WEBVTT 00:00:01.236 --> 00:00:03.866 - So far you've seen the First Law of Thermodynamics. 00:00:03.866 --> 00:00:05.367 This is what it says. 00:00:05.367 --> 00:00:06.600 Let's see how you use it. 00:00:06.600 --> 00:00:08.733 Let's look at a particular example. 00:00:08.733 --> 00:00:10.900 This one says, let's say you've got this problem, 00:00:10.900 --> 00:00:14.666 and it said 60 joules of work is done on a gas, 00:00:14.666 --> 00:00:18.933 and the gas loses 150 joules of heat to its surroundings. 00:00:18.933 --> 00:00:21.000 What is the change in internal energy? 00:00:21.000 --> 00:00:22.633 Well, we're going to use the First Law. 00:00:22.633 --> 00:00:24.466 That's what the First Law lets us determine. 00:00:24.466 --> 00:00:28.233 The change in internal energy is going to equal 00:00:28.233 --> 00:00:30.666 the amount of heat that's added to the gas. 00:00:30.666 --> 00:00:32.600 So let's see, heat added to the gas. 00:00:32.600 --> 00:00:36.614 Well it says that the gas loses 150 joules of heat 00:00:36.614 --> 00:00:37.934 to its surroundings. 00:00:37.934 --> 00:00:40.368 So that means heat left of the gas 00:00:40.368 --> 00:00:42.900 so heat left the gas. 00:00:42.900 --> 00:00:45.299 This must have been put into a cooler environment 00:00:45.299 --> 00:00:47.000 so that heat could leave. 00:00:47.000 --> 00:00:49.260 And so it lost 150 joules. 00:00:49.260 --> 00:00:51.466 A lot of people just stick 150 here. 00:00:51.466 --> 00:00:53.667 It's got to be negative 150 because 00:00:53.667 --> 00:00:55.967 this Q represents the heat added to the gas, 00:00:55.967 --> 00:00:58.870 if you lost 150 joules, it's a negative 150. 00:00:58.870 --> 00:01:02.633 And then plus, all right how much work was done. 00:01:02.633 --> 00:01:05.466 It says 60 joules of work is done on a gas 00:01:05.466 --> 00:01:08.666 so that's work done on the gas. 00:01:08.666 --> 00:01:10.984 That means it's a positive contribution 00:01:10.984 --> 00:01:12.052 to the internal energy. 00:01:12.052 --> 00:01:14.836 That's energy you're adding to the gas. 00:01:14.836 --> 00:01:18.366 So 60 joules has to be positive, 00:01:18.366 --> 00:01:23.366 and so this is plus the work done is positive 60 joules. 00:01:23.433 --> 00:01:27.666 Now we can figure it out the change in internal would be 00:01:27.666 --> 00:01:30.100 negative 90 joules. 00:01:30.100 --> 00:01:31.169 But why do we care? 00:01:31.169 --> 00:01:32.853 Why do we care about the change in 00:01:32.853 --> 00:01:34.200 internal energy of the gas? 00:01:34.200 --> 00:01:35.666 Well here's something important. 00:01:35.666 --> 00:01:40.166 Whether it's a monatomic or diatomic or triatomic molecule 00:01:40.166 --> 00:01:44.000 the internal energy of the gas is always proportional 00:01:44.000 --> 00:01:45.467 to the temperature. 00:01:45.467 --> 00:01:47.667 This means if the temperature goes up, 00:01:47.667 --> 00:01:49.366 the internal energy goes up. 00:01:49.366 --> 00:01:51.866 And it also means if the internal energy goes up, 00:01:51.866 --> 00:01:53.100 the temperature goes up. 00:01:53.100 --> 00:01:55.633 So one thing we can say, just going over here, 00:01:55.633 --> 00:01:58.933 looking that the change in internal energy was negative. 00:01:58.933 --> 00:02:02.266 This means the energy went down by 90 joules. 00:02:02.266 --> 00:02:06.286 Overall when all is said and done, this gas lost 00:02:06.286 --> 00:02:08.300 90 joules of internal energy. 00:02:08.300 --> 00:02:09.766 That means the temperature went down. 00:02:09.766 --> 00:02:12.400 That means this gas is going to be cooler 00:02:12.400 --> 00:02:15.151 when you end this process compared to when it started. 00:02:15.151 --> 00:02:18.200 Even though you added 60 joules of work energy 00:02:18.200 --> 00:02:20.966 it lost 150 joules of heat energy. 00:02:20.966 --> 00:02:22.167 That's a net loss. 00:02:22.167 --> 00:02:23.567 The temperature is going to go down. 00:02:23.567 --> 00:02:25.833 So this is an important key fact. 00:02:25.833 --> 00:02:27.333 Whatever the internal energy does, 00:02:27.333 --> 00:02:28.866 that's what the temperature does. 00:02:28.866 --> 00:02:31.766 And it makes sense since we know that an increase in 00:02:31.766 --> 00:02:35.633 internal energy means an increase in translational 00:02:35.633 --> 00:02:37.733 kinetic energy, rotational kinetic energy, 00:02:37.733 --> 00:02:39.200 vibrational energy. 00:02:39.200 --> 00:02:42.733 That temperature is also a measure of that internal energy. 00:02:42.733 --> 00:02:45.302 Note that we cannot say exactly how low 00:02:45.302 --> 00:02:46.633 the temperature went. 00:02:46.633 --> 00:02:48.666 This is a loss of 90 joules 00:02:48.666 --> 00:02:52.033 but this doesn't mean a loss of 90 degrees. 00:02:52.033 --> 00:02:53.100 These are proportional. 00:02:53.100 --> 00:02:54.300 They're not equal. 00:02:54.300 --> 00:02:55.933 If I go down 90 joules that doesn't mean 00:02:55.933 --> 00:02:57.767 I go down 90 degrees. 00:02:57.767 --> 00:03:00.400 I would have to know more about the make up of this gas 00:03:00.400 --> 00:03:01.567 in order to do that. 00:03:01.567 --> 00:03:02.566 But the internal energy 00:03:02.566 --> 00:03:04.702 and the temperature are proportional. 00:03:04.702 --> 00:03:06.033 Let's try another one. 00:03:06.033 --> 00:03:10.666 Let's say a gas started with 200 joules of internal energy 00:03:10.666 --> 00:03:13.533 and while you add 180 joules of heat to the gas, 00:03:13.533 --> 00:03:15.733 the gas does 70 joules of work. 00:03:15.733 --> 00:03:18.133 What is the final internal energy of the gas? 00:03:18.133 --> 00:03:21.600 All right, so the change in internal energy 00:03:21.600 --> 00:03:24.467 equals Q. 00:03:24.467 --> 00:03:27.233 Let's see, gas starts with 200 joules of internal energy, 00:03:27.233 --> 00:03:28.466 that's not heat. 00:03:28.466 --> 00:03:30.100 While you add 180 joules of heat, 00:03:30.100 --> 00:03:33.200 here we go, 180 joules should it be positive or negative? 00:03:33.200 --> 00:03:34.000 It's going to be positive. 00:03:34.000 --> 00:03:36.267 You're adding heat to that system. 00:03:36.267 --> 00:03:40.490 So positive 180 joules of heat are added 00:03:40.490 --> 00:03:43.600 plus the amount of work done on the gas, 00:03:43.600 --> 00:03:46.602 it says the gas does 70 joules of work. 00:03:46.602 --> 00:03:50.266 So most people would just do, all right, 70 joules. 00:03:50.266 --> 00:03:51.600 So there we go. 00:03:51.600 --> 00:03:52.833 But this is wrong. 00:03:52.833 --> 00:03:56.400 This is wrong because this is how much work the gas does. 00:03:56.400 --> 00:03:58.696 This W up here with the plus sign represents 00:03:58.696 --> 00:04:01.400 how much work was done on the gas. 00:04:01.400 --> 00:04:03.653 If the gas does 70 joules of work, 00:04:03.653 --> 00:04:07.067 negative 70 joules of work were done on the gas. 00:04:07.067 --> 00:04:08.700 You have to be really careful about that. 00:04:08.700 --> 00:04:10.600 So we can find the change in internal energy. 00:04:10.600 --> 00:04:15.600 In this case it's going to equal positive 110 joules. 00:04:15.633 --> 00:04:17.367 But that's not our answer. 00:04:17.367 --> 00:04:18.933 The question's asking us for the 00:04:18.933 --> 00:04:21.266 final internal energy of the gas. 00:04:21.266 --> 00:04:23.300 This is not the final internal energy of the gas. 00:04:23.300 --> 00:04:27.117 This is the amount by which the internal energy changed. 00:04:27.117 --> 00:04:29.300 So we know the internal energy went up, 00:04:29.300 --> 00:04:30.300 because this is positive 00:04:30.300 --> 00:04:32.266 and this is the change in internal energy. 00:04:32.266 --> 00:04:35.366 Internal energy went up by 110 joules. 00:04:35.366 --> 00:04:37.800 That means the temperature is also going to go up. 00:04:37.800 --> 00:04:39.900 So what's the final internal energy of the gas? 00:04:39.900 --> 00:04:43.400 Well, if the internal energy goes up by 110 joules 00:04:43.400 --> 00:04:46.367 and the gas started with 200 joules 00:04:46.367 --> 00:04:50.167 we know the final internal energy, U final, 00:04:50.167 --> 00:04:54.666 is just going to be 200 plus 110 is 310, 00:04:54.666 --> 00:04:57.133 or if you want to be more careful about it, 00:04:57.133 --> 00:04:58.300 you can write this out. 00:04:58.300 --> 00:05:03.300 Delta U, we can call U final, minus U initial. 00:05:03.333 --> 00:05:05.233 That's what delta U stands for. 00:05:05.233 --> 00:05:07.666 U final is what we want to find 00:05:07.666 --> 00:05:11.034 minus U initial is 200. 00:05:11.034 --> 00:05:14.466 So positive 200 joules was what the gas started with. 00:05:14.466 --> 00:05:17.233 Equals, that's the change and that's what we found, 00:05:17.233 --> 00:05:19.200 110 joules. 00:05:19.200 --> 00:05:21.200 Now you've solved this for U final. 00:05:21.200 --> 00:05:24.333 You would add 200 to both sides and again you would get 00:05:24.333 --> 00:05:29.181 310 joules as the final internal energy of the gas. 00:05:29.766 --> 00:05:30.766 Let's look at one more. 00:05:30.766 --> 00:05:33.150 Let's say you got this one on a test and it said that 00:05:33.150 --> 00:05:35.967 40 joules of work are done on a gas, 00:05:35.967 --> 00:05:39.015 and the internal energy goes down by 150 joules. 00:05:39.015 --> 00:05:41.700 What was the value of the heat added to the gas? 00:05:41.700 --> 00:05:44.633 Note we're not solving for the internal energy this time 00:05:44.633 --> 00:05:46.167 or the change in internal energy. 00:05:46.167 --> 00:05:47.500 We're trying to solve for the heat. 00:05:47.500 --> 00:05:49.500 What's heat? Heat is Q. 00:05:49.500 --> 00:05:51.366 So this time we're going to plug in for the other two 00:05:51.366 --> 00:05:52.600 and solve for Q. 00:05:52.600 --> 00:05:53.500 What do we know? 00:05:53.500 --> 00:05:56.833 40 joules of work are done on a gas, 00:05:56.833 --> 00:05:59.867 so this work has got to be a positive 40 00:05:59.867 --> 00:06:03.367 because the work is done on the gas and not by the gas. 00:06:03.367 --> 00:06:06.466 And we know the internal energy goes down by 150 joules. 00:06:06.466 --> 00:06:08.266 It means the change in internal energy 00:06:08.266 --> 00:06:10.066 has to be negative 150. 00:06:10.066 --> 00:06:12.567 So if I plug in here my delta U, 00:06:12.567 --> 00:06:15.400 since my internal energy went down by 150, 00:06:15.400 --> 00:06:18.133 delta U is going to be negative 150. 00:06:18.133 --> 00:06:19.466 Q we don't know 00:06:19.466 --> 00:06:21.366 so I'm just going to put a variable in there. 00:06:21.366 --> 00:06:22.400 Q I don't know. 00:06:22.400 --> 00:06:23.566 I'm just going to put a Q in there. 00:06:23.566 --> 00:06:24.833 I'm going to name my ignorance 00:06:24.833 --> 00:06:25.766 and I'm going to solve for it. 00:06:25.766 --> 00:06:28.100 Plus the work done. 00:06:28.100 --> 00:06:31.133 We know the work done was 40 joules and it's positive 40. 00:06:31.133 --> 00:06:34.066 Positive 40 because work was done on the gas. 00:06:34.066 --> 00:06:35.633 Now we can solve for Q. 00:06:35.633 --> 00:06:36.766 The amount of heat. 00:06:36.766 --> 00:06:40.200 The value of the heat added to the gas is going to be, 00:06:40.200 --> 00:06:42.933 if I move my 40 over here I subtract it from both sides, 00:06:42.933 --> 00:06:46.169 I'm going to get negative 190 joules. 00:06:46.169 --> 00:06:49.100 This means a lot of heat left. 00:06:49.100 --> 00:06:52.166 190 joules of heat left the system 00:06:52.166 --> 00:06:54.633 in order for it to make the internal energy 00:06:54.633 --> 00:06:56.966 go down by 150 joules. 00:06:56.966 --> 00:06:57.801 And that makes sense. 00:06:57.801 --> 00:06:59.500 40 joules of work were added. 00:06:59.500 --> 00:07:01.566 But we said the internal energy went down. 00:07:01.566 --> 00:07:03.733 That means the heat has to take away 00:07:03.733 --> 00:07:07.933 not only the 40 that you added but also another 150 00:07:07.933 --> 00:07:12.033 to make the energy go down overall so the heat taken away 00:07:12.033 --> 00:07:15.200 has to be negative 190 joules. 00:07:15.200 --> 00:07:16.633 All right, so those were a few examples 00:07:16.633 --> 00:07:18.433 of using the First Law. 00:07:18.433 --> 00:07:20.613 Basically, you've got to be careful with your positive 00:07:20.613 --> 00:07:21.900 and negative signs. 00:07:21.900 --> 00:07:23.933 You've got to remember what these things are 00:07:23.933 --> 00:07:27.000 that Q is the heat, W is the work, delta U 00:07:27.000 --> 00:07:29.000 is the change in the internal energy 00:07:29.000 --> 00:07:31.700 which don't forget that also gives you an idea 00:07:31.700 --> 00:07:33.903 of what happens to the temperature.