0:00:06.875,0:00:10.453 There's a concept that's crucial[br]to chemistry and physics. 0:00:10.453,0:00:15.293 It helps explain why physical processes[br]go one way and not the other: 0:00:15.293,0:00:16.849 why ice melts, 0:00:16.849,0:00:19.279 why cream spreads in coffee, 0:00:19.279,0:00:22.529 why air leaks out of a punctured tire. 0:00:22.529,0:00:27.039 It's entropy, and it's notoriously[br]difficult to wrap our heads around. 0:00:27.039,0:00:31.879 Entropy is often described as[br]a measurement of disorder. 0:00:31.879,0:00:35.739 That's a convenient image,[br]but it's unfortunately misleading. 0:00:35.739,0:00:38.511 For example, which is more disordered - 0:00:38.511,0:00:43.469 a cup of crushed ice or a glass[br]of room temperature water? 0:00:43.469,0:00:45.373 Most people would say the ice, 0:00:45.373,0:00:49.069 but that actually has lower entropy. 0:00:49.069,0:00:52.898 So here's another way of thinking[br]about it through probability. 0:00:52.898,0:00:57.290 This may be trickier to understand,[br]but take the time to internalize it 0:00:57.290,0:01:01.260 and you'll have a much better [br]understanding of entropy. 0:01:01.260,0:01:03.661 Consider two small solids 0:01:03.661,0:01:07.541 which are comprised [br]of six atomic bonds each. 0:01:07.541,0:01:12.781 In this model, the energy in each solid[br]is stored in the bonds. 0:01:12.781,0:01:15.292 Those can be thought of [br]as simple containers, 0:01:15.292,0:01:20.070 which can hold indivisible units of energy[br]known as quanta. 0:01:20.070,0:01:24.601 The more energy a solid has,[br]the hotter it is. 0:01:24.601,0:01:29.042 It turns out that there are numerous[br]ways that the energy can be distributed 0:01:29.042,0:01:30.552 in the two solids 0:01:30.552,0:01:34.592 and still have the same [br]total energy in each. 0:01:34.592,0:01:38.502 Each of these options [br]is called a microstate. 0:01:38.502,0:01:43.341 For six quanta of energy in Solid A[br]and two in Solid B, 0:01:43.341,0:01:47.832 there are 9,702 microstates. 0:01:47.832,0:01:52.861 Of course, there are other ways our eight[br]quanta of energy can be arranged. 0:01:52.861,0:01:57.833 For example, all of the energy[br]could be in Solid A and none in B, 0:01:57.833,0:02:00.872 or half in A and half in B. 0:02:00.872,0:02:04.154 If we assume that each microstate[br]is equally likely, 0:02:04.154,0:02:06.794 we can see that some of the energy[br]configurations 0:02:06.794,0:02:10.543 have a higher probability of occurring[br]than others. 0:02:10.543,0:02:14.184 That's due to their greater number[br]of microstates. 0:02:14.184,0:02:20.143 Entropy is a direct measure of each[br]energy configuration's probability. 0:02:20.143,0:02:23.193 What we see is that the energy[br]configuration 0:02:23.193,0:02:26.843 in which the energy[br]is most spread out between the solids 0:02:26.843,0:02:28.924 has the highest entropy. 0:02:28.924,0:02:30.474 So in a general sense, 0:02:30.474,0:02:34.853 entropy can be thought of as a measurement[br]of this energy spread. 0:02:34.853,0:02:37.893 Low entropy means [br]the energy is concentrated. 0:02:37.893,0:02:41.623 High entropy means it's spread out. 0:02:41.623,0:02:45.765 To see why entropy is useful for[br]explaining spontaneous processes, 0:02:45.765,0:02:48.075 like hot objects cooling down, 0:02:48.075,0:02:52.434 we need to look at a dynamic system[br]where the energy moves. 0:02:52.434,0:02:54.935 In reality, energy doesn't stay put. 0:02:54.935,0:02:58.065 It continuously moves between [br]neighboring bonds. 0:02:58.065,0:03:00.206 As the energy moves, 0:03:00.206,0:03:02.955 the energy configuration can change. 0:03:02.955,0:03:05.085 Because of the distribution [br]of microstates, 0:03:05.085,0:03:09.836 there's a 21% chance that the system[br]will later be in the configuration 0:03:09.836,0:03:13.595 in which the energy is maximally [br]spread out, 0:03:13.595,0:03:17.357 there's a 13% chance that it will[br]return to its starting point, 0:03:17.357,0:03:22.857 and an 8% chance that A will actually[br]gain energy. 0:03:22.857,0:03:26.935 Again, we see that because there are[br]more ways to have dispersed energy 0:03:26.935,0:03:30.026 and high entropy than concentrated energy, 0:03:30.026,0:03:32.558 the energy tends to spread out. 0:03:32.558,0:03:35.509 That's why if you put a hot object[br]next to a cold one, 0:03:35.509,0:03:40.420 the cold one will warm up[br]and the hot one will cool down. 0:03:40.420,0:03:41.867 But even in that example, 0:03:41.867,0:03:47.116 there is an 8% chance that the hot object[br]would get hotter. 0:03:47.116,0:03:51.427 Why doesn't this ever happen[br]in real life? 0:03:51.427,0:03:54.177 It's all about the size of the system. 0:03:54.177,0:03:58.057 Our hypothetical solids only had[br]six bonds each. 0:03:58.057,0:04:03.938 Let's scale the solids up to 6,000 bonds[br]and 8,000 units of energy, 0:04:03.938,0:04:07.527 and again start the system with[br]three-quarters of the energy in A 0:04:07.527,0:04:10.127 and one-quarter in B. 0:04:10.127,0:04:14.337 Now we find that chance of A[br]spontaneously acquiring more energy 0:04:14.337,0:04:17.247 is this tiny number. 0:04:17.247,0:04:22.308 Familiar, everyday objects have many, many[br]times more particles than this. 0:04:22.308,0:04:25.920 The chance of a hot object [br]in the real world getting hotter 0:04:25.920,0:04:28.011 is so absurdly small, 0:04:28.011,0:04:30.409 it just never happens. 0:04:30.409,0:04:31.528 Ice melts, 0:04:31.528,0:04:32.918 cream mixes in, 0:04:32.918,0:04:34.676 and tires deflate 0:04:34.676,0:04:39.942 because these states have more[br]dispersed energy than the originals. 0:04:39.942,0:04:43.630 There's no mysterious force[br]nudging the system towards higher entropy. 0:04:43.630,0:04:48.928 It's just that higher entropy is always[br]statistically more likely. 0:04:48.928,0:04:52.480 That's why entropy has been called[br]time's arrow. 0:04:52.480,0:04:56.739 If energy has the opportunity[br]to spread out, it will.