# Charles Law

**Charles Law** states that the volume of a given mass of a gas is directly proportional to its Kevin temperature at constant pressure. In mathematical terms, the relationship between temperature and volume is expressed as *V1/T1=V2/T2.*

Alright. One of the gas laws that you might come across is called Charles Law, and Charles law was formed by Jacque Charles in France in the 1800s. And he discovered that the volume of a given mass of a gas is directly proportional to its kelvin temperature at constant pressure. There are two things that you want to make sure you know or you notice when you're reading this gas law. One is the kelvin temperature where you make sure our temperature is always always always in kelvin or else we are going to get the wrong answer when dealing with this Charles law and you also want to notice it's a constant pressure. So two variables that are changing is volume and, volume and temperature. Okay, those are the two variables we're dealing with.

So let's say we have two canisters. They are at this, notice they are at the same pressure. So this, this canister we have gas pressure. We know normal temperature and pressure and then we actually heat it up. Okay. So now we're increasing the kinetic energy. Those gas particles are now moving at a faster rate and they are able, if we want to make sure the pressure is constant. They are actually going to push against this the top of this thing and actually move making the volume larger. So if you notice, the relationship between temperature and volume as we increase temperature, we also increase the volume as long as pressure is constant. Okay?

So, Charles law, its relationship is -- we have a direct relationship as stated in the actual law and we can now actually make it mathematically equal. Volume one over divided by the temperature of one equals the volume of the second one divided by the temperature of the second scenario. So this is actually Charles law mathematically. If you were to make a graph, the graph of Charles law is at zero kelvin and we're going to have zero volume because it's zero kelvin, nothing moves and the volume of a gas is actually going to be zero, and it increases as the other one increases also. So you're going to have linear relationship that looks like this. As temperature increases so does the volume of the gas. It also increases. Also as temperature decreases, volume of the gas actually decreases. Let's actually do a demonstration that shows this.

Okay. So over here I have a candle floating in some water. I'm going to light that candle. Let me just put safety goggles on first. And let's do that. Okay. Alright. I'm going to put this in here just to be safe. Make sure I don't burn anything down. Okay, so what's happening, the air particles around this candle are actually heating up, okay. So they're expanding. I'm going to capture this, I'm going to capture this. I'm going to put this glass on top of this candle and what that's going to do is going to end up going out because it's going to all the oxygen in this glass container is going to go away. It's going to be used up. So as it's being used up the candle is going to go out. And notice, when it went out, a lot of the volume in the water level rose inside the canister. Now why did that happen? Because when the candle went out, the temperature of the gas particles inside the ga- inside this glass chamber actually dropped and that made the temp- the gas particles actually have a lower volume. Because the gas particles had a lower volume, they had, that volume had to replaced by something. And it was replaced by the water at the bottom. So the water is actually able to be sucked in to the glass container to replace that volume that was then lost due to the drop in temperature.

Okay. So let's do a problem that you might see in class. Okay. something that you might see in class I'm going to take off my glass my goggles. Don't need them anymore. A gas at 40 degrees celsius occupies a volume at 2.32 litres. If the temperature is raised to 75 degrees celsius, what will the new volume be if the pressure is constant. So I'm dealing with temperature and volume. So I know in my head that's Charles law. Charles law deals with temperature and volume. Okay. It also deals with temperature in kelvins. So I want to make sure I change these temperatures to kelvin. So knowing that my formula is v1 over t1 equals v2 over t2. The first volume that we're going to deal with is 2.32 litres. The first temperature is 40 degrees celsius. We add 273 to that and we get 313 kelvin and then our second volume is, we don't know. It's what we're looking for. It's what we're looking for. Our second temperature is I'm just going to turn this on real quick. Our second temperature is 75 degrees celsius. We're going to add 273 to that and we get two, 348 kelvin. We cross multiply 348 times 232 divided by 313, we get our new volume which is 2.58 litres and let's see if that makes sense, okay?

So we increased the temperature. We went from 313 to 348, what's going to happen to volume? It should also increase which it did. 2.32 increased to now 2.58 litres. So mathematically, this is correct. So hopefully, all these, the demonstration, the graphs and the problem helps you understand that Charl- how Charles law works.

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