1 00:00:03,350 --> 00:00:07,279 The development of the incandescent light bulb took many years and relied on the talents 2 00:00:07,279 --> 00:00:12,039 of many inventors from around the world. One of the key changes was the use of an inert 3 00:00:12,039 --> 00:00:17,350 gas, rather than a vacuum, in the bulb itself. In this video, we'll use the kinetic theory 4 00:00:17,350 --> 00:00:22,590 of gases to explain why the addition of an inert gas had such a significant impact on 5 00:00:22,590 --> 00:00:27,110 the usability and longevity of the humble incandescent bulb. 6 00:00:27,110 --> 00:00:31,440 This video is part of the Governing Rules video series. A small number of rules describe 7 00:00:31,440 --> 00:00:35,659 the physical and chemical interactions that are possible in our universe. 8 00:00:35,659 --> 00:00:41,429 Hi. My name is Jeff Grossman and I am a professor in the Department of Materials Science and 9 00:00:41,429 --> 00:00:46,149 Engineering at MIT. Today, I'm going to talk to you about the 10 00:00:46,149 --> 00:00:52,539 development of the incandescent light bulb. In order to understand the topic of this video, 11 00:00:52,539 --> 00:00:56,829 you should be familiar with the kinetic theory of gases. 12 00:00:56,829 --> 00:01:01,519 After watching this video, you should be able to discuss the physical significance of a 13 00:01:01,519 --> 00:01:07,390 gas molecule's mean free path. You should also be able to discuss the physical parameters 14 00:01:07,390 --> 00:01:11,689 that affect the mean free path. 15 00:01:11,689 --> 00:01:17,240 Imagine that you are a consultant for a light bulb manufacturer. They have a problem with 16 00:01:17,240 --> 00:01:22,140 their incandescent light bulbs. After the light bulbs have been operating for a period 17 00:01:22,140 --> 00:01:28,920 of time, the inner walls of the bulb begin to blacken. This reduces the light output. 18 00:01:28,920 --> 00:01:33,189 Not a desirable outcome for a light bulb. You have been hired to figure out why this 19 00:01:33,189 --> 00:01:37,380 is happening and to determine a way to fix the problem. 20 00:01:37,380 --> 00:01:43,479 So, what questions do you have? What do you think is going on? What chemical principles 21 00:01:43,479 --> 00:01:49,960 might be important here? Take a moment to pause the video and jot down some things that 22 00:01:49,960 --> 00:01:56,960 you think might be relevant to the problem. It's okay to brainstorm with a partner. 23 00:02:02,090 --> 00:02:07,469 It may be helpful to understand a few things about the construction of the light bulb. 24 00:02:07,469 --> 00:02:14,469 Looking inside, we see that there is a coil of metal, called the filament. This filament 25 00:02:14,530 --> 00:02:20,510 is typically made of tungsten. What you can't see is that the inside of this light bulb 26 00:02:20,510 --> 00:02:27,510 is a vacuum. What would happen if there was air in the light bulb? Because the filament 27 00:02:27,770 --> 00:02:33,610 reaches such high temperatures, the filament will oxidize if oxygen is present. 28 00:02:33,610 --> 00:02:38,360 Some of you may have been wondering about the temperature of the tungsten filament. 29 00:02:38,360 --> 00:02:45,360 When the light bulb is on, the tungsten filament gets very hot, around 3000 °C. 30 00:02:45,630 --> 00:02:50,450 While this temperature is below the melting and boiling points for tungsten, the occasional 31 00:02:50,450 --> 00:02:57,450 tungsten atom sublimes and condenses on the wall of the light bulb. Not only does this 32 00:02:57,610 --> 00:03:04,480 reduce the light output of the bulb, but it also causes deterioration of the filament. 33 00:03:04,480 --> 00:03:11,230 Knowing what you know about gases, how can you explain what is happening and what solution 34 00:03:11,230 --> 00:03:17,200 might you propose? It might help to review some of the assumptions 35 00:03:17,200 --> 00:03:19,790 of the kinetic theory of gases. 36 00:03:19,790 --> 00:03:25,260 One assumption is that the molecules in a gas are separated by distances that are much 37 00:03:25,260 --> 00:03:28,870 larger than the size of the molecules themselves. 38 00:03:28,870 --> 00:03:34,000 Another is that the molecules are constantly moving in random directions. 39 00:03:34,000 --> 00:03:39,920 The molecules obey Newton's laws of motion and thus continue in straight-line motion 40 00:03:39,920 --> 00:03:46,050 until they collide with other molecules or the walls of the container. 41 00:03:46,050 --> 00:03:53,050 Gas molecules that are not in physical contact do not exert forces on one another, so between 42 00:03:53,190 --> 00:03:58,440 collisions, they move with constant velocity. Collisions between molecules or between a 43 00:03:58,440 --> 00:04:04,660 molecule and the wall of the container are assumed to be perfectly elastic. In other 44 00:04:04,660 --> 00:04:08,900 words, energy is conserved. 45 00:04:08,900 --> 00:04:14,250 What factors do you think affect a molecule's collision frequency? Pause the video and take 46 00:04:14,250 --> 00:04:20,060 a moment to think about it. 47 00:04:20,060 --> 00:04:25,330 You may have realized that the diameter of a molecule, as well as the number of molecules 48 00:04:25,330 --> 00:04:28,400 in the region will affect collision frequency. 49 00:04:28,400 --> 00:04:35,400 So when a tungsten atom evaporated off of the hot filament under vacuum, what happened? 50 00:04:35,680 --> 00:04:42,510 Pause the video and take a moment to think about it. 51 00:04:42,510 --> 00:04:47,470 The atom proceeded in a straight line, and in the absence of other molecules to collide 52 00:04:47,470 --> 00:04:54,040 with, condensed on the cool wall of the light bulb. Under vacuum, the mean free path of 53 00:04:54,040 --> 00:04:58,260 tungsten atoms in the vapor state is quite large. 54 00:04:58,260 --> 00:05:00,370 What is the mean free path? 55 00:05:00,370 --> 00:05:05,850 The mean free path is the average distance traveled by a molecule between collisions. 56 00:05:05,850 --> 00:05:11,180 The mean free path for a molecule can be approximated by the distance traveled by the molecule in 57 00:05:11,180 --> 00:05:17,280 a given time t divided by the number of collisions the molecule experienced. 58 00:05:17,280 --> 00:05:21,760 Although the molecule may exhibit a random walk and change direction with each collision 59 00:05:21,760 --> 00:05:28,220 it experiences, we are simply interested in the scalar quantity of total distance traveled. 60 00:05:28,220 --> 00:05:32,810 The total distance traveled can be found by multiplying the velocity of the molecule by 61 00:05:32,810 --> 00:05:34,240 the time. 62 00:05:34,240 --> 00:05:39,460 How do we find the number of collisions? Let's break this down. 63 00:05:39,460 --> 00:05:45,000 If we assume that the molecule is spherical with diameter d, as it moves, it will sweep 64 00:05:45,000 --> 00:05:52,000 out a cylindrical volume equal to pi*r-squared*vt. As a first approximation, let's assume that 65 00:05:53,090 --> 00:05:59,210 our molecule is moving through other gas molecules of the same diameter. Any molecule whose center 66 00:05:59,210 --> 00:06:05,550 lies within a distance r of this cylinder will collide with our molecule of interest. 67 00:06:05,550 --> 00:06:11,800 So to find the number of collisions, we need to look at the volume pi*d-squared*vt and 68 00:06:11,800 --> 00:06:16,260 multiply this by the density of gas molecules n sub v. 69 00:06:16,260 --> 00:06:21,560 We're not quite done. When looking at the number of collisions, we need to keep in mind 70 00:06:21,560 --> 00:06:28,169 that all of the gas molecules are moving, so we should use a relative velocity. The 71 00:06:28,169 --> 00:06:34,080 relative velocity is equal to square root of 2 multiplied by the average velocity. 72 00:06:34,080 --> 00:06:41,080 It would be good for you to think about how we got this. 73 00:07:03,300 --> 00:07:07,100 So now we have this expression for the mean free path. 74 00:07:07,100 --> 00:07:12,060 What would happen to the mean free path of a tungsten atom if we introduced other gas 75 00:07:12,060 --> 00:07:19,060 molecules into the bulb? Would the mean free path increase, decrease, or stay the same? 76 00:07:21,480 --> 00:07:28,480 Pause the video and take a moment to think about it. 77 00:07:29,520 --> 00:07:34,400 You might have realized that by introducing other gas molecules into the light bulb, we 78 00:07:34,400 --> 00:07:39,840 can increase the number of collisions a tungsten atom will experience and decrease its mean 79 00:07:39,840 --> 00:07:46,840 free path. Would this be desirable or undesirable? Why? 80 00:07:47,070 --> 00:07:52,940 Decreasing a tungsten atom's mean free path is desirable. While some vaporized tungsten 81 00:07:52,940 --> 00:07:57,610 atoms will still condense on the walls of the light bulb, some collisions will result 82 00:07:57,610 --> 00:08:01,520 in tungsten atoms re-condensing on the filament. 83 00:08:01,520 --> 00:08:06,479 You may have noticed blackening near the top of incandescent bulbs after they have been 84 00:08:06,479 --> 00:08:13,340 used for a while. Heat transfer from the filament to the fill gas creates convection currents 85 00:08:13,340 --> 00:08:20,229 that carry many of the vaporized tungsten atoms to the top of the bulb where they condense. 86 00:08:20,229 --> 00:08:25,330 This localized darkening allows the light output from other regions of the bulb to remain 87 00:08:25,330 --> 00:08:27,639 relatively constant. 88 00:08:27,639 --> 00:08:32,990 You can see how kinetic theory has helped us think about this problem. Of course, there 89 00:08:32,990 --> 00:08:38,169 are some other things we need to think about. For example, what gas should we use? What 90 00:08:38,169 --> 00:08:43,578 properties do you think the gas should have? Pause the video here and take a moment to 91 00:08:43,578 --> 00:08:47,309 think about it. 92 00:08:47,309 --> 00:08:54,309 Well, if we are going to fill our light bulb with gas, we probably want to use something 93 00:08:54,519 --> 00:09:01,519 that is inert to avoid undesirable reactions. For common household use, we would also want 94 00:09:02,420 --> 00:09:08,699 our fill gas to be non-toxic in case the glass breaks. And of course, low cost is always 95 00:09:08,699 --> 00:09:10,730 desirable. 96 00:09:10,730 --> 00:09:15,649 Irving Langmuir actually solved this problem when he was working at General Electric in 97 00:09:15,649 --> 00:09:22,649 the early 1900s. Langmuir chose argon as the fill gas because it is inert and non-toxic, 98 00:09:23,740 --> 00:09:28,449 but if you look at the periodic table you might ask why he didn't chose a more massive 99 00:09:28,449 --> 00:09:35,449 inert gas. Argon is much lower in cost compared to other inert gases. 100 00:09:35,869 --> 00:09:41,990 Krypton and xenon are used in more expensive light bulbs, but not in household light bulbs. 101 00:09:41,990 --> 00:09:47,410 Argon continues to be used in standard incandescent light bulbs, although the use of incandescent 102 00:09:47,410 --> 00:09:51,230 light bulbs in general is being phased out. 103 00:09:51,230 --> 00:09:58,230 To Review, we saw how kinetic theory can be used to help us analyze a real-world problem—that 104 00:09:58,329 --> 00:10:05,089 of light bulb blackening. We derived an equation to allow us to estimate a gas molecule's mean 105 00:10:05,089 --> 00:10:11,949 free path. The mean free path provides an estimate of the average distance traveled 106 00:10:11,949 --> 00:10:18,850 by a molecule between collisions. We saw that the mean free path is inversely proportional 107 00:10:18,850 --> 00:10:24,439 to the density of gas molecules. Realizing that the mean free path of tungsten atoms 108 00:10:24,439 --> 00:10:30,329 in a light bulb was too long helped us think about what parameters we might manipulate 109 00:10:30,329 --> 00:10:37,329 in order to solve our problem.