[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.24,0:00:03.87,Default,,0000,0000,0000,,- So far you've seen the\NFirst Law of Thermodynamics.
Dialogue: 0,0:00:03.87,0:00:05.37,Default,,0000,0000,0000,,This is what it says.
Dialogue: 0,0:00:05.37,0:00:06.60,Default,,0000,0000,0000,,Let's see how you use it.
Dialogue: 0,0:00:06.60,0:00:08.73,Default,,0000,0000,0000,,Let's look at a particular example.
Dialogue: 0,0:00:08.73,0:00:10.90,Default,,0000,0000,0000,,This one says, let's say\Nyou've got this problem,
Dialogue: 0,0:00:10.90,0:00:14.67,Default,,0000,0000,0000,,and it said 60 joules of\Nwork is done on a gas,
Dialogue: 0,0:00:14.67,0:00:18.93,Default,,0000,0000,0000,,and the gas loses 150 joules\Nof heat to its surroundings.
Dialogue: 0,0:00:18.93,0:00:21.00,Default,,0000,0000,0000,,What is the change in internal energy?
Dialogue: 0,0:00:21.00,0:00:22.63,Default,,0000,0000,0000,,Well, we're going to use the First Law.
Dialogue: 0,0:00:22.63,0:00:24.47,Default,,0000,0000,0000,,That's what the First\NLaw lets us determine.
Dialogue: 0,0:00:24.47,0:00:28.23,Default,,0000,0000,0000,,The change in internal\Nenergy is going to equal
Dialogue: 0,0:00:28.23,0:00:30.67,Default,,0000,0000,0000,,the amount of heat\Nthat's added to the gas.
Dialogue: 0,0:00:30.67,0:00:32.60,Default,,0000,0000,0000,,So let's see, heat added to the gas.
Dialogue: 0,0:00:32.60,0:00:36.61,Default,,0000,0000,0000,,Well it says that the gas\Nloses 150 joules of heat
Dialogue: 0,0:00:36.61,0:00:37.93,Default,,0000,0000,0000,,to its surroundings.
Dialogue: 0,0:00:37.93,0:00:40.37,Default,,0000,0000,0000,,So that means heat left of the gas
Dialogue: 0,0:00:40.37,0:00:42.90,Default,,0000,0000,0000,,so heat left the gas.
Dialogue: 0,0:00:42.90,0:00:45.30,Default,,0000,0000,0000,,This must have been put\Ninto a cooler environment
Dialogue: 0,0:00:45.30,0:00:47.00,Default,,0000,0000,0000,,so that heat could leave.
Dialogue: 0,0:00:47.00,0:00:49.26,Default,,0000,0000,0000,,And so it lost 150 joules.
Dialogue: 0,0:00:49.26,0:00:51.47,Default,,0000,0000,0000,,A lot of people just stick 150 here.
Dialogue: 0,0:00:51.47,0:00:53.67,Default,,0000,0000,0000,,It's got to be negative 150 because
Dialogue: 0,0:00:53.67,0:00:55.97,Default,,0000,0000,0000,,this Q represents the\Nheat added to the gas,
Dialogue: 0,0:00:55.97,0:00:58.87,Default,,0000,0000,0000,,if you lost 150 joules,\Nit's a negative 150.
Dialogue: 0,0:00:58.87,0:01:02.63,Default,,0000,0000,0000,,And then plus, all right\Nhow much work was done.
Dialogue: 0,0:01:02.63,0:01:05.47,Default,,0000,0000,0000,,It says 60 joules of work is done on a gas
Dialogue: 0,0:01:05.47,0:01:08.67,Default,,0000,0000,0000,,so that's work done on the gas.
Dialogue: 0,0:01:08.67,0:01:10.98,Default,,0000,0000,0000,,That means it's a positive contribution
Dialogue: 0,0:01:10.98,0:01:12.05,Default,,0000,0000,0000,,to the internal energy.
Dialogue: 0,0:01:12.05,0:01:14.84,Default,,0000,0000,0000,,That's energy you're adding to the gas.
Dialogue: 0,0:01:14.84,0:01:18.37,Default,,0000,0000,0000,,So 60 joules has to be positive,
Dialogue: 0,0:01:18.37,0:01:23.37,Default,,0000,0000,0000,,and so this is plus the work\Ndone is positive 60 joules.
Dialogue: 0,0:01:23.43,0:01:27.67,Default,,0000,0000,0000,,Now we can figure it out the\Nchange in internal would be
Dialogue: 0,0:01:27.67,0:01:30.10,Default,,0000,0000,0000,,negative 90 joules.
Dialogue: 0,0:01:30.10,0:01:31.17,Default,,0000,0000,0000,,But why do we care?
Dialogue: 0,0:01:31.17,0:01:32.85,Default,,0000,0000,0000,,Why do we care about the change in
Dialogue: 0,0:01:32.85,0:01:34.20,Default,,0000,0000,0000,,internal energy of the gas?
Dialogue: 0,0:01:34.20,0:01:35.67,Default,,0000,0000,0000,,Well here's something important.
Dialogue: 0,0:01:35.67,0:01:40.17,Default,,0000,0000,0000,,Whether it's a monatomic or\Ndiatomic or triatomic molecule
Dialogue: 0,0:01:40.17,0:01:44.00,Default,,0000,0000,0000,,the internal energy of the\Ngas is always proportional
Dialogue: 0,0:01:44.00,0:01:45.47,Default,,0000,0000,0000,,to the temperature.
Dialogue: 0,0:01:45.47,0:01:47.67,Default,,0000,0000,0000,,This means if the temperature goes up,
Dialogue: 0,0:01:47.67,0:01:49.37,Default,,0000,0000,0000,,the internal energy goes up.
Dialogue: 0,0:01:49.37,0:01:51.87,Default,,0000,0000,0000,,And it also means if the\Ninternal energy goes up,
Dialogue: 0,0:01:51.87,0:01:53.10,Default,,0000,0000,0000,,the temperature goes up.
Dialogue: 0,0:01:53.10,0:01:55.63,Default,,0000,0000,0000,,So one thing we can say,\Njust going over here,
Dialogue: 0,0:01:55.63,0:01:58.93,Default,,0000,0000,0000,,looking that the change in\Ninternal energy was negative.
Dialogue: 0,0:01:58.93,0:02:02.27,Default,,0000,0000,0000,,This means the energy\Nwent down by 90 joules.
Dialogue: 0,0:02:02.27,0:02:06.29,Default,,0000,0000,0000,,Overall when all is said\Nand done, this gas lost
Dialogue: 0,0:02:06.29,0:02:08.30,Default,,0000,0000,0000,,90 joules of internal energy.
Dialogue: 0,0:02:08.30,0:02:09.77,Default,,0000,0000,0000,,That means the temperature went down.
Dialogue: 0,0:02:09.77,0:02:12.40,Default,,0000,0000,0000,,That means this gas is going to be cooler
Dialogue: 0,0:02:12.40,0:02:15.15,Default,,0000,0000,0000,,when you end this process\Ncompared to when it started.
Dialogue: 0,0:02:15.15,0:02:18.20,Default,,0000,0000,0000,,Even though you added\N60 joules of work energy
Dialogue: 0,0:02:18.20,0:02:20.97,Default,,0000,0000,0000,,it lost 150 joules of heat energy.
Dialogue: 0,0:02:20.97,0:02:22.17,Default,,0000,0000,0000,,That's a net loss.
Dialogue: 0,0:02:22.17,0:02:23.57,Default,,0000,0000,0000,,The temperature is going to go down.
Dialogue: 0,0:02:23.57,0:02:25.83,Default,,0000,0000,0000,,So this is an important key fact.
Dialogue: 0,0:02:25.83,0:02:27.33,Default,,0000,0000,0000,,Whatever the internal energy does,
Dialogue: 0,0:02:27.33,0:02:28.87,Default,,0000,0000,0000,,that's what the temperature does.
Dialogue: 0,0:02:28.87,0:02:31.77,Default,,0000,0000,0000,,And it makes sense since\Nwe know that an increase in
Dialogue: 0,0:02:31.77,0:02:35.63,Default,,0000,0000,0000,,internal energy means an\Nincrease in translational
Dialogue: 0,0:02:35.63,0:02:37.73,Default,,0000,0000,0000,,kinetic energy, rotational kinetic energy,
Dialogue: 0,0:02:37.73,0:02:39.20,Default,,0000,0000,0000,,vibrational energy.
Dialogue: 0,0:02:39.20,0:02:42.73,Default,,0000,0000,0000,,That temperature is also a\Nmeasure of that internal energy.
Dialogue: 0,0:02:42.73,0:02:45.30,Default,,0000,0000,0000,,Note that we cannot say exactly how low
Dialogue: 0,0:02:45.30,0:02:46.63,Default,,0000,0000,0000,,the temperature went.
Dialogue: 0,0:02:46.63,0:02:48.67,Default,,0000,0000,0000,,This is a loss of 90 joules
Dialogue: 0,0:02:48.67,0:02:52.03,Default,,0000,0000,0000,,but this doesn't mean\Na loss of 90 degrees.
Dialogue: 0,0:02:52.03,0:02:53.10,Default,,0000,0000,0000,,These are proportional.
Dialogue: 0,0:02:53.10,0:02:54.30,Default,,0000,0000,0000,,They're not equal.
Dialogue: 0,0:02:54.30,0:02:55.93,Default,,0000,0000,0000,,If I go down 90 joules that doesn't mean
Dialogue: 0,0:02:55.93,0:02:57.77,Default,,0000,0000,0000,,I go down 90 degrees.
Dialogue: 0,0:02:57.77,0:03:00.40,Default,,0000,0000,0000,,I would have to know more\Nabout the make up of this gas
Dialogue: 0,0:03:00.40,0:03:01.57,Default,,0000,0000,0000,,in order to do that.
Dialogue: 0,0:03:01.57,0:03:02.57,Default,,0000,0000,0000,,But the internal energy
Dialogue: 0,0:03:02.57,0:03:04.70,Default,,0000,0000,0000,,and the temperature are proportional.
Dialogue: 0,0:03:04.70,0:03:06.03,Default,,0000,0000,0000,,Let's try another one.
Dialogue: 0,0:03:06.03,0:03:10.67,Default,,0000,0000,0000,,Let's say a gas started with\N200 joules of internal energy
Dialogue: 0,0:03:10.67,0:03:13.53,Default,,0000,0000,0000,,and while you add 180\Njoules of heat to the gas,
Dialogue: 0,0:03:13.53,0:03:15.73,Default,,0000,0000,0000,,the gas does 70 joules of work.
Dialogue: 0,0:03:15.73,0:03:18.13,Default,,0000,0000,0000,,What is the final internal\Nenergy of the gas?
Dialogue: 0,0:03:18.13,0:03:21.60,Default,,0000,0000,0000,,All right, so the change\Nin internal energy
Dialogue: 0,0:03:21.60,0:03:24.47,Default,,0000,0000,0000,,equals Q.
Dialogue: 0,0:03:24.47,0:03:27.23,Default,,0000,0000,0000,,Let's see, gas starts with\N200 joules of internal energy,
Dialogue: 0,0:03:27.23,0:03:28.47,Default,,0000,0000,0000,,that's not heat.
Dialogue: 0,0:03:28.47,0:03:30.10,Default,,0000,0000,0000,,While you add 180 joules of heat,
Dialogue: 0,0:03:30.10,0:03:33.20,Default,,0000,0000,0000,,here we go, 180 joules should\Nit be positive or negative?
Dialogue: 0,0:03:33.20,0:03:34.00,Default,,0000,0000,0000,,It's going to be positive.
Dialogue: 0,0:03:34.00,0:03:36.27,Default,,0000,0000,0000,,You're adding heat to that system.
Dialogue: 0,0:03:36.27,0:03:40.49,Default,,0000,0000,0000,,So positive 180 joules of heat are added
Dialogue: 0,0:03:40.49,0:03:43.60,Default,,0000,0000,0000,,plus the amount of work done on the gas,
Dialogue: 0,0:03:43.60,0:03:46.60,Default,,0000,0000,0000,,it says the gas does 70 joules of work.
Dialogue: 0,0:03:46.60,0:03:50.27,Default,,0000,0000,0000,,So most people would just\Ndo, all right, 70 joules.
Dialogue: 0,0:03:50.27,0:03:51.60,Default,,0000,0000,0000,,So there we go.
Dialogue: 0,0:03:51.60,0:03:52.83,Default,,0000,0000,0000,,But this is wrong.
Dialogue: 0,0:03:52.83,0:03:56.40,Default,,0000,0000,0000,,This is wrong because this is\Nhow much work the gas does.
Dialogue: 0,0:03:56.40,0:03:58.70,Default,,0000,0000,0000,,This W up here with the\Nplus sign represents
Dialogue: 0,0:03:58.70,0:04:01.40,Default,,0000,0000,0000,,how much work was done on the gas.
Dialogue: 0,0:04:01.40,0:04:03.65,Default,,0000,0000,0000,,If the gas does 70 joules of work,
Dialogue: 0,0:04:03.65,0:04:07.07,Default,,0000,0000,0000,,negative 70 joules of\Nwork were done on the gas.
Dialogue: 0,0:04:07.07,0:04:08.70,Default,,0000,0000,0000,,You have to be really careful about that.
Dialogue: 0,0:04:08.70,0:04:10.60,Default,,0000,0000,0000,,So we can find the change\Nin internal energy.
Dialogue: 0,0:04:10.60,0:04:15.60,Default,,0000,0000,0000,,In this case it's going to\Nequal positive 110 joules.
Dialogue: 0,0:04:15.63,0:04:17.37,Default,,0000,0000,0000,,But that's not our answer.
Dialogue: 0,0:04:17.37,0:04:18.93,Default,,0000,0000,0000,,The question's asking us for the
Dialogue: 0,0:04:18.93,0:04:21.27,Default,,0000,0000,0000,,final internal energy of the gas.
Dialogue: 0,0:04:21.27,0:04:23.30,Default,,0000,0000,0000,,This is not the final\Ninternal energy of the gas.
Dialogue: 0,0:04:23.30,0:04:27.12,Default,,0000,0000,0000,,This is the amount by which\Nthe internal energy changed.
Dialogue: 0,0:04:27.12,0:04:29.30,Default,,0000,0000,0000,,So we know the internal energy went up,
Dialogue: 0,0:04:29.30,0:04:30.30,Default,,0000,0000,0000,,because this is positive
Dialogue: 0,0:04:30.30,0:04:32.27,Default,,0000,0000,0000,,and this is the change in internal energy.
Dialogue: 0,0:04:32.27,0:04:35.37,Default,,0000,0000,0000,,Internal energy went up by 110 joules.
Dialogue: 0,0:04:35.37,0:04:37.80,Default,,0000,0000,0000,,That means the temperature\Nis also going to go up.
Dialogue: 0,0:04:37.80,0:04:39.90,Default,,0000,0000,0000,,So what's the final\Ninternal energy of the gas?
Dialogue: 0,0:04:39.90,0:04:43.40,Default,,0000,0000,0000,,Well, if the internal\Nenergy goes up by 110 joules
Dialogue: 0,0:04:43.40,0:04:46.37,Default,,0000,0000,0000,,and the gas started with 200 joules
Dialogue: 0,0:04:46.37,0:04:50.17,Default,,0000,0000,0000,,we know the final\Ninternal energy, U final,
Dialogue: 0,0:04:50.17,0:04:54.67,Default,,0000,0000,0000,,is just going to be 200 plus 110 is 310,
Dialogue: 0,0:04:54.67,0:04:57.13,Default,,0000,0000,0000,,or if you want to be\Nmore careful about it,
Dialogue: 0,0:04:57.13,0:04:58.30,Default,,0000,0000,0000,,you can write this out.
Dialogue: 0,0:04:58.30,0:05:03.30,Default,,0000,0000,0000,,Delta U, we can call U\Nfinal, minus U initial.
Dialogue: 0,0:05:03.33,0:05:05.23,Default,,0000,0000,0000,,That's what delta U stands for.
Dialogue: 0,0:05:05.23,0:05:07.67,Default,,0000,0000,0000,,U final is what we want to find
Dialogue: 0,0:05:07.67,0:05:11.03,Default,,0000,0000,0000,,minus U initial is 200.
Dialogue: 0,0:05:11.03,0:05:14.47,Default,,0000,0000,0000,,So positive 200 joules was\Nwhat the gas started with.
Dialogue: 0,0:05:14.47,0:05:17.23,Default,,0000,0000,0000,,Equals, that's the change\Nand that's what we found,
Dialogue: 0,0:05:17.23,0:05:19.20,Default,,0000,0000,0000,,110 joules.
Dialogue: 0,0:05:19.20,0:05:21.20,Default,,0000,0000,0000,,Now you've solved this for U final.
Dialogue: 0,0:05:21.20,0:05:24.33,Default,,0000,0000,0000,,You would add 200 to both\Nsides and again you would get
Dialogue: 0,0:05:24.33,0:05:29.18,Default,,0000,0000,0000,,310 joules as the final\Ninternal energy of the gas.
Dialogue: 0,0:05:29.77,0:05:30.77,Default,,0000,0000,0000,,Let's look at one more.
Dialogue: 0,0:05:30.77,0:05:33.15,Default,,0000,0000,0000,,Let's say you got this one\Non a test and it said that
Dialogue: 0,0:05:33.15,0:05:35.97,Default,,0000,0000,0000,,40 joules of work are done on a gas,
Dialogue: 0,0:05:35.97,0:05:39.02,Default,,0000,0000,0000,,and the internal energy\Ngoes down by 150 joules.
Dialogue: 0,0:05:39.02,0:05:41.70,Default,,0000,0000,0000,,What was the value of the\Nheat added to the gas?
Dialogue: 0,0:05:41.70,0:05:44.63,Default,,0000,0000,0000,,Note we're not solving for\Nthe internal energy this time
Dialogue: 0,0:05:44.63,0:05:46.17,Default,,0000,0000,0000,,or the change in internal energy.
Dialogue: 0,0:05:46.17,0:05:47.50,Default,,0000,0000,0000,,We're trying to solve for the heat.
Dialogue: 0,0:05:47.50,0:05:49.50,Default,,0000,0000,0000,,What's heat? Heat is Q.
Dialogue: 0,0:05:49.50,0:05:51.37,Default,,0000,0000,0000,,So this time we're going to\Nplug in for the other two
Dialogue: 0,0:05:51.37,0:05:52.60,Default,,0000,0000,0000,,and solve for Q.
Dialogue: 0,0:05:52.60,0:05:53.50,Default,,0000,0000,0000,,What do we know?
Dialogue: 0,0:05:53.50,0:05:56.83,Default,,0000,0000,0000,,40 joules of work are done on a gas,
Dialogue: 0,0:05:56.83,0:05:59.87,Default,,0000,0000,0000,,so this work has got to be a positive 40
Dialogue: 0,0:05:59.87,0:06:03.37,Default,,0000,0000,0000,,because the work is done on\Nthe gas and not by the gas.
Dialogue: 0,0:06:03.37,0:06:06.47,Default,,0000,0000,0000,,And we know the internal\Nenergy goes down by 150 joules.
Dialogue: 0,0:06:06.47,0:06:08.27,Default,,0000,0000,0000,,It means the change in internal energy
Dialogue: 0,0:06:08.27,0:06:10.07,Default,,0000,0000,0000,,has to be negative 150.
Dialogue: 0,0:06:10.07,0:06:12.57,Default,,0000,0000,0000,,So if I plug in here my delta U,
Dialogue: 0,0:06:12.57,0:06:15.40,Default,,0000,0000,0000,,since my internal energy went down by 150,
Dialogue: 0,0:06:15.40,0:06:18.13,Default,,0000,0000,0000,,delta U is going to be negative 150.
Dialogue: 0,0:06:18.13,0:06:19.47,Default,,0000,0000,0000,,Q we don't know
Dialogue: 0,0:06:19.47,0:06:21.37,Default,,0000,0000,0000,,so I'm just going to\Nput a variable in there.
Dialogue: 0,0:06:21.37,0:06:22.40,Default,,0000,0000,0000,,Q I don't know.
Dialogue: 0,0:06:22.40,0:06:23.57,Default,,0000,0000,0000,,I'm just going to put a Q in there.
Dialogue: 0,0:06:23.57,0:06:24.83,Default,,0000,0000,0000,,I'm going to name my ignorance
Dialogue: 0,0:06:24.83,0:06:25.77,Default,,0000,0000,0000,,and I'm going to solve for it.
Dialogue: 0,0:06:25.77,0:06:28.10,Default,,0000,0000,0000,,Plus the work done.
Dialogue: 0,0:06:28.10,0:06:31.13,Default,,0000,0000,0000,,We know the work done was 40\Njoules and it's positive 40.
Dialogue: 0,0:06:31.13,0:06:34.07,Default,,0000,0000,0000,,Positive 40 because work\Nwas done on the gas.
Dialogue: 0,0:06:34.07,0:06:35.63,Default,,0000,0000,0000,,Now we can solve for Q.
Dialogue: 0,0:06:35.63,0:06:36.77,Default,,0000,0000,0000,,The amount of heat.
Dialogue: 0,0:06:36.77,0:06:40.20,Default,,0000,0000,0000,,The value of the heat added\Nto the gas is going to be,
Dialogue: 0,0:06:40.20,0:06:42.93,Default,,0000,0000,0000,,if I move my 40 over here I\Nsubtract it from both sides,
Dialogue: 0,0:06:42.93,0:06:46.17,Default,,0000,0000,0000,,I'm going to get negative 190 joules.
Dialogue: 0,0:06:46.17,0:06:49.10,Default,,0000,0000,0000,,This means a lot of heat left.
Dialogue: 0,0:06:49.10,0:06:52.17,Default,,0000,0000,0000,,190 joules of heat left the system
Dialogue: 0,0:06:52.17,0:06:54.63,Default,,0000,0000,0000,,in order for it to make\Nthe internal energy
Dialogue: 0,0:06:54.63,0:06:56.97,Default,,0000,0000,0000,,go down by 150 joules.
Dialogue: 0,0:06:56.97,0:06:57.80,Default,,0000,0000,0000,,And that makes sense.
Dialogue: 0,0:06:57.80,0:06:59.50,Default,,0000,0000,0000,,40 joules of work were added.
Dialogue: 0,0:06:59.50,0:07:01.57,Default,,0000,0000,0000,,But we said the internal energy went down.
Dialogue: 0,0:07:01.57,0:07:03.73,Default,,0000,0000,0000,,That means the heat has to take away
Dialogue: 0,0:07:03.73,0:07:07.93,Default,,0000,0000,0000,,not only the 40 that you\Nadded but also another 150
Dialogue: 0,0:07:07.93,0:07:12.03,Default,,0000,0000,0000,,to make the energy go down\Noverall so the heat taken away
Dialogue: 0,0:07:12.03,0:07:15.20,Default,,0000,0000,0000,,has to be negative 190 joules.
Dialogue: 0,0:07:15.20,0:07:16.63,Default,,0000,0000,0000,,All right, so those were a few examples
Dialogue: 0,0:07:16.63,0:07:18.43,Default,,0000,0000,0000,,of using the First Law.
Dialogue: 0,0:07:18.43,0:07:20.61,Default,,0000,0000,0000,,Basically, you've got to be\Ncareful with your positive
Dialogue: 0,0:07:20.61,0:07:21.90,Default,,0000,0000,0000,,and negative signs.
Dialogue: 0,0:07:21.90,0:07:23.93,Default,,0000,0000,0000,,You've got to remember\Nwhat these things are
Dialogue: 0,0:07:23.93,0:07:27.00,Default,,0000,0000,0000,,that Q is the heat, W is the work, delta U
Dialogue: 0,0:07:27.00,0:07:29.00,Default,,0000,0000,0000,,is the change in the internal energy
Dialogue: 0,0:07:29.00,0:07:31.70,Default,,0000,0000,0000,,which don't forget that\Nalso gives you an idea
Dialogue: 0,0:07:31.70,0:07:33.90,Default,,0000,0000,0000,,of what happens to the temperature.