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what are the different kinds of energy that a gas molecule can have well since the gas molecule can move around we know it can have just regular kinetic energy sometimes we call that translational kinetic energy and if it's a molecule like this look at a diatomic molecule it can rotate about some center point and so if we had a molecule built out of multiple atoms it can rotate and because of this it can also have rotational kinetic energy this would not be true if it was just monatomic in other words if it was just a single atom the rotation of a single atom it turns out is not a meaningful significant contribution to the energy that a gas can have but if it's diatomic or tri atomic or any multi atomic atom it can have a rotational kinetic energy as well and you might think that's it it can rotate it can move around what are the kind of energy can it have turns out it can have one more again if it's a diatomic atom like this the atoms that make up the molecule are bonded they can oscillate kind of like two masses on a spring and because of this you can get an oscillation form of energy this degree of freedom we call it is another place that the energy can go so if you add energy to a gas those gas molecules are going to either start moving around faster start rotating faster or start oscillating faster or some combination of all of those those are the three ways that energy shows up when it gets added to a gas the three ways that energy manifests itself when you put energy into a gas and physicists created a name for all that energy if you add up all that energy for a gas we call it the internal energy and we give it the letter U so U is the internal energy of the gas and by internal energy of a gas we mean all the energy the kinetic the rotational kinetic the vibrational energy all that energy added up is what we mean by the internal energy of a gas but why am I telling you all this I'm telling you this because I want to talk to you about the first law of thermodynamics and the first law of thermodynamics is really an answer to the question how do you change the internal energy of a gas how do you increase the internal energy or decrease the internal energy we know what's going to happen once you increase or decrease it the gas molecules are either going to speed up or slow down rotate faster rotate slower and so on but how do you get the energy in there it's usually formulated this first law of thermodynamics is usually formulated in the context of a gas that's contained in an enclosed container usually some sort of cylinder is the way it's shown and in equation form the first law looks like this we want to know how you change the internal energy of a gas so it looks like this Delta which represents the change in the final value minus the initial value of the internal energy equals so this is the equation representation of the first law what's going to go on the right-hand side all the ways you can change the internal energy of a gas one way you can do that well just stick a fire underneath this in container let's say this container is closed up and you put a fire underneath that heat is going to enter into the gas and that gas will start moving around faster start vibrating faster rotating faster depending on the temperature and this heat is the first way you can change the internal energy of a gas so if heat enters this enclosed container the internal energy will go up so if you add heat and that's represented with the letter Q q is the letter we choose to represent the heat energy if I add a hundred joules of heat energy that's a hundred joules that can go into increasing the internal energy of a gas but it doesn't have to be fire that you use to add heat energy to a gas you could imagine just submerging this enclosed container in some sort of heat reservoir maybe some boiling hot water or just warm water and that would also add heat to the gas you might object you might say wait it's enclosed that means nothing can get in or out how can heat get in well by enclosed we mean no particles no molecules can get in or out but he's just a former of energy so it's really happening is this heat is causing the sides of this container the atoms and molecules that make up the container to start vibrating faster back and forth what happens is when this molecule collides with that faster vibrating side it gets a kick a boost so every time it hits one of those faster moving molecules it gets a boost that's how energy is entering but just energy is entering there's no molecules actually entering into this gas so it really isn't closed okay so heat is the first way we talk about internal energy of a gas changing but there's another common way to add internal energy to a gas so we need another term over here and the additional way to add internal energy to a gas is imagine instead of having a container where none of the sides can move right where this container is completely rigid nothing can move imagine the top of this container being such that it has a tightly fitted piston and this piston imagine can move up and down so this piston can change the volume in which this gas gets to play in here so since this piston can move up or down well what can happen how could we add energy you can just exert a big force downward and compress the gas into a smaller and smaller region we said that the gas when it hits the faster-moving molecules in the wall gets a kick well the same is true here if we take this gas molecule and imagine we're pushing the piston down when it collides up here with this piston that's moving downward again it gets a kick and it starts moving faster gains energy and that can manifest itself as translational kinetic energy rotational kinetic energy vibrational regardless it's all internal energy and so what we're exerting a force this force is exerted over a certain amount of distance if we're pushing this thing down and we know what force times distance is we're doing work that's how we're adding energy into this gas is work is being done by pushing the piston down and if we do work on the gas that means we're adding internal energy to the gas and the value of the work is the amount of energy we're trying to add to the internal energy of the gas so these are the two common ways that you can add energy internal energy to a gas and this is the formula version of the first law of thermodynamics so this is it these are the two ways you can add energy Q is the heat W is the work done on the gas now important point here this is the work done on the gas and that's why I put a plus sign here because we're by doing work on the gas we're adding energy to the internal energy we're adding energy the gas is gaining energy because we're doing work on it now some textbooks and other resources you'll see the first law written like this except instead of a plus sign you'll see a minus sign and it'll be a minus sign here instead of a plus sign because they'll be talking about the work done instead of on the gas they'll be talking about the work done by the gas which is to say if the gas were to push the piston up it would be losing energy it'd be doing work on its surrounding environment out here losing that energy that would be energy that's getting taken away from the internal energy of the gas because we're talking about the gas in the piston here inside the cylinder so you've got to be careful I've formulated it in the version with the plus sign but you can also see this with the minus sign ending problems with questions you've got to be really careful you've got to look at is it asking you for the work done on the gas or is it asking you for the work done by the gas you might think oh my gosh it's gonna be really hard how do i how do I figure out one if I know the work done on the gas how do I figure out the work done by the gas well that's really easy the work done on the gas is equal to negative the work done by the gas and vice versa the work done by the gas is equal to negative the work done on the gas because if the gas does a hundred joules of work that's like someone doing negative 100 joules of work on the gas because if you do negative work on an object you're actually taking energy away from it so that's the first law of thermodynamics it tells you how to add internal energy to a gas now if you're clever you might object at this point and say wait a minute this isn't a new law of physics this is just conservation of energy it says the energy you add into a gas shows up as the energy in the gas and what I have to say to that is you're right this is just conservation of energy it's not really a new law at all why do we give it a special name well the reason is when physicists were developing this law it wasn't clear what he was it wasn't clear that heat was just another form of energy it took a while to realize that heat is just another form of energy for a while there was talk about heat being some sort of weird fluid that could actually enter a substance and now we laugh at that we're like haha what a bunch of dopes but this is a macro or a microscopic property and it's hard to see unless you have an ability to talk about these things microscopically which took a while to do that's not obvious what we should think about this material of heat as being so that's why I got a special name and the name stuck we like it it's the first law of thermodynamics now the way you use it in problems got to be careful he can't just enter it could also exit so if heat enters Q is a positive number so of a hundred joules of heat enters you'd plug in a positive hundred joules of heat for Q but if heat leaves if you stick this whole thing in an ice bath and a certain amount of heat leaves maybe a hundred joules of heat leaves you'd have to plug in negative 100 because this Q represents the heat added to the gas and if you're taking heat away well that's like negative heat being added to the gas so if heat leaves your gas that's a negative Q if heats added that's a positive Q how about work this is work done on the gas how do you know if this is positive or negative well if you're pushing the piston down well it doesn't matter if the piston moves down whether you're pushing it or not work is being done on the gas so this is positive work done so if you if the piston is moving down positive work is being done on the gas that means energy is entering that's a positive value for W now if the piston expands that is to say if the gas expands and the piston moves up well that's gas doing work on the piston in the environment that's negative work done on the gas remember we're talking about work done on the gas so if piston moves down positive work done on the gas got to plug in a positive value here if the piston moves up at negative value of the work done on the gas you'd have to plug in a negative value for the work here so be very careful this is a way to calculate the internal energy it's the first law of thermodynamics and one of the most fundamental and most often used equations in all of thermodynamics
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