:10.630
How many zoos have
fewer than 46 turtles?

00:00:10.630 --> 00:00:12.900
So what the
stem-and-leaf plot does

00:00:12.900 --> 00:00:15.150
is it gives us the first
digit in each number

00:00:15.150 --> 00:00:17.600
and essentially you could
call this the tens place.

00:00:17.600 --> 00:00:19.100
And then it gives
us the ones place.

00:00:19.100 --> 00:00:21.570
So there was only one zoo
that had four turtles.

00:00:21.570 --> 00:00:26.130
So you could view this
as 0, 0, 4, or 4 turtles.

00:00:26.130 --> 00:00:30.510
Then everything here,
the tens place, is a 1.

00:00:30.510 --> 00:00:33.160
So this number right
here is really an 11.

00:00:33.160 --> 00:00:34.800
This is a 14.

00:00:34.800 --> 00:00:37.790
This right over
here would be a 16.

00:00:37.790 --> 00:00:40.510
That's a 16, and
so forth and so on.

00:00:40.510 --> 00:00:42.160
This would be 17, 18.

00:00:42.160 --> 00:00:43.350
All of this is 23.

00:00:43.350 --> 00:00:44.060
This is 23.

00:00:44.060 --> 00:00:46.660
This is 26 because we have our
tens place right over here.

00:00:46.660 --> 00:00:48.120
This is the first digit.

00:00:48.120 --> 00:00:49.350
So let's answer the question.

00:00:49.350 --> 00:00:52.940
How many zoos have
fewer than 46 turtles?

00:00:52.940 --> 00:00:56.670
So there are no zoos that
had 40 anything turtles.

00:00:56.670 --> 00:00:58.770
And so all of these zoos
here-- so all of these

00:00:58.770 --> 00:01:01.990
had 30 something turtles,
these had 20 something turtles,

00:01:01.990 --> 00:01:04.519
these have in the teens,
this has single digits.

00:01:04.519 --> 00:01:07.190
So it's literally as many
zoos as we have listed here.

00:01:07.190 --> 00:01:16.164
So 1, 2, 3, 4, 5, 6, 7, 8, 9,
10, 11, 12, 13, 14, 15, 16, 17.

00:01:16.164 --> 00:01:19.610
17 zoos have fewer
than 46 turtles.

00:01:19.610 --> 00:01:21.700
Let's do another one.

00:01:21.700 --> 00:01:23.384
The buyer for a
chain of supermarkets

00:01:23.384 --> 00:01:25.050
created the following
stem-and-leaf plot

00:01:25.050 --> 00:01:28.060
showing the number of coconuts
at each of the stores.

00:01:28.060 --> 00:01:32.370
What was the smallest number
of coconuts at any one grocery

00:01:32.370 --> 00:01:33.274
store?

00:01:33.274 --> 00:01:34.940
So the buyer for a
chain of supermarkets

00:01:34.940 --> 00:01:36.606
created the following
stem-and-leaf plot

00:01:36.606 --> 00:01:39.580
showing the number of coconuts
at each of the stores.

00:01:39.580 --> 00:01:42.750
So at any one grocery store
the smallest number-- well,

00:01:42.750 --> 00:01:44.710
that's this one right over here.

00:01:44.710 --> 00:01:45.835
And remember, it's not two.

00:01:45.835 --> 00:01:47.501
We have our tens
places right over here.

00:01:47.501 --> 00:01:48.100
It's a one.

00:01:48.100 --> 00:01:49.516
So this right over
here represents

00:01:49.516 --> 00:01:51.380
12 coconuts at that store.

00:01:51.380 --> 00:01:53.940
So we'll put 12 right over here.

00:01:53.940 --> 00:01:55.770
Let's try another one.

00:01:55.770 --> 00:01:58.344
A statistician for a
chain of department stores

00:01:58.344 --> 00:02:00.010
created the following
stem-and-leaf plot

00:02:00.010 --> 00:02:02.950
showing the number of watches
at each of the stores.

00:02:02.950 --> 00:02:06.830
How many department stores
have exactly seven watches?

00:02:06.830 --> 00:02:11.210
Well that's only this one
right over here-- 07 watches.

00:02:11.210 --> 00:02:14.770
This one, this, this,
and that one are not 7.

00:02:14.770 --> 00:02:17.910
This is representing 17
because it's in the row with 1

00:02:17.910 --> 00:02:18.950
at the beginning.

00:02:18.950 --> 00:02:22.560
This right over
here represents 27

00:02:22.560 --> 00:02:24.730
because it's in the row
with the 2 at the beginning.

00:02:24.730 --> 00:02:29.100
So there's only one store that
has exactly seven watches.

00:02:29.100 --> 00:02:29.890
Let's do one more.

00:02:29.890 --> 00:02:31.390
This is kind of fun.

00:02:31.390 --> 00:02:33.910
A zookeeper created the
following stem-and-leaf plot

00:02:33.910 --> 00:02:36.520
showing the number of tigers at
each major zoo in the country.

00:02:36.520 --> 00:02:39.790
How many zoos have
more than 24 tigers?

00:02:39.790 --> 00:02:42.840
So we can ignore the
zeros and the teens

00:02:42.840 --> 00:02:44.110
and we get in the 20s.

00:02:44.110 --> 00:02:45.200
This is 25.

00:02:45.200 --> 00:02:46.460
So that meets the criteria.

00:02:46.460 --> 00:02:48.880
And then you go to 28, 29.

00:02:48.880 --> 00:02:51.810
So all of these in the 30s and
all of these right over here.

00:02:51.810 --> 00:02:53.720
This 3, 0-- this
doesn't mean 0 tigers.

00:02:53.720 --> 00:02:54.870
This is 30 tigers.

00:02:54.870 --> 00:02:56.520
This is 40 tigers.

00:02:56.520 --> 00:03:02.480
So we count 1, 2, 3,
4, 5, 6, 7, 8, 9, 9

00:03:02.480 --> 00:03:05.420
zoos have more than 24 tigers.

00:03:05.420 --> 00:03:06.650
9 zoos.

00:03:06.650 --> 00:03:08.400
And we're done.


Solving ratio problems with graph

WEBVTT
Kind: captions
Language: en

00:00:00.850 --> 00:00:03.860
In a recent gum-chewing
contest, Violet

00:00:03.860 --> 00:00:08.621
tried to blow the biggest
blueberry-flavored bubble ever.

00:00:08.621 --> 00:00:12.320
Every 3 seconds, she
added 1 piece of gum

00:00:12.320 --> 00:00:14.540
to her huge bubble.

00:00:14.540 --> 00:00:18.350
On the graph below, the x-axis
represents time in seconds.

00:00:18.350 --> 00:00:20.800
So this right over
here is our x-axis.

00:00:20.800 --> 00:00:25.080
And the y-axis represents pieces
of gum in Violet's bubble.

00:00:25.080 --> 00:00:27.640
So this is the y-axis
right over here.

00:00:27.640 --> 00:00:30.060
Plot points to show
how many pieces of gum

00:00:30.060 --> 00:00:33.830
were in Violet's bubble
after 3, 6, and 9 seconds.

00:00:33.830 --> 00:00:36.070
So every 3 seconds, she
adds one piece of gum.

00:00:36.070 --> 00:00:39.530
So let me throw
all of my-- so what

00:00:39.530 --> 00:00:45.210
we care is about 3 seconds,
6 seconds, and 9 seconds.

00:00:45.210 --> 00:00:49.270
So every 3 seconds, we know
that she adds one piece of gum.

00:00:49.270 --> 00:00:50.880
This is 0 right over here.

00:00:50.880 --> 00:00:52.930
We're not going to worry
about negative time.

00:00:52.930 --> 00:00:57.770
So after 3 seconds, she would
have added one piece of gum

00:00:57.770 --> 00:00:59.550
to her bubble.

00:00:59.550 --> 00:01:03.300
Now, if 3 more seconds pass by,
she would have added 1 more,

00:01:03.300 --> 00:01:06.770
and now she would have 2
pieces of gum in her bubble.

00:01:06.770 --> 00:01:10.160
And then if 3 more seconds pass
by, now we're at 9 seconds,

00:01:10.160 --> 00:01:11.970
she would have added
1 more piece of gum,

00:01:11.970 --> 00:01:14.340
and now we're at 3
total pieces of gum.

00:01:14.340 --> 00:01:17.320
And notice, the ratio
between the pieces of gum

00:01:17.320 --> 00:01:19.500
and the time that has
passed has stayed constant,

00:01:19.500 --> 00:01:21.340
because she's doing
it at a constant rate.

00:01:21.340 --> 00:01:25.350
1 to 3 is the same
ratio as 2 to 6,

00:01:25.350 --> 00:01:29.410
which is the same
ratio as 3 to 9.

00:01:29.410 --> 00:01:31.840
So, let's check our answer.

00:01:31.840 --> 00:01:33.700
Very good.


Solving ratio problems with tables example 2

WEBVTT
Kind: captions
Language: en

00:00:00.840 --> 00:00:03.890
We're told Ryan and
Sabrina are running a race.

00:00:03.890 --> 00:00:07.987
Ryan runs 3 miles
every 17 minutes.

00:00:07.987 --> 00:00:09.320
And we see that right over here.

00:00:09.320 --> 00:00:10.160
This is Ryan.

00:00:10.160 --> 00:00:13.330
After 17 minutes,
he's run 3 miles.

00:00:13.330 --> 00:00:15.910
And Sabrina runs 5
miles every 29 minutes.

00:00:15.910 --> 00:00:17.160
And we see it right over here.

00:00:17.160 --> 00:00:20.930
After 29 minutes,
she has run 5 miles.

00:00:20.930 --> 00:00:24.870
The tables below show each
of their distance over time.

00:00:24.870 --> 00:00:27.080
Who runs at a faster rate?

00:00:27.080 --> 00:00:29.590
Ryan or Sabrina?

00:00:29.590 --> 00:00:33.350
So these are hard to compare
directly-- 3 miles every 17

00:00:33.350 --> 00:00:36.230
minutes versus 5 miles
every 29 minutes.

00:00:36.230 --> 00:00:38.770
So what you want to do is
find a point on this table

00:00:38.770 --> 00:00:41.740
where the ratios between
time and distance

00:00:41.740 --> 00:00:43.420
are easier to compare.

00:00:43.420 --> 00:00:44.990
And the easiest
ones to compare are

00:00:44.990 --> 00:00:47.080
when you have the
same numerator or you

00:00:47.080 --> 00:00:48.312
have the same denominator.

00:00:48.312 --> 00:00:49.270
So let's see over here.

00:00:49.270 --> 00:00:51.270
Are there any points in
which the numerators are

00:00:51.270 --> 00:00:55.080
the same or the
denominators are the same?

00:00:55.080 --> 00:01:00.430
Well, it looks like over
here, it took Ryan 85 minutes

00:01:00.430 --> 00:01:03.740
to go 15 miles, and it
looks like it took Sabrina

00:01:03.740 --> 00:01:07.270
87 minutes to go 15 miles.

00:01:07.270 --> 00:01:10.500
So it took Sabrina 2 more
minutes to go 15 miles,

00:01:10.500 --> 00:01:12.520
so she is clearly a
little bit slower.

00:01:12.520 --> 00:01:14.310
Ryan's a little bit faster.

00:01:14.310 --> 00:01:17.650
So Ryan runs at a faster rate.

00:01:17.650 --> 00:01:19.206
Let's check our answer.

00:01:19.206 --> 00:01:20.330
Let's do one more of these.

00:01:20.330 --> 00:01:22.210
These are a lot of fun.

00:01:22.210 --> 00:01:25.990
The following table shows
equivalent fractions to 9/100.

00:01:25.990 --> 00:01:26.490
Fair enough.

00:01:26.490 --> 00:01:30.110
The table shows equivalent
fractions to 99/1000.

00:01:30.110 --> 00:01:32.110
And then they ask us,
which fraction is greater?

00:01:32.110 --> 00:01:36.100
9/100 or 99/1,000?

00:01:36.100 --> 00:01:39.030
And this actually is not
so hard to compare even

00:01:39.030 --> 00:01:39.910
without the tables.

00:01:39.910 --> 00:01:42.285
You could multiply the numerator
and the denominator here

00:01:42.285 --> 00:01:47.110
by 1,000, or by 10, and
you would get 90/1,000.

00:01:47.110 --> 00:01:51.860
And comparing that to 99/1,000,
and 90/1,000 is clearly

00:01:51.860 --> 00:01:58.970
smaller, so you could say that
9/100 is less than 99/1,000.

00:01:58.970 --> 00:02:01.350
But another way to do it
is to look at the tables,

00:02:01.350 --> 00:02:04.965
is to look at a point where
you have the same numerator

00:02:04.965 --> 00:02:06.290
or denominator.

00:02:06.290 --> 00:02:11.585
And you see that 9/1,000 is
the same thing as 450/5,000 And

00:02:11.585 --> 00:02:19.820
99/1,000 is the same thing as
495/5,000 So you have the same

00:02:19.820 --> 00:02:22.800
denominator, but this
numerator is larger.

00:02:22.800 --> 00:02:25.810
99/1,000 is a larger number.

00:02:25.810 --> 00:02:28.440
And we mark that
right over there.


Solving ratio problems with tables example 1

WEBVTT
Kind: captions
Language: en

00:00:00.670 --> 00:00:06.060
We're told this table shows
equivalent ratios to 24 to 40.

00:00:06.060 --> 00:00:07.820
Fill in the missing values.

00:00:07.820 --> 00:00:10.450
And they write the ratio
24 to 40 right over here.

00:00:10.450 --> 00:00:14.720
24-- when the numerator is
24, the denominator is 40.

00:00:14.720 --> 00:00:16.631
So in that way, you
could think of 24/40.

00:00:16.631 --> 00:00:18.630
But then they want us to
write equivalent ratios

00:00:18.630 --> 00:00:20.520
where we have to fill
in different blanks

00:00:20.520 --> 00:00:22.090
over here-- here
in the denominator

00:00:22.090 --> 00:00:23.370
and here in the numerator.

00:00:23.370 --> 00:00:25.994
And there's a bunch of ways that
we could actually tackle this.

00:00:25.994 --> 00:00:27.994
But maybe the easiest is
to start with the ratio

00:00:27.994 --> 00:00:29.535
that they gave us,
where they gave us

00:00:29.535 --> 00:00:31.410
both the numerator
and the denominator,

00:00:31.410 --> 00:00:32.710
and then move from there.

00:00:32.710 --> 00:00:35.640
So for example, if we look
at this one right over here,

00:00:35.640 --> 00:00:36.950
the numerator is 12.

00:00:36.950 --> 00:00:39.220
It is half of the 24.

00:00:39.220 --> 00:00:42.310
So the denominator is also going
to be half of the denominator

00:00:42.310 --> 00:00:42.810
here.

00:00:42.810 --> 00:00:44.460
It's going to be half of 40.

00:00:44.460 --> 00:00:48.000
So we could stick a
20 right over there.

00:00:48.000 --> 00:00:49.500
And then we could go up here.

00:00:49.500 --> 00:00:52.960
If you compare the 3 to
the 12, to go from 12 to 3,

00:00:52.960 --> 00:00:54.460
you have to divide by 4.

00:00:54.460 --> 00:00:56.474
So in the numerator,
you're dividing by 4.

00:00:56.474 --> 00:00:58.640
So in the denominator, you
also want to divide by 4.

00:00:58.640 --> 00:01:01.889
So 20 divided by 4 is 5.

00:01:01.889 --> 00:01:03.430
And then we have
one more to fill in,

00:01:03.430 --> 00:01:04.881
this numerator right over here.

00:01:04.881 --> 00:01:07.380
And we see from the denominator,
we doubled the denominator.

00:01:07.380 --> 00:01:09.880
We went from 40 to 80.

00:01:09.880 --> 00:01:11.810
So we would double
the numerator as well,

00:01:11.810 --> 00:01:14.240
and so you would get 48.

00:01:14.240 --> 00:01:17.370
And what we just did here is we
wrote four equivalent ratios.

00:01:17.370 --> 00:01:21.730
The ratio 3 to 5 or 3/5 is
the same thing as 12 to 20,

00:01:21.730 --> 00:01:26.830
is the same thing as 24 to 40,
is the same thing as 48 to 80.

00:01:26.830 --> 00:01:28.800
Let's make sure we
got the right answer.

00:01:28.800 --> 00:01:31.470
Let's do a couple more of these.

00:01:31.470 --> 00:01:37.280
The following table shows
equivalent fractions to 27/75.

00:01:37.280 --> 00:01:41.130
So then they wrote all of the
different equivalent fractions.

00:01:41.130 --> 00:01:45.180
This table shows ratios
equivalent to 18/55.

00:01:45.180 --> 00:01:45.930
Fair enough.

00:01:45.930 --> 00:01:50.280
All right, so these are
all equivalent to 27/75.

00:01:50.280 --> 00:01:54.910
These are all equivalent
to 18/55, so all of these.

00:01:54.910 --> 00:02:01.480
Which fraction is
greater, 27/75 or 18/55?

00:02:01.480 --> 00:02:03.100
So this is an interesting thing.

00:02:03.100 --> 00:02:05.190
What we want to do-- because
you look at these two things.

00:02:05.190 --> 00:02:06.390
And you're like,
well, I don't know.

00:02:06.390 --> 00:02:07.990
Their denominators
are different.

00:02:07.990 --> 00:02:09.740
How do I compare them?

00:02:09.740 --> 00:02:12.000
And the best way that I
can think of comparing them

00:02:12.000 --> 00:02:15.950
is look at a point where you're
getting an equivalent fraction.

00:02:15.950 --> 00:02:18.646
And either the numerators
are going to be the same,

00:02:18.646 --> 00:02:20.520
or the denominators are
going to be the same.

00:02:20.520 --> 00:02:22.800
So let's see if there's
any situation here.

00:02:22.800 --> 00:02:30.300
So you have this situation
where we see 27/75 is 54/150.

00:02:30.300 --> 00:02:34.140
And over here, we see
that 18/55 is 54--

00:02:34.140 --> 00:02:36.190
and this 54 jumped
out at me because it's

00:02:36.190 --> 00:02:39.100
the same numerator-- over 165.

00:02:39.100 --> 00:02:40.920
And that makes the
comparison much easier.

00:02:40.920 --> 00:02:42.520
What is smaller?

00:02:42.520 --> 00:02:45.716
54/150 or 54/165?

00:02:48.410 --> 00:02:50.150
Well, if you have
the same numerator,

00:02:50.150 --> 00:02:53.630
having a larger denominator
will make the number smaller.

00:02:53.630 --> 00:02:58.790
So 54/165 is smaller than
54/150, which tells us

00:02:58.790 --> 00:03:03.802
that 18/55 is
smaller than 27/75.

00:03:03.802 --> 00:03:05.010
So let's see, which of these?

00:03:05.010 --> 00:03:10.030
So this is saying that
27/75 is greater than 18/55,

00:03:10.030 --> 00:03:12.460
and that is absolutely right.

00:03:12.460 --> 00:03:16.220
And let's do one more of these.

00:03:16.220 --> 00:03:18.840
Lunara's friends
are running a race.

00:03:18.840 --> 00:03:22.910
Each of them runs at a constant
speed starting at time 0.

00:03:22.910 --> 00:03:25.950
Which of these tables might
show the distances one

00:03:25.950 --> 00:03:29.337
of Lunara's friends
traveled over time?

00:03:29.337 --> 00:03:30.420
So they're running a race.

00:03:30.420 --> 00:03:33.110
Each of them runs at a constant
speed starting at time 0.

00:03:33.110 --> 00:03:38.560
So table 1-- so
distance run in meters.

00:03:38.560 --> 00:03:41.550
So they're running
at a constant speed.

00:03:41.550 --> 00:03:45.340
So really, the ratio
between distance and time

00:03:45.340 --> 00:03:49.770
should be constant throughout
all of these possible tables.

00:03:49.770 --> 00:03:51.910
So here you have
a ratio of 3 to 2.

00:03:51.910 --> 00:03:55.290
If you triple the distance,
we're tripling the time.

00:03:55.290 --> 00:03:58.090
If you multiply
the distance by 5,

00:03:58.090 --> 00:04:00.400
we're multiplying the time by 5.

00:04:00.400 --> 00:04:02.850
So table 1 seems
completely reasonable.

00:04:02.850 --> 00:04:03.620
Let's keep going.

00:04:03.620 --> 00:04:08.280
Table 2-- 11 to 4
and then 12 to 5.

00:04:08.280 --> 00:04:09.720
Here, it's just
incrementing by 1,

00:04:09.720 --> 00:04:11.210
but the ratios are not the same.

00:04:11.210 --> 00:04:14.170
11 to 4 is not the
same thing as 12 to 5.

00:04:14.170 --> 00:04:18.589
So we're not going to be able
to-- this right over here

00:04:18.589 --> 00:04:23.100
is not a legitimate table.

00:04:23.100 --> 00:04:26.210
Table 3-- so 1 to 1.

00:04:26.210 --> 00:04:28.980
Then when you double the
distance, we double the time.

00:04:28.980 --> 00:04:33.180
When you triple the
distance from 1,

00:04:33.180 --> 00:04:34.490
you didn't triple the time.

00:04:34.490 --> 00:04:37.050
So table 3 doesn't seem
to make sense, either.

00:04:37.050 --> 00:04:40.480
Table 4-- so 14 to 10.

00:04:40.480 --> 00:04:42.530
So that's the same
thing as-- let's see,

00:04:42.530 --> 00:04:45.920
that's the same ratio as, if
we were to divide by 2, as

00:04:45.920 --> 00:04:48.280
7 to 5 ratio.

00:04:48.280 --> 00:04:52.170
If we divide both of these by
3, this is also a 7 to 5 ratio.

00:04:52.170 --> 00:04:55.140
And if you divide both of these
by 7, this is also a 7 to 5

00:04:55.140 --> 00:04:55.980
ratio.

00:04:55.980 --> 00:05:01.130
So table 4 seems like a
completely reasonable scenario.

00:05:01.130 --> 00:05:04.740
And we can check our
answer, and it is.


Understanding division of fractions

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:02.840
Let's think about what
it means to take 8/3

00:00:02.840 --> 00:00:04.790
and divide it by 1/3.

00:00:04.790 --> 00:00:07.500
So let me draw a
number line here.

00:00:07.500 --> 00:00:10.010
So there is my number line.

00:00:10.010 --> 00:00:11.510
This is 0.

00:00:11.510 --> 00:00:13.880
This is 1.

00:00:13.880 --> 00:00:16.230
And this is 2.

00:00:16.230 --> 00:00:18.610
Maybe this is 3 right over here.

00:00:18.610 --> 00:00:20.210
And let me plot 8/3.

00:00:20.210 --> 00:00:23.560
So to do that, I just need
to break up each whole

00:00:23.560 --> 00:00:24.800
into thirds.

00:00:24.800 --> 00:00:25.380
So let's see.

00:00:25.380 --> 00:00:35.520
That's 1/3, 2/3, 3/3,
4/3, 5/3, 6/3, 7/3, 8/3.

00:00:35.520 --> 00:00:36.390
So right over here.

00:00:36.390 --> 00:00:38.690
And then of course,
9/3 would get us to 3.

00:00:38.690 --> 00:00:40.456
So this right over here is 8/3.

00:00:43.050 --> 00:00:45.980
Now, one way to think
about 8/3 divided by 3

00:00:45.980 --> 00:00:48.920
is what if we take this length.

00:00:48.920 --> 00:00:50.700
And we say, how
many jumps would it

00:00:50.700 --> 00:00:53.950
take to get there, if we're
doing it in jumps of 1/3?

00:00:53.950 --> 00:00:55.790
Or essentially, we're
breaking this up.

00:00:55.790 --> 00:00:59.690
If we were to break up
8/3 into sections of 1/3,

00:00:59.690 --> 00:01:03.510
how many sections would I have,
or how many jumps would I have?

00:01:03.510 --> 00:01:05.220
Well, let's think about that.

00:01:05.220 --> 00:01:07.560
If we're trying to
take jumps of 1/3,

00:01:07.560 --> 00:01:17.500
we're going to have to go 1,
2, 3, 4, 5, 6, 7, 8 jumps.

00:01:17.500 --> 00:01:20.080
So we could view
this as-- let me

00:01:20.080 --> 00:01:21.630
do this in a different color.

00:01:21.630 --> 00:01:22.713
I'll do it in this orange.

00:01:22.713 --> 00:01:25.390
So we took these 8
jumps right over here.

00:01:25.390 --> 00:01:31.530
So we could view 8/3 divided
by 1/3 as being equal to 8.

00:01:31.530 --> 00:01:34.640
Now, why does this
actually make sense?

00:01:34.640 --> 00:01:37.480
Well, when you're dividing
things into thirds,

00:01:37.480 --> 00:01:41.460
for every whole, you're
now going to have 3 jumps.

00:01:41.460 --> 00:01:43.680
So whatever value
you're trying to get to,

00:01:43.680 --> 00:01:47.040
you're going to have that
number times 3 jumps.

00:01:47.040 --> 00:01:57.000
So another way of thinking about
it is that 8/3 divided by 1/3

00:01:57.000 --> 00:02:03.526
is the same thing
as 8/3 times 3.

00:02:03.526 --> 00:02:05.150
And we could either
write it like this.

00:02:05.150 --> 00:02:08.250
We could write
times 3 like that.

00:02:08.250 --> 00:02:10.130
Or, if we want to
write 3 as a fraction,

00:02:10.130 --> 00:02:12.725
we know that 3 is the
same thing as 3/1.

00:02:15.280 --> 00:02:18.110
And we already know how
to multiply fractions.

00:02:18.110 --> 00:02:19.770
Multiply the numerators.

00:02:19.770 --> 00:02:20.930
8 times 3.

00:02:20.930 --> 00:02:23.870
So you have 8-- let me
do that that same color.

00:02:23.870 --> 00:02:29.410
You have 8 times 3 in the
numerator now, 8 times 3.

00:02:29.410 --> 00:02:31.585
And then you have 3 times
1 in the denominator.

00:02:38.030 --> 00:02:42.080
Which would give you 24/3, which
is the same thing as 24 divided

00:02:42.080 --> 00:02:52.424
by 3, which once
again is equal to 8.

00:02:52.424 --> 00:02:54.090
Now let's see if this
still makes sense.

00:02:54.090 --> 00:02:58.130
Instead of dividing by 1/3,
if we were to divide by 2/3.

00:02:58.130 --> 00:03:02.875
So let's think about what
8/3 divided by 2/3 is.

00:03:07.660 --> 00:03:10.370
Well, once again, this is
like asking the question,

00:03:10.370 --> 00:03:13.800
if we wanted to break up
this section from 0 to 8/3

00:03:13.800 --> 00:03:17.580
into sections of
2/3, or jumps of 2/3,

00:03:17.580 --> 00:03:20.910
how many sections, or how many
jumps, would I have to make?

00:03:20.910 --> 00:03:22.210
Well, think about it.

00:03:22.210 --> 00:03:25.350
1 jump-- we'll do this
in a different color.

00:03:25.350 --> 00:03:27.595
We could make 1 jump.

00:03:27.595 --> 00:03:29.960
No, that's the same
color as my 8/3.

00:03:29.960 --> 00:03:32.520
We could do 1 jump.

00:03:32.520 --> 00:03:35.230
My computer is doing
something strange.

00:03:35.230 --> 00:03:42.490
We could do 1 jump, 2
jumps, 3 jumps, and 4 jumps.

00:03:42.490 --> 00:03:49.270
So we see 8/3 divided
by 2/3 is equal to 4.

00:03:49.270 --> 00:03:52.770
Now, does this make sense in
this world right over here?

00:03:52.770 --> 00:03:56.974
Well, if we take 8/3 and we
do the same thing, saying hey,

00:03:56.974 --> 00:03:58.890
look, dividing by a
fraction is the same thing

00:03:58.890 --> 00:04:00.920
as multiplying by a reciprocal.

00:04:00.920 --> 00:04:03.950
Well, let's multiply by 3/2.

00:04:03.950 --> 00:04:07.505
Let's multiply by the
reciprocal of 2/3.

00:04:07.505 --> 00:04:09.380
So we swap the numerator
and the denominator.

00:04:09.380 --> 00:04:11.830
So we multiply it times 3/2.

00:04:11.830 --> 00:04:13.460
And then what do we get?

00:04:13.460 --> 00:04:18.930
In the numerator, once again,
we get 8 times 3, which is 24.

00:04:18.930 --> 00:04:23.250
And in the denominator, we
get 3 times 2, which is 6.

00:04:23.250 --> 00:04:27.400
So now we get 24 divided
by 6 is equal to 4.

00:04:27.400 --> 00:04:29.604
Now, does it make sense
that we got half the answer?

00:04:29.604 --> 00:04:31.520
If you think about the
difference between what

00:04:31.520 --> 00:04:33.850
we did here and
what we did here,

00:04:33.850 --> 00:04:36.447
these are almost the same,
except here we really just

00:04:36.447 --> 00:04:37.030
didn't divide.

00:04:37.030 --> 00:04:41.070
Or you could say you divided by
1, while here you divided by 2.

00:04:41.070 --> 00:04:42.600
Well, does that make sense?

00:04:42.600 --> 00:04:43.160
Well, sure.

00:04:43.160 --> 00:04:47.270
Because here you
jumped twice as far.

00:04:47.270 --> 00:04:50.300
So you had to take half
the number of steps.

00:04:50.300 --> 00:04:52.160
And so in the first
example, you saw

00:04:52.160 --> 00:04:54.500
why it makes sense
to multiply by 3.

00:04:54.500 --> 00:04:58.100
When you divide by a
fraction, for every whole,

00:04:58.100 --> 00:05:00.280
you're making 3 jumps.

00:05:00.280 --> 00:05:04.070
So that's why when you
divide by this fraction,

00:05:04.070 --> 00:05:06.200
or whatever is in
the denominator,

00:05:06.200 --> 00:05:07.720
you multiply by it.

00:05:07.720 --> 00:05:11.120
And now when the numerator
is greater than 1,

00:05:11.120 --> 00:05:12.910
every jump you're
going twice as far

00:05:12.910 --> 00:05:14.970
as you did in this first
one right over here.

00:05:14.970 --> 00:05:18.090
And so you would have to
do half as many jumps.

00:05:18.090 --> 00:05:20.150
Hopefully that makes sense.

00:05:20.150 --> 00:05:22.030
It's easy to think
about just mechanically

00:05:22.030 --> 00:05:24.480
how to divide fractions.

00:05:24.480 --> 00:05:29.350
Taking 8/3 divided by 1/3 is
the same thing as 8/3 times 3/1.

00:05:29.350 --> 00:05:34.940
Or 8/3 divided by 2/3 is the
same thing as 8/3 times 3/2.

00:05:34.940 --> 00:05:37.660
But hopefully this video
gives you a little bit more

00:05:37.660 --> 00:05:41.310
of an intuition of
why this is the case.


Introduction to entropy

WEBVTT
Kind: captions
Language: en

00:00:00.143 --> 00:00:03.719
What I want to do in this video
is start exploring entropy.

00:00:03.719 --> 00:00:06.923
When you first get exposed
to the idea entropy

00:00:06.923 --> 00:00:08.386
it seems a little bit mysterious.

00:00:08.386 --> 00:00:11.242
But as we do more videos we'll
hopefully build a very strong

00:00:11.242 --> 00:00:12.565
intuition of what it is.

00:00:12.565 --> 00:00:15.073
So one of the more typical definitions,

00:00:15.073 --> 00:00:17.023
or a lot of the definitions
you'll see of entropy,

00:00:17.023 --> 00:00:20.367
they'll involve the word disorder.

00:00:20.367 --> 00:00:23.664
So it might be considered
the disorder of a system.

00:00:30.820 --> 00:00:33.787
Now with just that
definition in your head,

00:00:33.787 --> 00:00:36.156
I want you to pause this video
and I want you to compare

00:00:36.156 --> 00:00:38.222
this system to this system.

00:00:38.222 --> 00:00:39.964
I want you to compare
this room to this room,

00:00:39.964 --> 00:00:43.028
and ask yourself, which
of these has more entropy.

00:00:43.028 --> 00:00:47.347
And then I want you to compare
the moon here to the sun,

00:00:47.347 --> 00:00:49.158
and these clearly aren't
at scale, the sun would

00:00:49.158 --> 00:00:51.991
be way more massive or way larger

00:00:51.991 --> 00:00:53.315
if I was drawing it to scale.

00:00:53.315 --> 00:00:55.961
But which of these
systems has more entropy?

00:00:55.961 --> 00:00:59.142
Alright, so I'm assuming
you've had a go at it.

00:00:59.142 --> 00:01:01.998
So when you look at
these rooms you might say

00:01:01.998 --> 00:01:05.087
okay this room over
here, this looks ordered,

00:01:05.087 --> 00:01:07.246
It's a clean room.

00:01:07.246 --> 00:01:10.148
And this over here looks
disordered, it's a messy room.

00:01:12.876 --> 00:01:15.345
So if all you had is this
definition, you'd say okay

00:01:15.345 --> 00:01:16.645
maybe this one is more disordered,

00:01:16.645 --> 00:01:18.154
maybe this one has more entropy.

00:01:18.154 --> 00:01:20.615
And you wouldn't be
alone in thinking that.

00:01:20.615 --> 00:01:22.241
In fact, even in a lot
of textbooks they'll use

00:01:22.241 --> 00:01:25.073
this analogy of a clean
room verses a messy room.

00:01:25.073 --> 00:01:27.047
And the messy room
somehow being indicative

00:01:27.047 --> 00:01:28.626
of having more entropy.

00:01:28.626 --> 00:01:30.646
But this isn't exactly the case.

00:01:30.646 --> 00:01:33.130
This form of disorder
is not the same thing

00:01:33.130 --> 00:01:34.872
as this form of disorder.

00:01:34.872 --> 00:01:37.705
So let me make this very, very clear.

00:01:37.705 --> 00:01:39.434
So something being messy,

00:01:43.364 --> 00:01:44.902
does not equal entropy.

00:01:48.882 --> 00:01:51.538
To think about what disorder
means in the entropy sense

00:01:51.538 --> 00:01:54.115
we're going to have to
flex our visualization

00:01:54.115 --> 00:01:55.531
of muscles a little bit more,

00:01:55.531 --> 00:01:56.948
but hopefully it'll all sink in.

00:01:56.948 --> 00:02:00.640
Entropy, this kind of a
disorder is more of the number

00:02:00.640 --> 00:02:02.869
of states that a system can take on.

00:02:02.869 --> 00:02:05.353
What do I mean by states of a system?

00:02:06.543 --> 00:02:09.360
Well if I have a container like this,

00:02:10.210 --> 00:02:14.091
and if I have four molecules

00:02:14.091 --> 00:02:15.554
that are bouncing around.

00:02:15.554 --> 00:02:20.554
So I have this magenta molecule,
I have this blue molecule,

00:02:23.951 --> 00:02:28.918
I have this yellow
molecule right over here,

00:02:31.678 --> 00:02:33.098
and then I have a green molecule.

00:02:33.098 --> 00:02:36.674
Well this would be a particular state,

00:02:36.674 --> 00:02:38.043
a particular configuration.

00:02:38.043 --> 00:02:40.574
But that system these
molecules are bouncing around

00:02:40.574 --> 00:02:42.316
could take on other configurations.

00:02:42.316 --> 00:02:43.779
Or it could take on other states.

00:02:43.779 --> 00:02:47.169
Or maybe the yellow molecule is over here,

00:02:47.169 --> 00:02:48.771
they bounce around enough
for the yellow molecule

00:02:48.771 --> 00:02:51.766
to get there, the blue
molecule to get over here,

00:02:51.766 --> 00:02:56.365
maybe the pink molecule is now over here,

00:02:56.365 --> 00:03:00.845
and the green molecule is now over here.

00:03:01.535 --> 00:03:03.935
And so a system can take on
a bunch of different states.

00:03:03.935 --> 00:03:05.607
I've just drawn two
states for this system.

00:03:05.607 --> 00:03:07.859
But there could be many, many
more states for this system.

00:03:07.859 --> 00:03:10.901
So each of these are a
particular state for the system.

00:03:10.901 --> 00:03:15.034
So imagine this system
where I have this box with

00:03:15.034 --> 00:03:16.659
the four molecules in it,

00:03:16.659 --> 00:03:18.852
and let's compare it to another system

00:03:21.802 --> 00:03:23.273
where I have a larger box.

00:03:25.693 --> 00:03:27.400
And let's say it has even
more molecules in it.

00:03:27.400 --> 00:03:31.946
Let's say that it has
two yellow molecules,

00:03:33.596 --> 00:03:36.790
let's say that is has a blue molecule,

00:03:36.790 --> 00:03:39.867
let's say that it has a green molecule,

00:03:39.867 --> 00:03:44.036
let's say that it has a
magenta molecule, this is fun.

00:03:44.036 --> 00:03:47.937
Let's say it has a mauve
molecule right over here.

00:03:47.937 --> 00:03:50.607
So this system that is
larger, there's more places

00:03:50.607 --> 00:03:52.186
for the molecules to
be and there's actually

00:03:52.186 --> 00:03:53.301
more molecules in it.

00:03:53.301 --> 00:03:55.576
This can actually take
on more configurations

00:03:55.576 --> 00:03:56.598
or more states.

00:03:58.398 --> 00:03:59.661
I've just drawn one of
them but there's many more.

00:03:59.661 --> 00:04:01.937
If you imagine these
molecules all bouncing around

00:04:01.937 --> 00:04:05.118
in different ways there's
many, many different states

00:04:05.118 --> 00:04:06.186
that it could take on.

00:04:06.186 --> 00:04:07.695
So the system without even knowing

00:04:07.695 --> 00:04:09.018
what the actual molecules are doing

00:04:09.018 --> 00:04:11.503
at that given moment in
time, we would say that

00:04:11.503 --> 00:04:14.127
there's more possible states

00:04:18.687 --> 00:04:21.041
relative to this one, this
has fewer possible states.

00:04:28.361 --> 00:04:31.230
And because this system over
here has more possible states,

00:04:31.230 --> 00:04:33.969
more configurations, it would take more

00:04:33.969 --> 00:04:37.127
to tell you exactly where everything is.

00:04:37.127 --> 00:04:39.217
We would say that this has more entropy.

00:04:43.797 --> 00:04:46.128
So when we talk about disorder,
we're really talking about

00:04:46.128 --> 00:04:48.659
the number of states something could have.

00:04:48.659 --> 00:04:51.514
And it makes sense that
this thing you could imagine

00:04:51.514 --> 00:04:53.627
there's a lot more stuff moving around

00:04:53.627 --> 00:04:55.276
and a lot more different
directions and they have

00:04:55.276 --> 00:04:56.530
a lot more space to move around.

00:04:56.530 --> 00:04:58.364
So it makes sense that
the system as a whole

00:04:58.364 --> 00:04:59.479
has more entropy.

00:04:59.479 --> 00:05:01.777
So when we talk about entropy
we're not talking about

00:05:01.777 --> 00:05:03.960
any one of the particular states,

00:05:03.960 --> 00:05:06.073
any one of the particular configurations,

00:05:06.073 --> 00:05:07.977
we're talking about the system as a whole

00:05:07.977 --> 00:05:11.065
without really knowing exactly
where the molecules are.

00:05:11.065 --> 00:05:13.364
In this example with the rooms,

00:05:13.364 --> 00:05:15.221
we're just talking
about particular states.

00:05:15.221 --> 00:05:19.261
Messy is a particular state,
clean is a particular state.

00:05:19.261 --> 00:05:21.351
But we're not talking about
the number of configurations

00:05:21.351 --> 00:05:23.185
that a room could actually have.

00:05:23.185 --> 00:05:25.855
In fact if this room is
larger, this room actually

00:05:25.855 --> 00:05:30.308
could have more configurations.

00:05:30.308 --> 00:05:31.823
And if we're talking
about the molecular level

00:05:31.823 --> 00:05:34.354
if this room was warm
and this room were cold,

00:05:34.354 --> 00:05:36.977
and actually if this room is
just larger, it's going to have

00:05:36.977 --> 00:05:38.022
more molecules in it.

00:05:38.022 --> 00:05:39.415
And those molecules are going to be

00:05:39.415 --> 00:05:41.505
in way more configurations
that they could be arranged

00:05:41.505 --> 00:05:43.847
so there could be an argument that this

00:05:43.867 --> 00:05:45.419
actually has a higher entropy.

00:05:45.419 --> 00:05:47.718
And so using that same
reasoning, let's go back

00:05:47.718 --> 00:05:50.319
to that comparison of
the moon and the sun.

00:05:50.319 --> 00:05:52.176
Which of these would have more entropy?

00:05:52.176 --> 00:05:54.057
Well let's think about it.

00:05:54.057 --> 00:05:58.794
The sun is larger, it has
way, way more molecules

00:05:58.794 --> 00:06:01.626
and those molecules are
moving around way faster

00:06:01.626 --> 00:06:03.948
and they're hotter and they're
moving past each other.

00:06:03.948 --> 00:06:07.222
While the moon is small, it's
cold, it has fewer molecules.

00:06:09.972 --> 00:06:10.979
It's for the most part rigid,

00:06:10.979 --> 00:06:12.953
it doesn't have a very high
temperature so these things

00:06:12.953 --> 00:06:14.160
aren't moving around a lot.

00:06:14.160 --> 00:06:17.387
It has way fewer states,
way fewer configurations

00:06:17.387 --> 00:06:18.757
than the sun does.

00:06:18.757 --> 00:06:21.265
So the sun's entropy, if
you view it as a system.

00:06:21.265 --> 00:06:25.932
If you view the sun as a system,
it's entropy is way higher

00:06:25.932 --> 00:06:27.460
than the moon.

00:06:30.670 --> 00:06:35.670
It's entropy is much larger
than the entropy of the moon.

00:06:36.258 --> 00:06:38.069
Think about it, how much
information you would need.

00:06:38.069 --> 00:06:40.159
You would need a lot of
information if someone wanted

00:06:40.159 --> 00:06:42.272
to tell you where every molecule

00:06:42.272 --> 00:06:44.524
or every atom on the moon is.

00:06:44.524 --> 00:06:46.823
But you would need even more
to know where every atom

00:06:46.823 --> 00:06:49.144
or molecule for in a given
moment on the sun is.

00:06:49.144 --> 00:06:50.677
If you're just looking at
the sun, wow all these things

00:06:50.677 --> 00:06:53.277
are moving around and
it's this huge volume.

00:06:53.277 --> 00:06:55.994
And they're very energetic
and all of these molecules.

00:06:55.994 --> 00:06:58.223
So hopefully this starts
to give you a sense

00:06:58.223 --> 00:06:59.338
of what entropy is.

00:06:59.338 --> 00:07:00.545
And you might say okay this is all

00:07:00.545 --> 00:07:02.449
fun intellectual discussion,
what's the big deal?

00:07:02.449 --> 00:07:05.212
But the big deal is that to some degree

00:07:05.212 --> 00:07:08.579
you can describe the
universe in terms of entropy.

00:07:08.579 --> 00:07:12.480
As we learn in the second
law of thermodynamics,

00:07:12.480 --> 00:07:15.893
the entropy in the universe
is constantly increasing.

00:07:15.893 --> 00:07:18.354
We are constantly moving to a universe

00:07:18.354 --> 00:07:20.304
with more possible states,

00:07:20.304 --> 00:07:24.001
which has all sorts of
interesting implications.


First Law of Thermodynamics introduction

WEBVTT
Kind: captions
Language: en

00:00:00.078 --> 00:00:02.111
- [Voiceover] Let's now explore the first

00:00:02.111 --> 00:00:04.094
law of thermodynamics.

00:00:04.094 --> 00:00:06.291
And before even talking
about the first law of

00:00:06.291 --> 00:00:08.312
thermodynamics, some
of you might be saying,

00:00:08.312 --> 00:00:09.961
"Well, what are thermodynamics?"

00:00:09.961 --> 00:00:12.331
And you could tell from
the roots of this word.

00:00:12.331 --> 00:00:14.270
You have thermo, related to thermal,

00:00:14.270 --> 00:00:15.826
it's dealing with temperature.

00:00:15.826 --> 00:00:18.403
And the dynamics, the
properties of temperature,

00:00:18.403 --> 00:00:20.838
how do they move, how
does temperature behave?

00:00:20.838 --> 00:00:22.781
And that's pretty much
what thermodynamics is,

00:00:22.781 --> 00:00:25.138
it's about, it's the study
of heat and temperature,

00:00:25.138 --> 00:00:27.695
and how it relates to energy and work,

00:00:27.695 --> 00:00:29.284
and how different forms of energy can be

00:00:29.284 --> 00:00:31.226
transferred from one form to another.

00:00:31.226 --> 00:00:32.725
And that's actually the heart of the

00:00:32.725 --> 00:00:35.061
first law of thermodynamics
which we touched on

00:00:35.061 --> 00:00:37.770
on the introduction to energy video.

00:00:37.770 --> 00:00:40.240
And the first law of
thermodynamics tell us

00:00:40.240 --> 00:00:42.079
that energy,

00:00:42.079 --> 00:00:44.592
this is an important one,
I'm going to write it down,

00:00:44.592 --> 00:00:47.140
energy cannot be created or destroyed.

00:00:47.140 --> 00:00:49.861
Cannot be created,

00:00:49.861 --> 00:00:53.090
or destroyed.

00:00:55.785 --> 00:00:59.786
It can only be converted
from one form to another.

00:00:59.786 --> 00:01:04.140
It can only

00:01:04.140 --> 00:01:06.976
only be converted

00:01:06.976 --> 00:01:09.956
only be converted,

00:01:09.956 --> 00:01:11.735
I'm having trouble writing today.

00:01:11.735 --> 00:01:15.110
Converted from one form,

00:01:15.110 --> 00:01:18.446
from one form,

00:01:18.446 --> 00:01:21.090
to another.

00:01:21.090 --> 00:01:23.226
Or you could transfer it
but you're not going to,

00:01:23.226 --> 00:01:25.669
you're not going to create or destroy it.

00:01:25.669 --> 00:01:27.586
And the whole thing that
I, the rest of this video

00:01:27.586 --> 00:01:30.211
I just want to really
have you internalize that,

00:01:30.211 --> 00:01:32.420
and I want to look at a bunch
of examples and think about,

00:01:32.420 --> 00:01:34.266
well, what is the energy
that we're observing,

00:01:34.266 --> 00:01:36.132
or that we're seeing in a system?

00:01:36.132 --> 00:01:37.551
And then thinking about
where is that energy

00:01:37.551 --> 00:01:39.578
coming from, to appreciate
that it's not just

00:01:39.578 --> 00:01:41.749
coming out of nowhere,
and that it's not just

00:01:41.749 --> 00:01:43.988
disappearing, it's not
getting destroyed either.

00:01:43.988 --> 00:01:47.263
And so let's start with
this example of a lightbulb.

00:01:47.263 --> 00:01:49.144
And I encourage you to pause this video,

00:01:49.144 --> 00:01:52.061
think about the forms of
energy that we can see here,

00:01:52.061 --> 00:01:54.286
and then think about where
is that energy coming from,

00:01:54.286 --> 00:01:56.226
and where is it going?

00:01:56.226 --> 00:01:59.382
Well, the most obvious form
of energy that you see here,

00:01:59.382 --> 00:02:01.556
and this, the whole point of a lightbulb,

00:02:01.556 --> 00:02:03.738
is you see the radiant energy, you see the

00:02:03.738 --> 00:02:06.519
you see the electromagnetic
waves, the light,

00:02:06.519 --> 00:02:08.200
being emitted from it.

00:02:08.200 --> 00:02:11.040
And that light, so this is radiant energy.

00:02:11.040 --> 00:02:14.104
Radiant energy.

00:02:14.104 --> 00:02:18.300
And that radiant energy,

00:02:18.300 --> 00:02:22.197
is due to the heat in the
filament right over here,

00:02:22.197 --> 00:02:25.272
as the electrons go through
it, it generates heat,

00:02:25.272 --> 00:02:27.274
so you have thermal energy.

00:02:27.274 --> 00:02:30.050
So you have thermal energy as well.

00:02:30.050 --> 00:02:32.935
Thermal energy.

00:02:32.935 --> 00:02:34.857
But where does this radiant and thermal

00:02:34.857 --> 00:02:36.244
energy come from?

00:02:36.244 --> 00:02:38.496
Again, first law of
thermodynamics it tells us,

00:02:38.496 --> 00:02:40.363
it's not just being
created out of thin air,

00:02:40.363 --> 00:02:43.731
it must be converted or being
transferred from some place.

00:02:43.731 --> 00:02:46.856
Well, I just gave you a
hint, this thermal energy

00:02:46.856 --> 00:02:50.008
is due to the electrons
moving through the filament.

00:02:50.008 --> 00:02:52.346
They're moving through
the filament which has

00:02:52.346 --> 00:02:54.980
some resistance, and that generates heat.

00:02:54.980 --> 00:02:58.323
So the electrons are moving through this,

00:02:58.323 --> 00:03:01.473
and as they move through that
resistor, they generate heat.

00:03:01.473 --> 00:03:04.258
So you actually have the
kinetic energy of the electrons.

00:03:04.258 --> 00:03:07.032
I'll just write KE for
short, kinetic energy

00:03:07.032 --> 00:03:09.445
of the actual electrons.

00:03:09.445 --> 00:03:11.894
Well, where is that
kinetic energy coming from?

00:03:11.894 --> 00:03:14.382
Well that's coming from
the potential energy.

00:03:14.382 --> 00:03:16.737
You know maybe this thing is plugged into,

00:03:16.737 --> 00:03:19.731
is plugged into a socket of some kind.

00:03:19.731 --> 00:03:21.646
So let me draw a little electric socket

00:03:21.646 --> 00:03:23.050
right over here.

00:03:23.050 --> 00:03:25.552
And the electric socket, I'll draw,

00:03:25.552 --> 00:03:28.436
the electric socket if
this is the electric socket

00:03:28.436 --> 00:03:30.653
in your home,

00:03:30.653 --> 00:03:33.623
there is an electrostatic
potential between

00:03:33.623 --> 00:03:35.331
these two terminals.

00:03:35.331 --> 00:03:37.100
And so when you make a connection,

00:03:37.100 --> 00:03:40.599
the electrons are able to move.

00:03:40.599 --> 00:03:42.863
And we'll get into the
details of AC and DC current

00:03:42.863 --> 00:03:46.195
in the future, but there's
an electrostatic potential,

00:03:46.195 --> 00:03:48.427
from this point to this
point if we assume that's

00:03:48.427 --> 00:03:50.236
the direction that the
electrons are going in.

00:03:50.236 --> 00:03:53.169
And so that, it's that
potential energy we convert to

00:03:53.169 --> 00:03:55.992
this kinetic energy of the electrons,

00:03:55.992 --> 00:03:57.752
which is really in the form of a current,

00:03:57.752 --> 00:04:00.349
and then that gets converted
into thermal energy

00:04:00.349 --> 00:04:02.010
and radiant energy.

00:04:02.010 --> 00:04:04.811
Now what happens after, let's
say you unplug the light,

00:04:04.811 --> 00:04:07.407
the light goes dark, what
happened to all of that energy?

00:04:07.407 --> 00:04:09.091
Is it still there?

00:04:09.091 --> 00:04:11.252
Well yeah, that thermal
energy is going to continue

00:04:11.252 --> 00:04:13.633
to dissipate through the system.

00:04:13.633 --> 00:04:15.562
And this right over here
would be an open system,

00:04:15.562 --> 00:04:16.603
it's going to,

00:04:16.603 --> 00:04:19.701
the air inside the lightbulb,
you can't fully see

00:04:19.701 --> 00:04:22.335
the lightbulb right here, but
it looks something like this.

00:04:22.335 --> 00:04:25.052
That's going to heat up, but
then it's going to heat up

00:04:25.052 --> 00:04:26.993
the glass surrounding the lightbulb,

00:04:26.993 --> 00:04:28.971
and that's going to heat
up the surrounding air.

00:04:28.971 --> 00:04:30.976
So the thermal energy is
going to be transferred,

00:04:30.976 --> 00:04:33.622
and that radiant energy
is going to move outward.

00:04:33.622 --> 00:04:35.805
And it could be used, it
could be converted into other

00:04:35.805 --> 00:04:38.148
forms of energy, most
likely thermal energy,

00:04:38.148 --> 00:04:40.861
it is also probably going
to heat up other things.

00:04:40.861 --> 00:04:42.835
Well, what about a pool table?

00:04:42.835 --> 00:04:45.537
When I hit a, if I hit a pool,

00:04:45.537 --> 00:04:47.942
a billiard ball or a pool
ball right over here,

00:04:47.942 --> 00:04:49.868
well, where is that energy going?

00:04:49.868 --> 00:04:52.058
Well some of that energy
might be going to go hit

00:04:52.058 --> 00:04:55.156
the next ball, which might
go to hit the next ball.

00:04:55.156 --> 00:04:58.176
But as we all know, if
we've ever played pool,

00:04:58.176 --> 00:05:00.108
at some point they're going to stop.

00:05:00.108 --> 00:05:01.925
So what happened to all of that energy?

00:05:01.925 --> 00:05:03.805
Well, while they were rolling,

00:05:03.805 --> 00:05:06.552
there was some air resistance,

00:05:06.552 --> 00:05:11.096
so they're bumping against
these, the air molecules,

00:05:11.096 --> 00:05:13.121
and it's really friction due to air.

00:05:13.121 --> 00:05:14.932
And that energy is essentially going to be

00:05:14.932 --> 00:05:16.215
converted to heat.

00:05:16.215 --> 00:05:17.956
And one trend that you're going to see

00:05:17.956 --> 00:05:21.565
very frequently, is as systems progress,

00:05:21.565 --> 00:05:25.756
a lot more of the energy
tends to turn into heat,

00:05:25.756 --> 00:05:28.441
rather than doing useful work.

00:05:28.441 --> 00:05:30.888
And so you're going to
have, as the billiard balls

00:05:30.888 --> 00:05:33.349
move, there's the air,
and so that's going to be,

00:05:33.349 --> 00:05:36.050
that's going to be converted,
some of that kinetic energy

00:05:36.050 --> 00:05:38.102
is going to be turned into heat energy.

00:05:38.102 --> 00:05:40.319
You're also going to have friction with

00:05:40.319 --> 00:05:42.168
the actual felt on the table.

00:05:42.168 --> 00:05:43.950
And that friction, you're
going to have molecules

00:05:43.950 --> 00:05:45.236
rubbing up against each other,

00:05:45.236 --> 00:05:48.332
that's also going to
be converted into heat.

00:05:48.332 --> 00:05:51.577
And so that, because that
kinetic energy gets sapped off,

00:05:51.577 --> 00:05:55.770
gets keeping sapped
away from the friction,

00:05:55.770 --> 00:05:58.737
which is essentially
converting the kinetic energy

00:05:58.737 --> 00:06:00.111
to heat energy, eventually you won't have

00:06:00.111 --> 00:06:01.794
any more kinetic energy.

00:06:01.794 --> 00:06:03.269
Now what about this weight lifter here?

00:06:03.269 --> 00:06:05.032
He's using the chemical energy in his,

00:06:05.032 --> 00:06:08.052
in the ATP in his muscles,
that converts into

00:06:08.052 --> 00:06:10.619
kinetic energy that moves his muscles,

00:06:10.619 --> 00:06:13.581
that moves this weight, but
once he's in this position,

00:06:13.581 --> 00:06:15.541
what happened to all of that energy?

00:06:15.541 --> 00:06:17.700
Well, a lot of that energy is
now being stored in potential.

00:06:17.700 --> 00:06:20.724
it's the potential energy,
he's got this big weight,

00:06:20.724 --> 00:06:23.103
he's got that big weight above his head,

00:06:23.103 --> 00:06:25.954
and if he were to just let
go, that thing would fall,

00:06:25.954 --> 00:06:27.596
I wouldn't recommend he do that,

00:06:27.596 --> 00:06:29.568
but that thing would fall quite fast.

00:06:29.568 --> 00:06:31.761
And so now it's all,
or a lot of it has been

00:06:31.761 --> 00:06:33.274
stored up in potential energy.

00:06:33.274 --> 00:06:34.722
But he would have also generated heat,

00:06:34.722 --> 00:06:36.304
his muscles would have generated heat.

00:06:36.304 --> 00:06:38.467
Even the act of moving it
through the air is going to be

00:06:38.467 --> 00:06:40.729
some heat in the air,
some friction with it.

00:06:40.729 --> 00:06:42.804
And so I want you to appreciate
that this energy is not

00:06:42.804 --> 00:06:46.037
coming out of nowhere,
it is being converted

00:06:46.037 --> 00:06:48.476
from one form or another,
or being transferred

00:06:48.476 --> 00:06:50.845
from one part of the system to another.

00:06:50.845 --> 00:06:53.314
Now we can look at these
examples over here.

00:06:53.314 --> 00:06:55.615
Same thing with our
runner, what happens after,

00:06:55.615 --> 00:06:58.371
you can buy the fact that
okay, his chemical energy is

00:06:58.371 --> 00:07:01.258
allowing his muscles to
move, and that's turning in

00:07:01.258 --> 00:07:05.076
his kinetic energy for his
entire body, his body is moving,

00:07:05.076 --> 00:07:08.392
but at some point he stops,
where did all that energy go?

00:07:08.392 --> 00:07:11.327
Well, some of it will be
heat in his body that's being

00:07:11.327 --> 00:07:13.947
dissipated into the broader
system, into the air.

00:07:13.947 --> 00:07:18.119
And also, when he was running,
there was this contact

00:07:18.119 --> 00:07:20.872
with the ground, that's
going to make the molecules

00:07:20.872 --> 00:07:23.430
of the ground vibrate a
little bit, some of it will be

00:07:23.430 --> 00:07:25.862
transferred as sound, so the air particles

00:07:25.862 --> 00:07:29.142
moving through the air, and
a lot of it will be heat.

00:07:29.142 --> 00:07:31.282
And we're going to see that
over and over and over again.

00:07:31.282 --> 00:07:34.203
The diver up here, you have
mostly potential energy.

00:07:34.203 --> 00:07:36.498
Then it converts to
kinetic energy as he's,

00:07:36.498 --> 00:07:38.190
as he gets almost in the water.

00:07:38.190 --> 00:07:40.028
But what happens once
he falls into the water?

00:07:40.028 --> 00:07:41.629
Well, then that energy's
going to be transferred,

00:07:41.629 --> 00:07:44.462
as you're going to have these
waves of water move away.

00:07:44.462 --> 00:07:47.136
And it will also increase
friction, so, well actually

00:07:47.136 --> 00:07:49.003
he would have had
friction as he fell down,

00:07:49.003 --> 00:07:50.780
so that would have generated some heat,

00:07:50.780 --> 00:07:52.042
and there would have
been also some heat with

00:07:52.042 --> 00:07:53.835
the friction with the water,
you normally don't think of

00:07:53.835 --> 00:07:55.922
friction with the water,
but there is some friction

00:07:55.922 --> 00:07:57.678
with the actual water, and there's also,

00:07:57.678 --> 00:08:00.193
these waves, you have
higher kinetic energy

00:08:00.193 --> 00:08:02.811
of the actual water
being transferred outward

00:08:02.811 --> 00:08:05.172
from where he actually dropped in.

00:08:05.172 --> 00:08:07.061
And I could keep going on and on.

00:08:07.061 --> 00:08:10.320
You have the chemical potential
energy of the fuel here

00:08:10.320 --> 00:08:13.085
being, you have combustion occurring,

00:08:13.085 --> 00:08:16.264
and then that gets converted
into the thermal energy,

00:08:16.264 --> 00:08:20.103
and the radiant energy of
what we associate with fire.

00:08:20.103 --> 00:08:21.520
And that doesn't disappear,

00:08:21.520 --> 00:08:23.631
it just keeps radiating outwards,

00:08:23.631 --> 00:08:25.234
the radiant energy just
keeps radiating outward,

00:08:25.234 --> 00:08:26.674
maybe it might heat up something.

00:08:26.674 --> 00:08:29.319
And the thermal energy will
just keep radiating outward,

00:08:29.319 --> 00:08:32.428
or I should say, the thermal
energy will just dissipate

00:08:32.428 --> 00:08:35.311
outward, and heat up the things around it.

00:08:35.311 --> 00:08:37.125
Same thing with our lightning example.

00:08:37.125 --> 00:08:41.049
You start with the
electrostatic potential,

00:08:41.049 --> 00:08:44.159
where the bottom of the
clouds were more negative,

00:08:44.159 --> 00:08:46.537
and then the ground is positive as well,

00:08:46.537 --> 00:08:49.312
and at some point, that
potential energy turns into

00:08:49.312 --> 00:08:53.387
kinetic energy as the electrons
transfer through the air,

00:08:53.387 --> 00:08:57.099
and then that gets converted
into, or a good bit is

00:08:57.099 --> 00:09:00.109
going to be converted to
heat and radiant energy.

00:09:00.109 --> 00:09:03.276
So the whole point of this
video is, no matter what

00:09:03.276 --> 00:09:06.443
example you look at, if you
think about it carefully enough,

00:09:06.443 --> 00:09:08.240
and I encourage you to do
this in your everyday life,

00:09:08.240 --> 00:09:10.204
the energy isn't just coming out of,

00:09:10.204 --> 00:09:11.716
you know, magically appearing,

00:09:11.716 --> 00:09:16.339
it's just being converted
from one form to another.