0:00:01.236,0:00:03.866 - So far you've seen the[br]First Law of Thermodynamics. 0:00:03.866,0:00:05.367 This is what it says. 0:00:05.367,0:00:06.600 Let's see how you use it. 0:00:06.600,0:00:08.733 Let's look at a particular example. 0:00:08.733,0:00:10.900 This one says, let's say[br]you've got this problem, 0:00:10.900,0:00:14.666 and it said 60 joules of[br]work is done on a gas, 0:00:14.666,0:00:18.933 and the gas loses 150 joules[br]of heat to its surroundings. 0:00:18.933,0:00:21.000 What is the change in internal energy? 0:00:21.000,0:00:22.633 Well, we're going to use the First Law. 0:00:22.633,0:00:24.466 That's what the First[br]Law lets us determine. 0:00:24.466,0:00:28.233 The change in internal[br]energy is going to equal 0:00:28.233,0:00:30.666 the amount of heat[br]that's added to the gas. 0:00:30.666,0:00:32.600 So let's see, heat added to the gas. 0:00:32.600,0:00:36.614 Well it says that the gas[br]loses 150 joules of heat 0:00:36.614,0:00:37.934 to its surroundings. 0:00:37.934,0:00:40.368 So that means heat left of the gas 0:00:40.368,0:00:42.900 so heat left the gas. 0:00:42.900,0:00:45.299 This must have been put[br]into a cooler environment 0:00:45.299,0:00:47.000 so that heat could leave. 0:00:47.000,0:00:49.260 And so it lost 150 joules. 0:00:49.260,0:00:51.466 A lot of people just stick 150 here. 0:00:51.466,0:00:53.667 It's got to be negative 150 because 0:00:53.667,0:00:55.967 this Q represents the[br]heat added to the gas, 0:00:55.967,0:00:58.870 if you lost 150 joules,[br]it's a negative 150. 0:00:58.870,0:01:02.633 And then plus, all right[br]how much work was done. 0:01:02.633,0:01:05.466 It says 60 joules of work is done on a gas 0:01:05.466,0:01:08.666 so that's work done on the gas. 0:01:08.666,0:01:10.984 That means it's a positive contribution 0:01:10.984,0:01:12.052 to the internal energy. 0:01:12.052,0:01:14.836 That's energy you're adding to the gas. 0:01:14.836,0:01:18.366 So 60 joules has to be positive, 0:01:18.366,0:01:23.366 and so this is plus the work[br]done is positive 60 joules. 0:01:23.433,0:01:27.666 Now we can figure it out the[br]change in internal would be 0:01:27.666,0:01:30.100 negative 90 joules. 0:01:30.100,0:01:31.169 But why do we care? 0:01:31.169,0:01:32.853 Why do we care about the change in 0:01:32.853,0:01:34.200 internal energy of the gas? 0:01:34.200,0:01:35.666 Well here's something important. 0:01:35.666,0:01:40.166 Whether it's a monatomic or[br]diatomic or triatomic molecule 0:01:40.166,0:01:44.000 the internal energy of the[br]gas is always proportional 0:01:44.000,0:01:45.467 to the temperature. 0:01:45.467,0:01:47.667 This means if the temperature goes up, 0:01:47.667,0:01:49.366 the internal energy goes up. 0:01:49.366,0:01:51.866 And it also means if the[br]internal energy goes up, 0:01:51.866,0:01:53.100 the temperature goes up. 0:01:53.100,0:01:55.633 So one thing we can say,[br]just going over here, 0:01:55.633,0:01:58.933 looking that the change in[br]internal energy was negative. 0:01:58.933,0:02:02.266 This means the energy[br]went down by 90 joules. 0:02:02.266,0:02:06.286 Overall when all is said[br]and done, this gas lost 0:02:06.286,0:02:08.300 90 joules of internal energy. 0:02:08.300,0:02:09.766 That means the temperature went down. 0:02:09.766,0:02:12.400 That means this gas is going to be cooler 0:02:12.400,0:02:15.151 when you end this process[br]compared to when it started. 0:02:15.151,0:02:18.200 Even though you added[br]60 joules of work energy 0:02:18.200,0:02:20.966 it lost 150 joules of heat energy. 0:02:20.966,0:02:22.167 That's a net loss. 0:02:22.167,0:02:23.567 The temperature is going to go down. 0:02:23.567,0:02:25.833 So this is an important key fact. 0:02:25.833,0:02:27.333 Whatever the internal energy does, 0:02:27.333,0:02:28.866 that's what the temperature does. 0:02:28.866,0:02:31.766 And it makes sense since[br]we know that an increase in 0:02:31.766,0:02:35.633 internal energy means an[br]increase in translational 0:02:35.633,0:02:37.733 kinetic energy, rotational kinetic energy, 0:02:37.733,0:02:39.200 vibrational energy. 0:02:39.200,0:02:42.733 That temperature is also a[br]measure of that internal energy. 0:02:42.733,0:02:45.302 Note that we cannot say exactly how low 0:02:45.302,0:02:46.633 the temperature went. 0:02:46.633,0:02:48.666 This is a loss of 90 joules 0:02:48.666,0:02:52.033 but this doesn't mean[br]a loss of 90 degrees. 0:02:52.033,0:02:53.100 These are proportional. 0:02:53.100,0:02:54.300 They're not equal. 0:02:54.300,0:02:55.933 If I go down 90 joules that doesn't mean 0:02:55.933,0:02:57.767 I go down 90 degrees. 0:02:57.767,0:03:00.400 I would have to know more[br]about the make up of this gas 0:03:00.400,0:03:01.567 in order to do that. 0:03:01.567,0:03:02.566 But the internal energy 0:03:02.566,0:03:04.702 and the temperature are proportional. 0:03:04.702,0:03:06.033 Let's try another one. 0:03:06.033,0:03:10.666 Let's say a gas started with[br]200 joules of internal energy 0:03:10.666,0:03:13.533 and while you add 180[br]joules of heat to the gas, 0:03:13.533,0:03:15.733 the gas does 70 joules of work. 0:03:15.733,0:03:18.133 What is the final internal[br]energy of the gas? 0:03:18.133,0:03:21.600 All right, so the change[br]in internal energy 0:03:21.600,0:03:24.467 equals Q. 0:03:24.467,0:03:27.233 Let's see, gas starts with[br]200 joules of internal energy, 0:03:27.233,0:03:28.466 that's not heat. 0:03:28.466,0:03:30.100 While you add 180 joules of heat, 0:03:30.100,0:03:33.200 here we go, 180 joules should[br]it be positive or negative? 0:03:33.200,0:03:34.000 It's going to be positive. 0:03:34.000,0:03:36.267 You're adding heat to that system. 0:03:36.267,0:03:40.490 So positive 180 joules of heat are added 0:03:40.490,0:03:43.600 plus the amount of work done on the gas, 0:03:43.600,0:03:46.602 it says the gas does 70 joules of work. 0:03:46.602,0:03:50.266 So most people would just[br]do, all right, 70 joules. 0:03:50.266,0:03:51.600 So there we go. 0:03:51.600,0:03:52.833 But this is wrong. 0:03:52.833,0:03:56.400 This is wrong because this is[br]how much work the gas does. 0:03:56.400,0:03:58.696 This W up here with the[br]plus sign represents 0:03:58.696,0:04:01.400 how much work was done on the gas. 0:04:01.400,0:04:03.653 If the gas does 70 joules of work, 0:04:03.653,0:04:07.067 negative 70 joules of[br]work were done on the gas. 0:04:07.067,0:04:08.700 You have to be really careful about that. 0:04:08.700,0:04:10.600 So we can find the change[br]in internal energy. 0:04:10.600,0:04:15.600 In this case it's going to[br]equal positive 110 joules. 0:04:15.633,0:04:17.367 But that's not our answer. 0:04:17.367,0:04:18.933 The question's asking us for the 0:04:18.933,0:04:21.266 final internal energy of the gas. 0:04:21.266,0:04:23.300 This is not the final[br]internal energy of the gas. 0:04:23.300,0:04:27.117 This is the amount by which[br]the internal energy changed. 0:04:27.117,0:04:29.300 So we know the internal energy went up, 0:04:29.300,0:04:30.300 because this is positive 0:04:30.300,0:04:32.266 and this is the change in internal energy. 0:04:32.266,0:04:35.366 Internal energy went up by 110 joules. 0:04:35.366,0:04:37.800 That means the temperature[br]is also going to go up. 0:04:37.800,0:04:39.900 So what's the final[br]internal energy of the gas? 0:04:39.900,0:04:43.400 Well, if the internal[br]energy goes up by 110 joules 0:04:43.400,0:04:46.367 and the gas started with 200 joules 0:04:46.367,0:04:50.167 we know the final[br]internal energy, U final, 0:04:50.167,0:04:54.666 is just going to be 200 plus 110 is 310, 0:04:54.666,0:04:57.133 or if you want to be[br]more careful about it, 0:04:57.133,0:04:58.300 you can write this out. 0:04:58.300,0:05:03.300 Delta U, we can call U[br]final, minus U initial. 0:05:03.333,0:05:05.233 That's what delta U stands for. 0:05:05.233,0:05:07.666 U final is what we want to find 0:05:07.666,0:05:11.034 minus U initial is 200. 0:05:11.034,0:05:14.466 So positive 200 joules was[br]what the gas started with. 0:05:14.466,0:05:17.233 Equals, that's the change[br]and that's what we found, 0:05:17.233,0:05:19.200 110 joules. 0:05:19.200,0:05:21.200 Now you've solved this for U final. 0:05:21.200,0:05:24.333 You would add 200 to both[br]sides and again you would get 0:05:24.333,0:05:29.181 310 joules as the final[br]internal energy of the gas. 0:05:29.766,0:05:30.766 Let's look at one more. 0:05:30.766,0:05:33.150 Let's say you got this one[br]on a test and it said that 0:05:33.150,0:05:35.967 40 joules of work are done on a gas, 0:05:35.967,0:05:39.015 and the internal energy[br]goes down by 150 joules. 0:05:39.015,0:05:41.700 What was the value of the[br]heat added to the gas? 0:05:41.700,0:05:44.633 Note we're not solving for[br]the internal energy this time 0:05:44.633,0:05:46.167 or the change in internal energy. 0:05:46.167,0:05:47.500 We're trying to solve for the heat. 0:05:47.500,0:05:49.500 What's heat? Heat is Q. 0:05:49.500,0:05:51.366 So this time we're going to[br]plug in for the other two 0:05:51.366,0:05:52.600 and solve for Q. 0:05:52.600,0:05:53.500 What do we know? 0:05:53.500,0:05:56.833 40 joules of work are done on a gas, 0:05:56.833,0:05:59.867 so this work has got to be a positive 40 0:05:59.867,0:06:03.367 because the work is done on[br]the gas and not by the gas. 0:06:03.367,0:06:06.466 And we know the internal[br]energy goes down by 150 joules. 0:06:06.466,0:06:08.266 It means the change in internal energy 0:06:08.266,0:06:10.066 has to be negative 150. 0:06:10.066,0:06:12.567 So if I plug in here my delta U, 0:06:12.567,0:06:15.400 since my internal energy went down by 150, 0:06:15.400,0:06:18.133 delta U is going to be negative 150. 0:06:18.133,0:06:19.466 Q we don't know 0:06:19.466,0:06:21.366 so I'm just going to[br]put a variable in there. 0:06:21.366,0:06:22.400 Q I don't know. 0:06:22.400,0:06:23.566 I'm just going to put a Q in there. 0:06:23.566,0:06:24.833 I'm going to name my ignorance 0:06:24.833,0:06:25.766 and I'm going to solve for it. 0:06:25.766,0:06:28.100 Plus the work done. 0:06:28.100,0:06:31.133 We know the work done was 40[br]joules and it's positive 40. 0:06:31.133,0:06:34.066 Positive 40 because work[br]was done on the gas. 0:06:34.066,0:06:35.633 Now we can solve for Q. 0:06:35.633,0:06:36.766 The amount of heat. 0:06:36.766,0:06:40.200 The value of the heat added[br]to the gas is going to be, 0:06:40.200,0:06:42.933 if I move my 40 over here I[br]subtract it from both sides, 0:06:42.933,0:06:46.169 I'm going to get negative 190 joules. 0:06:46.169,0:06:49.100 This means a lot of heat left. 0:06:49.100,0:06:52.166 190 joules of heat left the system 0:06:52.166,0:06:54.633 in order for it to make[br]the internal energy 0:06:54.633,0:06:56.966 go down by 150 joules. 0:06:56.966,0:06:57.801 And that makes sense. 0:06:57.801,0:06:59.500 40 joules of work were added. 0:06:59.500,0:07:01.566 But we said the internal energy went down. 0:07:01.566,0:07:03.733 That means the heat has to take away 0:07:03.733,0:07:07.933 not only the 40 that you[br]added but also another 150 0:07:07.933,0:07:12.033 to make the energy go down[br]overall so the heat taken away 0:07:12.033,0:07:15.200 has to be negative 190 joules. 0:07:15.200,0:07:16.633 All right, so those were a few examples 0:07:16.633,0:07:18.433 of using the First Law. 0:07:18.433,0:07:20.613 Basically, you've got to be[br]careful with your positive 0:07:20.613,0:07:21.900 and negative signs. 0:07:21.900,0:07:23.933 You've got to remember[br]what these things are 0:07:23.933,0:07:27.000 that Q is the heat, W is the work, delta U 0:07:27.000,0:07:29.000 is the change in the internal energy 0:07:29.000,0:07:31.700 which don't forget that[br]also gives you an idea 0:07:31.700,0:07:33.903 of what happens to the temperature.