Learn about Thermodynamics - part 3 Video

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Learn about Thermodynamics - part 3

So we just finished, hopefully getting intuition for why you know my initial pressure times my initial volume divided by my initial temperature is going to equal. You know if I change the volume or the pressure of the temperature or some combination of all them is going to equal my new pressure times my new volume divided by my new temperature. And once again, just remember all of these is you know pressure times volume is proportional to the amount of kinetic energy in the system and temperature is proportional to the amount of kinetic energy per molecules. So if we don’t change the number of molecules and since by the conservation of energy. The amount of kinetic energy isn't gonna change unless we you know do some work or get some potential energy or something. These quantities, this relationship won’t change and watch the last video and hopefully you’ll get some intuition. If still confusing I'll make another video for you guys and before I'll apply this, before I'll apply this equation which is really, this is going to get you pretty far in thermodynamics just knowing this and even more. I'm just having the intuition of what it means. I want to clarify something about temperature. So there's a lot of different ways to measure temperature. You know we know that in Fahrenheit what's freezing of water, its 32º-Fahrenheit is freezing. Well that’s also 0º-Celsius, right. And actually that’s how the Celsius scale was determined. They said okay where does water freeze zero and then where does water boil a 100º Celsius is boiling, and then that’s how they re-rated it. And of course you could be colder than the freezing of water and you have to negative in that situation. Fahrenheit, I'm actually not sure, I need to look that up in Wikipedia or that might be something for you to do in tell me how it came out. And I think boiling of water in Fahrenheit 212 degrees. So it’s a little arbitrary. I think Fahrenheit might be somehow related to human body temperature but I'm just guessing. But anyway, you can have different scales in this situation and there were all kind of a bit arbitrary when they were designed, kind of just have some type of relative to scale. You know you could say well when things are boiling. There definitely hotter. They have a higher temperature than when things are freezing but its not clear to say that it has that you know, you have well you can't divide 100 by a zero but if something is one degree. Is it necessary the case that something that’s it 100-degree Celsius is a 100 times hotter or has a 100 times the kinetic energy? Well actually we will see that no is not actually not the case. You don’t have a 100 times kinetic energy. So this is a bit of an arbitrary scale. So the actual inter volume might, you know the inter vols. arbitrary. You could pick the one degree as being 100 of the distance between zero and 100 but where you start at least in the Celsius scale is a bit arbitrary. They pick the freezing of water. So later on people figured out that there is an absolute point to start at and that absolute point to start at is the temperature which a molecule or an atom has absolutely no kinetic energy because we said temperature is equal to you know the average kinetic energy of the system or the total kinetic energy of the system divided by the number of molecules or we could say the average kinetic energy per molecule, right. So the only way to really say that the temperature is zero is if and this is proportional. I should say it’s proportional because the temperature scales are still little bit arbitrary. Its proportional, it’s not exactly related to but the only way to get to a temperature of zero should be when the kinetic energy of each and every molecule is zero. The average kinetic, so there not moving. There not vibrating. There not even blinking. These molecules are stationary and the point at which that occurs is called absolute zero. And that actually occurs; absolute zero and that’s also called zero Kelvin, zero Kelvin. And that is the same thing as minus 273º-Celsius. So nowhere in the universe at least that I'm aware of. Is it colder than minus 273º-Celsius at that temperature nothing moves even at the atomic scale? I mean I'm talking the electrons collapse into the nucleus. I mean nothing; everything is completely stationary at zero Kelvin. And it’s a theoretical absolute limit, people and maybe well do bunch of videos on how you can get close to that but in laboratory environment or maybe in deep space. It gets really, really close to this but I'm not sure. I'm pretty sure that nowhere in the universe is do we have absolutely zero Kelvin at least at any place where we actually have particles but I might be wrong there that’s a little bit out of the scope of what were talking about. So anyway, so the true in a measure temperature is Kelvin and then you’re measuring in Kelvin if I say I have something that is one Kelvin versus something that is five Kelvin. Since we kind of ail down the bottom at a point in which we really do not have kinetic energy. I can make the statement that this has five times the energy of this, something that’s at five Kelvin versus one Kelvin. So that whole long explanation about Kelvin that just to make the point that whenever we use this formula or really any formula in thermodynamic that involve temperature. We should convert to Kelvin unless were just doing change in temperature then you could probably keep the Celsius but when you’re doing proportionality or using it at multiplying or dividing by temperature. You have to use Kelvin and hopefully I made a little bit clear of why that is. So let’s do an example. So let’s, let me erase and you’d be surprise how far this takes you and really the main trick is just to remember to convert things to Kelvin that’s the number one reason why people miss questions on thermodynamics exams. Is that they didn’t convert to Kelvin. So I'm going to get a problem. This problem and this is very typical of most of what you’ll see. This is from the barons AP physics B on page 226 and it says; let me see. A confined gas is at temperature of 27º, so its initial temperature is 27º Celsius. When it has a pressure and volume, so its pressure is 1000-Pascals or Newton per meter squared and the volume is 30-meters cube. I'm thinking one of the other videos, I think I said newtons per meter cube. No its newtons per meter squared. I just want to make sure I didn’t confuse people previously. So that’s the initial volume and then it’s says the volume is decrease. So then we go to this state where my new volume is going to be 20-meters cube. The new temperature its increase, so the new temperature is now 50º-Celsius and they want to know what is my new pressure. So before we just substitute into the equation and solve for the new pressure, remember if they gave it to you in Celsius convert to Kelvin and if they gave it to you in Fahrenheit which they seldom do. Then convert into Celsius and then convert into Kelvin. Well we are you know that you know zero Kelvin is equal to 273, sorry minus two to 273 Celsius or another way you could say it is X Kelvin, Kelvin X Kelvin is equal to; well essentially whatever degree you get in Celsius. You just add 273 to it. Does that make sense? Because think of it this way, zero Kelvin, if your at zero degree Celsius. You’re already at 273º above zero Kelvin right. Think about that, hopefully that makes sense. Maybe you want to a draw a number line just to make sure. So whatever Celsius degrees you have just add 273 to it and you’ll get Kelvin. So this is equal to what? This is equal to; let me do in a new color. At 273 to 27 degree Celsius that’s 300 Kelvin and then 50º Celsius is what at 273 to it? So it's 50 + 273 = 323, right. So now we can substitute into this formula. So P1, 1000-Pascals times V1 times 30 divided by the first temperature, remember what we do in Kelvin, 300 is equal to P2 that we don’t know what that is. P2 x V1, I'm sorry times V2, there should be 2 here times V2 x 20 divided by our new temperature, 323.let see we can simplify this, we could take two zeros off here. take two zero off here and then we take a three out of here and take three out of here, and were left with 100, right. This is equal to 100. All right that’s 3000 divided, I'm sorry that’s 30,000 divided by 300 and so that’s a 100 on the left hand side. So we have a 100 is equal to P x 20/323 and then let me do it up here. I'm running out of time and so if I were to solve for it. 323 x 100 = divided by 20 equals—So my new pressure is 1615 Pascals and I just solved this equation and the hard part was converting to Kelvin. See you in the next video.

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So we just finished, hopefully getting intuition for why you know my initial pressure times my initial volume divided by my initial temperature is going to equal. You know if I change the volume or the pressure of the temperature or some combination of all them is going to equal my new pressure times my new volume divided by my new temperature. And once again, just remember all of these is you know pressure times volume is proportional to the amount of kinetic energy in the system and temperature is proportional to the amount of kinetic energy per molecules.

So if we don’t change the number of molecules and since by the conservation of energy. The amount of kinetic energy isn't gonna change unless we you know do some work or get some potential energy or something. These quantities, this relationship won’t change and watch the last video and hopefully you’ll get some intuition. If still confusing I'll make another video for you guys and before I'll apply this, before I'll apply this equation which is really, this is going to get you pretty far in thermodynamics just knowing this and even more.

I'm just having the intuition of what it means. I want to clarify something about temperature. So there's a lot of different ways to measure temperature. You know we know that in Fahrenheit what's freezing of water, its 32º-Fahrenheit is freezing. Well that’s also 0º-Celsius, right. And actually that’s how the Celsius scale was determined. They said okay where does water freeze zero and then where does water boil a 100º Celsius is boiling, and then that’s how they re-rated it. And of course you could be colder than the freezing of water and you have to negative in that situation.

Fahrenheit, I'm actually not sure, I need to look that up in Wikipedia or that might be something for you to do in tell me how it came out. And I think boiling of water in Fahrenheit 212 degrees. So it’s a little arbitrary. I think Fahrenheit might be somehow related to human body temperature but I'm just guessing. But anyway, you can have different scales in this situation and there were all kind of a bit arbitrary when they were designed, kind of just have some type of relative to scale. You know you could say well when things are boiling. There definitely hotter.

They have a higher temperature than when things are freezing but its not clear to say that it has that you know, you have well you can't divide 100 by a zero but if something is one degree. Is it necessary the case that something that’s it 100-degree Celsius is a 100 times hotter or has a 100 times the kinetic energy? Well actually we will see that no is not actually not the case. You don’t have a 100 times kinetic energy. So this is a bit of an arbitrary scale. So the actual inter volume might, you know the inter vols. arbitrary.

You could pick the one degree as being 100 of the distance between zero and 100 but where you start at least in the Celsius scale is a bit arbitrary. They pick the freezing of water. So later on people figured out that there is an absolute point to start at and that absolute point to start at is the temperature which a molecule or an atom has absolutely no kinetic energy because we said temperature is equal to you know the average kinetic energy of the system or the total kinetic energy of the system divided by the number of molecules or we could say the average kinetic energy per molecule, right.

So the only way to really say that the temperature is zero is if and this is proportional. I should say it’s proportional because the temperature scales are still little bit arbitrary. Its proportional, it’s not exactly related to but the only way to get to a temperature of zero should be when the kinetic energy of each and every molecule is zero. The average kinetic, so there not moving. There not vibrating. There not even blinking. These molecules are stationary and the point at which that occurs is called absolute zero.

And that actually occurs; absolute zero and that’s also called zero Kelvin, zero Kelvin. And that is the same thing as minus 273º-Celsius. So nowhere in the universe at least that I'm aware of. Is it colder than minus 273º-Celsius at that temperature nothing moves even at the atomic scale? I mean I'm talking the electrons collapse into the nucleus. I mean nothing; everything is completely stationary at zero Kelvin. And it’s a theoretical absolute limit, people and maybe well do bunch of videos on how you can get close to that but in laboratory environment or maybe in deep space. It gets really, really close to this but I'm not sure. I'm pretty sure that nowhere in the universe is do we have absolutely zero Kelvin at least at any place where we actually have particles but I might be wrong there that’s a little bit out of the scope of what were talking about.

So anyway, so the true in a measure temperature is Kelvin and then you’re measuring in Kelvin if I say I have something that is one Kelvin versus something that is five Kelvin. Since we kind of ail down the bottom at a point in which we really do not have kinetic energy. I can make the statement that this has five times the energy of this, something that’s at five Kelvin versus one Kelvin. So that whole long explanation about Kelvin that just to make the point that whenever we use this formula or really any formula in thermodynamic that involve temperature.

We should convert to Kelvin unless were just doing change in temperature then you could probably keep the Celsius but when you’re doing proportionality or using it at multiplying or dividing by temperature. You have to use Kelvin and hopefully I made a little bit clear of why that is. So let’s do an example. So let’s, let me erase and you’d be surprise how far this takes you and really the main trick is just to remember to convert things to Kelvin that’s the number one reason why people miss questions on thermodynamics exams.

Is that they didn’t convert to Kelvin. So I'm going to get a problem. This problem and this is very typical of most of what you’ll see. This is from the barons AP physics B on page 226 and it says; let me see. A confined gas is at temperature of 27º, so its initial temperature is 27º Celsius. When it has a pressure and volume, so its pressure is 1000-Pascals or Newton per meter squared and the volume is 30-meters cube. I'm thinking one of the other videos, I think I said newtons per meter cube. No its newtons per meter squared. I just want to make sure I didn’t confuse people previously. So that’s the initial volume and then it’s says the volume is decrease. So then we go to this state where my new volume is going to be 20-meters cube.

The new temperature its increase, so the new temperature is now 50º-Celsius and they want to know what is my new pressure. So before we just substitute into the equation and solve for the new pressure, remember if they gave it to you in Celsius convert to Kelvin and if they gave it to you in Fahrenheit which they seldom do. Then convert into Celsius and then convert into Kelvin.

Well we are you know that you know zero Kelvin is equal to 273, sorry minus two to 273 Celsius or another way you could say it is X Kelvin, Kelvin X Kelvin is equal to; well essentially whatever degree you get in Celsius. You just add 273 to it. Does that make sense? Because think of it this way, zero Kelvin, if your at zero degree Celsius. You’re already at 273º above zero Kelvin right. Think about that, hopefully that makes sense. Maybe you want to a draw a number line just to make sure. So whatever Celsius degrees you have just add 273 to it and you’ll get Kelvin.

So this is equal to what? This is equal to; let me do in a new color. At 273 to 27 degree Celsius that’s 300 Kelvin and then 50º Celsius is what at 273 to it? So it's 50 + 273 = 323, right. So now we can substitute into this formula. So P1, 1000-Pascals times V1 times 30 divided by the first temperature, remember what we do in Kelvin, 300 is equal to P2 that we don’t know what that is. P2 x V1, I'm sorry times V2, there should be 2 here times V2 x 20 divided by our new temperature, 323.let see we can simplify this, we could take two zeros off here. take two zero off here and then we take a three out of here and take three out of here, and were left with 100, right.

This is equal to 100. All right that’s 3000 divided, I'm sorry that’s 30,000 divided by 300 and so that’s a 100 on the left hand side. So we have a 100 is equal to P x 20/323 and then let me do it up here. I'm running out of time and so if I were to solve for it. 323 x 100 = divided by 20 equals—So my new pressure is 1615 Pascals and I just solved this equation and the hard part was converting to Kelvin. See you in the next video.

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