[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.29,0:00:03.73,Default,,0000,0000,0000,,- Something you see a lot\Nwhen doing thermodynamics
Dialogue: 0,0:00:03.73,0:00:06.32,Default,,0000,0000,0000,,especially problems\Ninvolving the first law
Dialogue: 0,0:00:06.32,0:00:08.21,Default,,0000,0000,0000,,are what are called PV Diagrams.
Dialogue: 0,0:00:08.21,0:00:09.81,Default,,0000,0000,0000,,Now, the P stands for Pressure
Dialogue: 0,0:00:09.81,0:00:11.46,Default,,0000,0000,0000,,and the V stands for Volume.
Dialogue: 0,0:00:11.46,0:00:12.79,Default,,0000,0000,0000,,And this gives you a diagram of what
Dialogue: 0,0:00:12.79,0:00:15.56,Default,,0000,0000,0000,,the pressure and volume\Nare in any given instant.
Dialogue: 0,0:00:15.56,0:00:16.48,Default,,0000,0000,0000,,So what does this mean?
Dialogue: 0,0:00:16.48,0:00:17.61,Default,,0000,0000,0000,,Well, imagine you had a container
Dialogue: 0,0:00:17.61,0:00:20.43,Default,,0000,0000,0000,,full of a gas and there's\Na movable piston on top.
Dialogue: 0,0:00:20.43,0:00:22.34,Default,,0000,0000,0000,,Piston can move up or down, changing
Dialogue: 0,0:00:22.34,0:00:23.92,Default,,0000,0000,0000,,the amount of volume, right?
Dialogue: 0,0:00:23.92,0:00:25.74,Default,,0000,0000,0000,,This is the volume we're talking about,
Dialogue: 0,0:00:25.74,0:00:27.88,Default,,0000,0000,0000,,is the volume within here.
Dialogue: 0,0:00:27.88,0:00:30.94,Default,,0000,0000,0000,,So that movable piston can\Nchange that amount of volume.
Dialogue: 0,0:00:30.94,0:00:33.06,Default,,0000,0000,0000,,And that would change the\Namount of pressure inside,
Dialogue: 0,0:00:33.06,0:00:35.96,Default,,0000,0000,0000,,depending on what heat is\Nadded, how much work is done.
Dialogue: 0,0:00:35.96,0:00:37.96,Default,,0000,0000,0000,,So say we started with a\Ncertain amount of volume, right?
Dialogue: 0,0:00:37.96,0:00:39.43,Default,,0000,0000,0000,,Let's say we start with that much volume.
Dialogue: 0,0:00:39.43,0:00:41.59,Default,,0000,0000,0000,,And the pressure inside\Nis probably not zero.
Dialogue: 0,0:00:41.59,0:00:43.83,Default,,0000,0000,0000,,If there's any gas\Ninside, it can't be zero.
Dialogue: 0,0:00:43.83,0:00:45.60,Default,,0000,0000,0000,,And so we come over to here,
Dialogue: 0,0:00:45.60,0:00:47.53,Default,,0000,0000,0000,,let's say we start at\Nthis point right here.
Dialogue: 0,0:00:47.53,0:00:48.50,Default,,0000,0000,0000,,Now, what do we do?
Dialogue: 0,0:00:48.50,0:00:53.50,Default,,0000,0000,0000,,I know if I push the piston\Ndown, my volume decreases.
Dialogue: 0,0:00:53.70,0:00:56.55,Default,,0000,0000,0000,,And if I pull the piston\Nup, my volume increases.
Dialogue: 0,0:00:56.55,0:01:01.55,Default,,0000,0000,0000,,So if I push the piston down,\NI know volume goes down.
Dialogue: 0,0:01:01.73,0:01:05.08,Default,,0000,0000,0000,,That means on this graph,\NI'm going that way.
Dialogue: 0,0:01:05.08,0:01:07.85,Default,,0000,0000,0000,,Piston going down means decreasing volume.
Dialogue: 0,0:01:07.85,0:01:09.34,Default,,0000,0000,0000,,What about piston going up?
Dialogue: 0,0:01:09.34,0:01:12.71,Default,,0000,0000,0000,,Well, if the piston goes up,\Nthen my volume's increasing
Dialogue: 0,0:01:12.71,0:01:15.65,Default,,0000,0000,0000,,and I know on my graph I'd\Nbetter be going to the right.
Dialogue: 0,0:01:15.65,0:01:17.86,Default,,0000,0000,0000,,Now maybe I'm going up and right.
Dialogue: 0,0:01:17.86,0:01:19.44,Default,,0000,0000,0000,,Maybe I'm going down and right.
Dialogue: 0,0:01:19.44,0:01:21.35,Default,,0000,0000,0000,,All I know is, my volume\Nbetter be increasing,
Dialogue: 0,0:01:21.35,0:01:24.91,Default,,0000,0000,0000,,so this is increasing volume,\Nthat's increasing volume,
Dialogue: 0,0:01:24.91,0:01:26.39,Default,,0000,0000,0000,,that's increasing volume.
Dialogue: 0,0:01:26.39,0:01:28.41,Default,,0000,0000,0000,,This is not increasing volume,
Dialogue: 0,0:01:28.41,0:01:29.81,Default,,0000,0000,0000,,so I know if my piston goes up,
Dialogue: 0,0:01:29.81,0:01:32.05,Default,,0000,0000,0000,,my volume increases, I gotta be going
Dialogue: 0,0:01:32.05,0:01:34.94,Default,,0000,0000,0000,,to the rightward in\Nsome way on this graph.
Dialogue: 0,0:01:34.94,0:01:36.40,Default,,0000,0000,0000,,And if my piston goes down, I better
Dialogue: 0,0:01:36.40,0:01:38.71,Default,,0000,0000,0000,,be going to the left\Non this graph somehow.
Dialogue: 0,0:01:38.71,0:01:40.32,Default,,0000,0000,0000,,Now, what happens to the pressure?
Dialogue: 0,0:01:40.32,0:01:42.62,Default,,0000,0000,0000,,You gotta know a little\Nmore detail about it.
Dialogue: 0,0:01:42.62,0:01:44.58,Default,,0000,0000,0000,,But just knowing the\Ndirection of the piston,
Dialogue: 0,0:01:44.58,0:01:46.37,Default,,0000,0000,0000,,that lets you know which\Nway you go on this graph.
Dialogue: 0,0:01:46.37,0:01:47.91,Default,,0000,0000,0000,,So say I push the piston down.
Dialogue: 0,0:01:47.91,0:01:50.05,Default,,0000,0000,0000,,Say I push it down really fast.
Dialogue: 0,0:01:50.05,0:01:51.71,Default,,0000,0000,0000,,What do you think's gonna\Nhappen to the pressure?
Dialogue: 0,0:01:51.71,0:01:52.79,Default,,0000,0000,0000,,The pressure's probably gonna go up.
Dialogue: 0,0:01:52.79,0:01:53.98,Default,,0000,0000,0000,,How would I represent that?
Dialogue: 0,0:01:53.98,0:01:57.71,Default,,0000,0000,0000,,Well, volume's gotta go down,\Npressure would have to go up,
Dialogue: 0,0:01:57.71,0:02:01.45,Default,,0000,0000,0000,,so I might take a path that\Nlooks something like this.
Dialogue: 0,0:02:01.45,0:02:03.80,Default,,0000,0000,0000,,Volume's gotta go down to the left.
Dialogue: 0,0:02:03.80,0:02:05.24,Default,,0000,0000,0000,,Pressure's gotta go up, so maybe
Dialogue: 0,0:02:05.24,0:02:06.54,Default,,0000,0000,0000,,it does something like that.
Dialogue: 0,0:02:06.54,0:02:08.64,Default,,0000,0000,0000,,There's really infinitely many ways
Dialogue: 0,0:02:08.64,0:02:11.02,Default,,0000,0000,0000,,the gas could get from\None state to another.
Dialogue: 0,0:02:11.02,0:02:12.71,Default,,0000,0000,0000,,It could take any possible range
Dialogue: 0,0:02:12.71,0:02:15.40,Default,,0000,0000,0000,,and unless you know the exact details,
Dialogue: 0,0:02:15.40,0:02:17.44,Default,,0000,0000,0000,,it's hard to say exactly\Nwhat's gonna happen.
Dialogue: 0,0:02:17.44,0:02:20.57,Default,,0000,0000,0000,,So there's infinitely many\Npossibilities on this diagram.
Dialogue: 0,0:02:20.57,0:02:23.30,Default,,0000,0000,0000,,You can loop around,\Nit's not like a function.
Dialogue: 0,0:02:23.30,0:02:24.70,Default,,0000,0000,0000,,You can do something like this.
Dialogue: 0,0:02:24.70,0:02:28.38,Default,,0000,0000,0000,,This gas can take some crazy\Npath through this PV Diagram.
Dialogue: 0,0:02:28.38,0:02:30.68,Default,,0000,0000,0000,,There's infinitely many ways it can take.
Dialogue: 0,0:02:30.68,0:02:33.82,Default,,0000,0000,0000,,But there are four thermodynamic processes
Dialogue: 0,0:02:33.82,0:02:37.42,Default,,0000,0000,0000,,that are most commonly\Nrepresented on a PV Diagram.
Dialogue: 0,0:02:37.42,0:02:40.44,Default,,0000,0000,0000,,Again, these are not the\Nonly four possibilities.
Dialogue: 0,0:02:40.44,0:02:42.22,Default,,0000,0000,0000,,These are just the four that are kind of
Dialogue: 0,0:02:42.22,0:02:44.47,Default,,0000,0000,0000,,the simplest to deal with mathematically.
Dialogue: 0,0:02:44.47,0:02:46.44,Default,,0000,0000,0000,,And they're often a good representation
Dialogue: 0,0:02:46.44,0:02:49.76,Default,,0000,0000,0000,,and accurate approximation\Nto a lot of processes
Dialogue: 0,0:02:49.76,0:02:52.07,Default,,0000,0000,0000,,so the math's good, they work pretty well,
Dialogue: 0,0:02:52.07,0:02:53.27,Default,,0000,0000,0000,,we talk about them a lot.
Dialogue: 0,0:02:53.27,0:02:56.39,Default,,0000,0000,0000,,The first one is called\Nin isobaric process.
Dialogue: 0,0:02:56.39,0:02:59.23,Default,,0000,0000,0000,,Iso means constant, so\Nwhenever you see iso
Dialogue: 0,0:02:59.23,0:03:01.81,Default,,0000,0000,0000,,before something, it means constant.
Dialogue: 0,0:03:01.81,0:03:05.72,Default,,0000,0000,0000,,Whatever follows next,\Nand this one's isobaric.
Dialogue: 0,0:03:05.72,0:03:08.49,Default,,0000,0000,0000,,Baric, well bars, that's\Na unit of pressure,
Dialogue: 0,0:03:08.49,0:03:10.70,Default,,0000,0000,0000,,so baric is talking about pressure.
Dialogue: 0,0:03:10.70,0:03:13.49,Default,,0000,0000,0000,,Isobaric means constant pressure.
Dialogue: 0,0:03:13.49,0:03:15.82,Default,,0000,0000,0000,,So how do you represent\Nthis on a PV DIagram?
Dialogue: 0,0:03:15.82,0:03:18.14,Default,,0000,0000,0000,,Well, if you wanna\Nmaintain constant pressure,
Dialogue: 0,0:03:18.14,0:03:20.25,Default,,0000,0000,0000,,you can't go up or down, because if I were
Dialogue: 0,0:03:20.25,0:03:22.30,Default,,0000,0000,0000,,to go up, my pressure would be increasing.
Dialogue: 0,0:03:22.30,0:03:24.59,Default,,0000,0000,0000,,If I were to go down, my\Npressure would be decreasing.
Dialogue: 0,0:03:24.59,0:03:28.43,Default,,0000,0000,0000,,The only option available is\Nto go along a horizontal line.
Dialogue: 0,0:03:28.43,0:03:31.23,Default,,0000,0000,0000,,So this would be in iso, well, sometimes
Dialogue: 0,0:03:31.23,0:03:35.03,Default,,0000,0000,0000,,they're called isobars,\Nand isobar for short.
Dialogue: 0,0:03:35.03,0:03:39.17,Default,,0000,0000,0000,,This is an isobar, this\Nis an isobaric expansion
Dialogue: 0,0:03:39.17,0:03:42.09,Default,,0000,0000,0000,,if I go to the right, cause\NI know volume's increasing.
Dialogue: 0,0:03:42.09,0:03:43.87,Default,,0000,0000,0000,,And if I go to the left it would be
Dialogue: 0,0:03:43.87,0:03:48.03,Default,,0000,0000,0000,,an isobaric compression because\Nvolume would be decreasing.
Dialogue: 0,0:03:48.03,0:03:50.07,Default,,0000,0000,0000,,But it doesn't have to be\Nin this particular spot.
Dialogue: 0,0:03:50.07,0:03:52.23,Default,,0000,0000,0000,,It could be anywhere on this PV Diagram,
Dialogue: 0,0:03:52.23,0:03:55.32,Default,,0000,0000,0000,,any horizontal line is gonna be an isobar,
Dialogue: 0,0:03:55.32,0:03:57.36,Default,,0000,0000,0000,,an isobaric process.
Dialogue: 0,0:03:57.36,0:03:59.93,Default,,0000,0000,0000,,Now, I bring up the isobaric process first
Dialogue: 0,0:03:59.93,0:04:02.26,Default,,0000,0000,0000,,because it allows me to\Nshow something important
Dialogue: 0,0:04:02.26,0:04:06.09,Default,,0000,0000,0000,,that's true of every process\Nthat's just easier to see
Dialogue: 0,0:04:06.09,0:04:07.81,Default,,0000,0000,0000,,for the isobaric process.
Dialogue: 0,0:04:07.81,0:04:10.45,Default,,0000,0000,0000,,In physics, the area under the curve
Dialogue: 0,0:04:10.45,0:04:13.13,Default,,0000,0000,0000,,often represents something significant.
Dialogue: 0,0:04:13.13,0:04:15.12,Default,,0000,0000,0000,,And that's gonna be true here as well.
Dialogue: 0,0:04:15.12,0:04:17.06,Default,,0000,0000,0000,,Let's try to figure out\Nwhat the area under this
Dialogue: 0,0:04:17.06,0:04:19.33,Default,,0000,0000,0000,,curve represents.
Dialogue: 0,0:04:19.33,0:04:20.65,Default,,0000,0000,0000,,So first of all, to find the area
Dialogue: 0,0:04:20.65,0:04:22.57,Default,,0000,0000,0000,,of this rectangle, we know it's gonna be
Dialogue: 0,0:04:22.57,0:04:25.00,Default,,0000,0000,0000,,the height times the\Nwidth, what's the height?
Dialogue: 0,0:04:25.00,0:04:26.50,Default,,0000,0000,0000,,The height's just the pressure, right?
Dialogue: 0,0:04:26.50,0:04:28.52,Default,,0000,0000,0000,,The value of this pressure over here
Dialogue: 0,0:04:28.52,0:04:30.29,Default,,0000,0000,0000,,is gonna be the height and the width
Dialogue: 0,0:04:30.29,0:04:32.75,Default,,0000,0000,0000,,is the change in volume so if I started
Dialogue: 0,0:04:32.75,0:04:35.28,Default,,0000,0000,0000,,with V initial and I ended with V final,
Dialogue: 0,0:04:35.28,0:04:38.54,Default,,0000,0000,0000,,let's say it was the expansion\Ninstead of the compression.
Dialogue: 0,0:04:38.54,0:04:42.13,Default,,0000,0000,0000,,This V final minus V initial, this delta V
Dialogue: 0,0:04:42.13,0:04:45.62,Default,,0000,0000,0000,,is going to represent the\Nwidth of this rectangle.
Dialogue: 0,0:04:45.62,0:04:49.74,Default,,0000,0000,0000,,So we know area is going to\Nbe the value of the pressure
Dialogue: 0,0:04:49.74,0:04:51.82,Default,,0000,0000,0000,,times the change in the volume.
Dialogue: 0,0:04:51.82,0:04:53.24,Default,,0000,0000,0000,,Well, what does that mean?
Dialogue: 0,0:04:53.24,0:04:56.03,Default,,0000,0000,0000,,We know that pressure, we know\Nthe definition of pressure,
Dialogue: 0,0:04:56.03,0:04:58.32,Default,,0000,0000,0000,,pressure is just the force per area.
Dialogue: 0,0:04:58.32,0:05:02.41,Default,,0000,0000,0000,,So on this gas, even on a\Nforce exerted on it per area,
Dialogue: 0,0:05:02.41,0:05:05.21,Default,,0000,0000,0000,,and the change in volume,\Nwhat do we know is the volume?
Dialogue: 0,0:05:05.21,0:05:07.23,Default,,0000,0000,0000,,How could I represent the volume in here?
Dialogue: 0,0:05:07.23,0:05:09.64,Default,,0000,0000,0000,,I know this piston has some area,
Dialogue: 0,0:05:09.64,0:05:12.60,Default,,0000,0000,0000,,so there's some area that this piston has.
Dialogue: 0,0:05:12.60,0:05:14.80,Default,,0000,0000,0000,,And then there's a certain height.
Dialogue: 0,0:05:14.80,0:05:17.30,Default,,0000,0000,0000,,This inner cylinder of volume in here
Dialogue: 0,0:05:17.30,0:05:19.97,Default,,0000,0000,0000,,has a certain height\Nand then a certain area
Dialogue: 0,0:05:19.97,0:05:22.64,Default,,0000,0000,0000,,so we know the volume is\Njust height times area.
Dialogue: 0,0:05:22.64,0:05:25.75,Default,,0000,0000,0000,,So it would be height times\Nthe area of the piston.
Dialogue: 0,0:05:25.75,0:05:27.99,Default,,0000,0000,0000,,Which of these is\Nchanging in this process?
Dialogue: 0,0:05:27.99,0:05:29.41,Default,,0000,0000,0000,,Well, the area is not changing.
Dialogue: 0,0:05:29.41,0:05:31.33,Default,,0000,0000,0000,,If the area of this piston changed,
Dialogue: 0,0:05:31.33,0:05:32.81,Default,,0000,0000,0000,,it either let some of the gas out
Dialogue: 0,0:05:32.81,0:05:35.51,Default,,0000,0000,0000,,or it would bust through\Nthe sides of the cylinder,
Dialogue: 0,0:05:35.51,0:05:37.79,Default,,0000,0000,0000,,both of which we're\Nassuming is not happening.
Dialogue: 0,0:05:37.79,0:05:40.41,Default,,0000,0000,0000,,So I can pull area out of this delta sign
Dialogue: 0,0:05:40.41,0:05:42.02,Default,,0000,0000,0000,,since the area is constant.
Dialogue: 0,0:05:42.02,0:05:46.72,Default,,0000,0000,0000,,And what I get is F times A over A times
Dialogue: 0,0:05:46.72,0:05:48.69,Default,,0000,0000,0000,,the change in the height.
Dialogue: 0,0:05:48.69,0:05:51.45,Default,,0000,0000,0000,,Well the A is canceled, A cancels A
Dialogue: 0,0:05:51.45,0:05:54.56,Default,,0000,0000,0000,,and I get F times the\Nchange in the height.
Dialogue: 0,0:05:54.56,0:05:57.49,Default,,0000,0000,0000,,But look at, this is just\Nforce times a distance.
Dialogue: 0,0:05:57.49,0:06:01.11,Default,,0000,0000,0000,,Times the distance by\Nwhich this height changes.
Dialogue: 0,0:06:01.11,0:06:04.01,Default,,0000,0000,0000,,So delta H will be the amount by which
Dialogue: 0,0:06:04.01,0:06:06.59,Default,,0000,0000,0000,,this piston goes up or down.
Dialogue: 0,0:06:06.59,0:06:08.87,Default,,0000,0000,0000,,And we know force times the distance
Dialogue: 0,0:06:08.87,0:06:12.23,Default,,0000,0000,0000,,by which you apply that\Nforce is just the work.
Dialogue: 0,0:06:12.23,0:06:16.51,Default,,0000,0000,0000,,So now we know the area\Nunder this isobaric process
Dialogue: 0,0:06:16.51,0:06:19.69,Default,,0000,0000,0000,,represents the work done either on the gas
Dialogue: 0,0:06:19.69,0:06:23.23,Default,,0000,0000,0000,,or by the gas depending\Non which way you're going.
Dialogue: 0,0:06:23.23,0:06:27.15,Default,,0000,0000,0000,,So this area is the work, this\Narea, the value of this area
Dialogue: 0,0:06:27.15,0:06:31.67,Default,,0000,0000,0000,,equals the amount of work\Ndone on the gas or by the gas.
Dialogue: 0,0:06:31.67,0:06:32.86,Default,,0000,0000,0000,,How do you figure out which?
Dialogue: 0,0:06:32.86,0:06:35.05,Default,,0000,0000,0000,,Well, technically this area represents
Dialogue: 0,0:06:35.05,0:06:38.06,Default,,0000,0000,0000,,the work done by the gas, because if we're
Dialogue: 0,0:06:38.06,0:06:39.83,Default,,0000,0000,0000,,talking about a positive area,
Dialogue: 0,0:06:39.83,0:06:42.54,Default,,0000,0000,0000,,mathematically that means\Nmoving to the right,
Dialogue: 0,0:06:42.54,0:06:44.26,Default,,0000,0000,0000,,like on a graph in math class.
Dialogue: 0,0:06:44.26,0:06:46.63,Default,,0000,0000,0000,,The area, positive area,\Nyou're moving to the right.
Dialogue: 0,0:06:46.63,0:06:49.82,Default,,0000,0000,0000,,So if we want to be\Nparticular and precise,
Dialogue: 0,0:06:49.82,0:06:52.15,Default,,0000,0000,0000,,we'll say that this is a\Nprocess moving to the right.
Dialogue: 0,0:06:52.15,0:06:55.05,Default,,0000,0000,0000,,And we know if the volume is going up
Dialogue: 0,0:06:55.05,0:06:56.63,Default,,0000,0000,0000,,like this graph is going to the right,
Dialogue: 0,0:06:56.63,0:06:58.04,Default,,0000,0000,0000,,which means volume is increasing,
Dialogue: 0,0:06:58.04,0:07:00.00,Default,,0000,0000,0000,,we know that gas is doing work.
Dialogue: 0,0:07:00.00,0:07:03.02,Default,,0000,0000,0000,,So technically, this area\Nis the work done by the gas.
Dialogue: 0,0:07:03.02,0:07:05.93,Default,,0000,0000,0000,,You can see that as well\Nsince this is P delta V.
Dialogue: 0,0:07:05.93,0:07:08.62,Default,,0000,0000,0000,,If your delta V comes out positive,
Dialogue: 0,0:07:08.62,0:07:10.87,Default,,0000,0000,0000,,pressure is always\Npositive, if your Delta V
Dialogue: 0,0:07:10.87,0:07:13.97,Default,,0000,0000,0000,,comes out positive, the\Nvolume is increasing.
Dialogue: 0,0:07:13.97,0:07:16.17,Default,,0000,0000,0000,,That means work is being done by the gas.
Dialogue: 0,0:07:16.17,0:07:17.27,Default,,0000,0000,0000,,So you have to be careful.
Dialogue: 0,0:07:17.27,0:07:19.02,Default,,0000,0000,0000,,If you calculate this P delta V
Dialogue: 0,0:07:19.02,0:07:21.78,Default,,0000,0000,0000,,and you go to your first law equation,
Dialogue: 0,0:07:21.78,0:07:25.96,Default,,0000,0000,0000,,which remember, says delta U is Q plus W,
Dialogue: 0,0:07:25.96,0:07:28.25,Default,,0000,0000,0000,,well you can't just plug\Nin the value of P delta V.
Dialogue: 0,0:07:28.25,0:07:29.73,Default,,0000,0000,0000,,This is the work done by the gas,
Dialogue: 0,0:07:29.73,0:07:32.06,Default,,0000,0000,0000,,so you have to plug in negative that value
Dialogue: 0,0:07:32.06,0:07:34.79,Default,,0000,0000,0000,,for the work done, and\Nalso correspondingly,
Dialogue: 0,0:07:34.79,0:07:36.15,Default,,0000,0000,0000,,if you were to go to the left,
Dialogue: 0,0:07:36.15,0:07:39.25,Default,,0000,0000,0000,,if you did have a process\Nthat went to the left.
Dialogue: 0,0:07:39.25,0:07:42.18,Default,,0000,0000,0000,,That is to say the volume was decreasing.
Dialogue: 0,0:07:42.18,0:07:44.20,Default,,0000,0000,0000,,If you find this area and you're careful,
Dialogue: 0,0:07:44.20,0:07:46.52,Default,,0000,0000,0000,,then you'll get a negative delta V
Dialogue: 0,0:07:46.52,0:07:49.05,Default,,0000,0000,0000,,if you're going leftward\Nbecause you'll end
Dialogue: 0,0:07:49.05,0:07:51.97,Default,,0000,0000,0000,,with a smaller value for the\Nvolume than you started with.
Dialogue: 0,0:07:51.97,0:07:54.70,Default,,0000,0000,0000,,So if you really treat\Nthe left one as the final,
Dialogue: 0,0:07:54.70,0:07:57.08,Default,,0000,0000,0000,,cause that's where you end\Nup if you're going left,
Dialogue: 0,0:07:57.08,0:07:59.12,Default,,0000,0000,0000,,and the rightward one as the initial,
Dialogue: 0,0:07:59.12,0:08:01.50,Default,,0000,0000,0000,,your leftward final point will be smaller
Dialogue: 0,0:08:01.50,0:08:04.39,Default,,0000,0000,0000,,than your initial point, you\Nwill get a negative value here.
Dialogue: 0,0:08:04.39,0:08:07.88,Default,,0000,0000,0000,,So again, you plug in negative\Nof that negative value.
Dialogue: 0,0:08:07.88,0:08:09.41,Default,,0000,0000,0000,,You'll get your positive work,
Dialogue: 0,0:08:09.41,0:08:11.71,Default,,0000,0000,0000,,cause positive work is\Nbeing done on the gas.
Dialogue: 0,0:08:11.71,0:08:13.46,Default,,0000,0000,0000,,That sounds very complicated.
Dialogue: 0,0:08:13.46,0:08:15.12,Default,,0000,0000,0000,,Here's what I do, quite honestly.
Dialogue: 0,0:08:15.12,0:08:17.43,Default,,0000,0000,0000,,I just look at the shape, I find the area,
Dialogue: 0,0:08:17.43,0:08:19.87,Default,,0000,0000,0000,,I do the magnitude of the height, right,
Dialogue: 0,0:08:19.87,0:08:21.36,Default,,0000,0000,0000,,the size of it, no negatives.
Dialogue: 0,0:08:21.36,0:08:23.69,Default,,0000,0000,0000,,The size of the width, no negatives.
Dialogue: 0,0:08:23.69,0:08:26.15,Default,,0000,0000,0000,,I multiply the two and then I just look.
Dialogue: 0,0:08:26.15,0:08:27.68,Default,,0000,0000,0000,,Am I going to the left?
Dialogue: 0,0:08:27.68,0:08:31.40,Default,,0000,0000,0000,,If I'm going to the left,\NI know my work is positive.
Dialogue: 0,0:08:31.40,0:08:33.87,Default,,0000,0000,0000,,If I'm going to the right,\NI know my work is negative
Dialogue: 0,0:08:33.87,0:08:36.66,Default,,0000,0000,0000,,that I plug into here, so I\Njust add the negative sign in.
Dialogue: 0,0:08:36.66,0:08:38.92,Default,,0000,0000,0000,,Makes it me easier for me to understand.
Dialogue: 0,0:08:38.92,0:08:42.38,Default,,0000,0000,0000,,So I said that this works for\Nany process, how is that so?
Dialogue: 0,0:08:42.38,0:08:43.75,Default,,0000,0000,0000,,If I take some random process,
Dialogue: 0,0:08:43.75,0:08:46.97,Default,,0000,0000,0000,,I'm not gonna get a nice\Nrectangle, how is this true?
Dialogue: 0,0:08:46.97,0:08:49.90,Default,,0000,0000,0000,,Well, if I did take a random process
Dialogue: 0,0:08:49.90,0:08:51.80,Default,,0000,0000,0000,,from one point to another, say I took
Dialogue: 0,0:08:51.80,0:08:53.78,Default,,0000,0000,0000,,this crazy path here.
Dialogue: 0,0:08:53.78,0:08:55.79,Default,,0000,0000,0000,,Even though it's not a perfect rectangle,
Dialogue: 0,0:08:55.79,0:08:58.26,Default,,0000,0000,0000,,I can break it up into small rectangles
Dialogue: 0,0:08:58.26,0:09:01.44,Default,,0000,0000,0000,,so I can take this, break\Nthis portion up into,
Dialogue: 0,0:09:01.44,0:09:03.68,Default,,0000,0000,0000,,if I make the rectangle small enough,
Dialogue: 0,0:09:03.68,0:09:06.75,Default,,0000,0000,0000,,I can approximate any\Narea as the summation
Dialogue: 0,0:09:06.75,0:09:09.33,Default,,0000,0000,0000,,of a whole bunch of little rectangles.
Dialogue: 0,0:09:09.33,0:09:11.77,Default,,0000,0000,0000,,And look at, each one of these rectangles,
Dialogue: 0,0:09:11.77,0:09:15.48,Default,,0000,0000,0000,,well, P delta V, that's the\Narea underneath for that one,
Dialogue: 0,0:09:15.48,0:09:17.44,Default,,0000,0000,0000,,add them all up, I get\Nthe total area undeneath.
Dialogue: 0,0:09:17.44,0:09:22.22,Default,,0000,0000,0000,,So even though it might be\Ndifficult to find this area,
Dialogue: 0,0:09:22.22,0:09:25.82,Default,,0000,0000,0000,,it's always true that if\NI could find this area
Dialogue: 0,0:09:25.82,0:09:30.82,Default,,0000,0000,0000,,under any process, this area\Ndoes represent the work done.
Dialogue: 0,0:09:31.01,0:09:33.70,Default,,0000,0000,0000,,And again, it's by the gas.
Dialogue: 0,0:09:33.70,0:09:36.09,Default,,0000,0000,0000,,So in other words, using the formula
Dialogue: 0,0:09:36.09,0:09:39.68,Default,,0000,0000,0000,,work done by the gas\Nthat we had previously
Dialogue: 0,0:09:39.68,0:09:42.96,Default,,0000,0000,0000,,equals P times delta V, that works
Dialogue: 0,0:09:42.96,0:09:46.86,Default,,0000,0000,0000,,for one small little rectangle\Nand you can add all those up,
Dialogue: 0,0:09:46.86,0:09:48.80,Default,,0000,0000,0000,,but it work for the entire process.
Dialogue: 0,0:09:48.80,0:09:51.81,Default,,0000,0000,0000,,If you tried to use the,\Nsay, initial pressure
Dialogue: 0,0:09:51.81,0:09:53.86,Default,,0000,0000,0000,,times the total change in volume,
Dialogue: 0,0:09:53.86,0:09:55.84,Default,,0000,0000,0000,,and that's not gonna\Ngive you an exact answer,
Dialogue: 0,0:09:55.84,0:09:58.34,Default,,0000,0000,0000,,that's assuming you\Nhave one big rectangle.
Dialogue: 0,0:09:58.34,0:10:01.18,Default,,0000,0000,0000,,So this formula won't work\Nfor the whole process.
Dialogue: 0,0:10:01.18,0:10:04.48,Default,,0000,0000,0000,,But we do know if you\Nhave an isobaric process,
Dialogue: 0,0:10:04.48,0:10:07.62,Default,,0000,0000,0000,,if it really is an isobaric process,
Dialogue: 0,0:10:07.62,0:10:09.68,Default,,0000,0000,0000,,then we can rewrite the first law.
Dialogue: 0,0:10:09.68,0:10:13.20,Default,,0000,0000,0000,,The first law says that delta U equals Q
Dialogue: 0,0:10:13.20,0:10:15.64,Default,,0000,0000,0000,,plus work done on the gas?
Dialogue: 0,0:10:15.64,0:10:18.48,Default,,0000,0000,0000,,Well, we know a formula for\Nthe work done by the gas.
Dialogue: 0,0:10:18.48,0:10:20.62,Default,,0000,0000,0000,,Work done by the gas is P delta V.
Dialogue: 0,0:10:20.62,0:10:21.98,Default,,0000,0000,0000,,So the work done on the gas is just
Dialogue: 0,0:10:21.98,0:10:25.08,Default,,0000,0000,0000,,negative P times delta V.
Dialogue: 0,0:10:25.08,0:10:27.06,Default,,0000,0000,0000,,Here's a formula for the first law
Dialogue: 0,0:10:27.06,0:10:31.54,Default,,0000,0000,0000,,if you happen to have an isobaric process.
Dialogue: 0,0:10:31.54,0:10:34.00,Default,,0000,0000,0000,,So an isobaric process is pretty nice.
Dialogue: 0,0:10:34.00,0:10:37.02,Default,,0000,0000,0000,,It gives you an exact\Nway to find the work done
Dialogue: 0,0:10:37.02,0:10:40.20,Default,,0000,0000,0000,,since the area underneath\Nis a perfect rectangle.
Dialogue: 0,0:10:40.20,0:10:42.08,Default,,0000,0000,0000,,But how would you physically set up
Dialogue: 0,0:10:42.08,0:10:44.22,Default,,0000,0000,0000,,an isobaric process in the lab?
Dialogue: 0,0:10:44.22,0:10:45.96,Default,,0000,0000,0000,,Well, imagine this, let's say you heat up
Dialogue: 0,0:10:45.96,0:10:49.04,Default,,0000,0000,0000,,this cylinder, you allow heat to flow in.
Dialogue: 0,0:10:49.04,0:10:51.30,Default,,0000,0000,0000,,That would tend to increase the pressure.
Dialogue: 0,0:10:51.30,0:10:54.13,Default,,0000,0000,0000,,So the only way we could\Nmaintain constant pressure,
Dialogue: 0,0:10:54.13,0:10:58.06,Default,,0000,0000,0000,,cause an isobaric process\Nmaintains constant pressure,
Dialogue: 0,0:10:58.06,0:11:00.77,Default,,0000,0000,0000,,if I want the pressure to stay\Nthe same as heat flows in,
Dialogue: 0,0:11:00.77,0:11:03.12,Default,,0000,0000,0000,,I better let this piston move upwards.
Dialogue: 0,0:11:03.12,0:11:06.14,Default,,0000,0000,0000,,While I add heat I can\Nmaintain constant pressure.
Dialogue: 0,0:11:06.14,0:11:08.71,Default,,0000,0000,0000,,In fact, you might think\Nthat's complicated.
Dialogue: 0,0:11:08.71,0:11:10.21,Default,,0000,0000,0000,,How are you going to do that exactly?
Dialogue: 0,0:11:10.21,0:11:11.86,Default,,0000,0000,0000,,It's not so bad, just allow the piston
Dialogue: 0,0:11:11.86,0:11:14.86,Default,,0000,0000,0000,,to come into equilibrium with whatever
Dialogue: 0,0:11:14.86,0:11:18.13,Default,,0000,0000,0000,,atmospheric pressure plus\Nthe weight of this piston is.
Dialogue: 0,0:11:18.13,0:11:20.17,Default,,0000,0000,0000,,So there's a certain pressure\Ndown from the outside
Dialogue: 0,0:11:20.17,0:11:21.92,Default,,0000,0000,0000,,and then there's the weight of the piston
Dialogue: 0,0:11:21.92,0:11:23.85,Default,,0000,0000,0000,,divided by the area\Ngives another pressure.
Dialogue: 0,0:11:23.85,0:11:25.85,Default,,0000,0000,0000,,This heat will try to make\Nthe pressure increase,
Dialogue: 0,0:11:25.85,0:11:27.58,Default,,0000,0000,0000,,but if you just allow this system
Dialogue: 0,0:11:27.58,0:11:30.36,Default,,0000,0000,0000,,to come into equilibrium\Nwith the outside pressure,
Dialogue: 0,0:11:30.36,0:11:32.62,Default,,0000,0000,0000,,the inside pressure is always gonna equal
Dialogue: 0,0:11:32.62,0:11:35.48,Default,,0000,0000,0000,,the outside pressure\Nbecause if it's not equal,
Dialogue: 0,0:11:35.48,0:11:37.89,Default,,0000,0000,0000,,this piston will move\Nup or down accordingly.
Dialogue: 0,0:11:37.89,0:11:39.52,Default,,0000,0000,0000,,So if this piston can move freely,
Dialogue: 0,0:11:39.52,0:11:41.64,Default,,0000,0000,0000,,it'll maintain a constant pressure
Dialogue: 0,0:11:41.64,0:11:44.02,Default,,0000,0000,0000,,and that would be a way\Nto physically ensure
Dialogue: 0,0:11:44.02,0:11:46.02,Default,,0000,0000,0000,,that the pressure remains constant
Dialogue: 0,0:11:46.02,0:11:49.29,Default,,0000,0000,0000,,and you have an isobaric process.
Dialogue: 0,0:11:49.29,0:11:52.08,Default,,0000,0000,0000,,I'll explain the next three\Nthermodynamic processes
Dialogue: 0,0:11:52.08,0:11:53.55,Default,,0000,0000,0000,,in the next video.