1
00:00:06,875 --> 00:00:10,453
There's a concept that's crucial
to chemistry and physics.

2
00:00:10,453 --> 00:00:15,293
It helps explain why physical processes
go one way and not the other:

3
00:00:15,293 --> 00:00:16,849
why ice melts,

4
00:00:16,849 --> 00:00:19,279
why cream spreads in coffee,

5
00:00:19,279 --> 00:00:22,529
why air leaks out of a punctured tire.

6
00:00:22,529 --> 00:00:27,039
It's entropy, and it's notoriously
difficult to wrap our heads around.

7
00:00:27,039 --> 00:00:31,879
Entropy is often described as
a measurement of disorder.

8
00:00:31,879 --> 00:00:35,739
That's a convenient image,
but it's unfortunately misleading.

9
00:00:35,739 --> 00:00:38,511
For example, which is more disordered -

10
00:00:38,511 --> 00:00:43,469
a cup of crushed ice or a glass
of room temperature water?

11
00:00:43,469 --> 00:00:45,373
Most people would say the ice,

12
00:00:45,373 --> 00:00:49,069
but that actually has lower entropy.

13
00:00:49,069 --> 00:00:52,898
So here's another way of thinking
about it through probability.

14
00:00:52,898 --> 00:00:57,290
This may be trickier to understand,
but take the time to internalize it

15
00:00:57,290 --> 00:01:01,260
and you'll have a much better 
understanding of entropy.

16
00:01:01,260 --> 00:01:03,661
Consider two small solids

17
00:01:03,661 --> 00:01:07,541
which are comprised 
of six atomic bonds each.

18
00:01:07,541 --> 00:01:12,781
In this model, the energy in each solid
is stored in the bonds.

19
00:01:12,781 --> 00:01:15,292
Those can be thought of 
as simple containers,

20
00:01:15,292 --> 00:01:20,070
which can hold indivisible units of energy
known as quanta.

21
00:01:20,070 --> 00:01:24,601
The more energy a solid has,
the hotter it is.

22
00:01:24,601 --> 00:01:29,042
It turns out that there are numerous
ways that the energy can be distributed

23
00:01:29,042 --> 00:01:30,552
in the two solids

24
00:01:30,552 --> 00:01:34,592
and still have the same 
total energy in each.

25
00:01:34,592 --> 00:01:38,502
Each of these options 
is called a microstate.

26
00:01:38,502 --> 00:01:43,341
For six quanta of energy in Solid A
and two in Solid B,

27
00:01:43,341 --> 00:01:47,832
there are 9,702 microstates.

28
00:01:47,832 --> 00:01:52,861
Of course, there are other ways our eight
quanta of energy can be arranged.

29
00:01:52,861 --> 00:01:57,833
For example, all of the energy
could be in Solid A and none in B,

30
00:01:57,833 --> 00:02:00,872
or half in A and half in B.

31
00:02:00,872 --> 00:02:04,154
If we assume that each microstate
is equally likely,

32
00:02:04,154 --> 00:02:06,794
we can see that some of the energy
configurations

33
00:02:06,794 --> 00:02:10,543
have a higher probability of occurring
than others.

34
00:02:10,543 --> 00:02:14,184
That's due to their greater number
of microstates.

35
00:02:14,184 --> 00:02:20,143
Entropy is a direct measure of each
energy configuration's probability.

36
00:02:20,143 --> 00:02:23,193
What we see is that the energy
configuration

37
00:02:23,193 --> 00:02:26,843
in which the energy
is most spread out between the solids

38
00:02:26,843 --> 00:02:28,924
has the highest entropy.

39
00:02:28,924 --> 00:02:30,474
So in a general sense,

40
00:02:30,474 --> 00:02:34,853
entropy can be thought of as a measurement
of this energy spread.

41
00:02:34,853 --> 00:02:37,893
Low entropy means 
the energy is concentrated.

42
00:02:37,893 --> 00:02:41,623
High entropy means it's spread out.

43
00:02:41,623 --> 00:02:45,765
To see why entropy is useful for
explaining spontaneous processes,

44
00:02:45,765 --> 00:02:48,075
like hot objects cooling down,

45
00:02:48,075 --> 00:02:52,434
we need to look at a dynamic system
where the energy moves.

46
00:02:52,434 --> 00:02:54,935
In reality, energy doesn't stay put.

47
00:02:54,935 --> 00:02:58,065
It continuously moves between 
neighboring bonds.

48
00:02:58,065 --> 00:03:00,206
As the energy moves,

49
00:03:00,206 --> 00:03:02,955
the energy configuration can change.

50
00:03:02,955 --> 00:03:05,085
Because of the distribution 
of microstates,

51
00:03:05,085 --> 00:03:09,836
there's a 21% chance that the system
will later be in the configuration

52
00:03:09,836 --> 00:03:13,595
in which the energy is maximally 
spread out,

53
00:03:13,595 --> 00:03:17,357
there's a 13% chance that it will
return to its starting point,

54
00:03:17,357 --> 00:03:22,857
and an 8% chance that A will actually
gain energy.

55
00:03:22,857 --> 00:03:26,935
Again, we see that because there are
more ways to have dispersed energy

56
00:03:26,935 --> 00:03:30,026
and high entropy than concentrated energy,

57
00:03:30,026 --> 00:03:32,558
the energy tends to spread out.

58
00:03:32,558 --> 00:03:35,509
That's why if you put a hot object
next to a cold one,

59
00:03:35,509 --> 00:03:40,420
the cold one will warm up
and the hot one will cool down.

60
00:03:40,420 --> 00:03:41,867
But even in that example,

61
00:03:41,867 --> 00:03:47,116
there is an 8% chance that the hot object
would get hotter.

62
00:03:47,116 --> 00:03:51,427
Why doesn't this ever happen
in real life?

63
00:03:51,427 --> 00:03:54,177
It's all about the size of the system.

64
00:03:54,177 --> 00:03:58,057
Our hypothetical solids only had
six bonds each.

65
00:03:58,057 --> 00:04:03,938
Let's scale the solids up to 6,000 bonds
and 8,000 units of energy,

66
00:04:03,938 --> 00:04:07,527
and again start the system with
three-quarters of the energy in A

67
00:04:07,527 --> 00:04:10,127
and one-quarter in B.

68
00:04:10,127 --> 00:04:14,337
Now we find that chance of A
spontaneously acquiring more energy

69
00:04:14,337 --> 00:04:17,247
is this tiny number.

70
00:04:17,247 --> 00:04:22,308
Familiar, everyday objects have many, many
times more particles than this.

71
00:04:22,308 --> 00:04:25,920
The chance of a hot object 
in the real world getting hotter

72
00:04:25,920 --> 00:04:28,011
is so absurdly small,

73
00:04:28,011 --> 00:04:30,409
it just never happens.

74
00:04:30,409 --> 00:04:31,528
Ice melts,

75
00:04:31,528 --> 00:04:32,918
cream mixes in,

76
00:04:32,918 --> 00:04:34,676
and tires deflate

77
00:04:34,676 --> 00:04:39,942
because these states have more
dispersed energy than the originals.

78
00:04:39,942 --> 00:04:43,630
There's no mysterious force
nudging the system towards higher entropy.

79
00:04:43,630 --> 00:04:48,928
It's just that higher entropy is always
statistically more likely.

80
00:04:48,928 --> 00:04:52,480
That's why entropy has been called
time's arrow.

81
00:04:52,480 --> 00:04:56,739
If energy has the opportunity
to spread out, it will.