# Gay Lussac's Law

**Gay-Lussac s Law** states that the pressure of a given mass of gas varies directly with the Kelvin temperature when the volume remains constant. Gay-Lussac s Law is expressed in a formula form as *P1/T1=P2/T2*. When dealing with Gay-Lussac s Law, the unit of the temperature should always be in Kelvin.

Alright. So one of the gas laws you'll see in class is going to be Gay Lussac's law. And Gay Lussac actually explained the relationship between pressure and temperature when the volume remains constant. Let's actually look at this ourselves.

So we have a container here and it's a five litre container of and has, inside has gas particles. Okay it's at room temperature and the gas particles are heating in some sort of pressure, that's fine. Let's say we heat it up. So we're increasing the, increasing the temperature and the kinetic energy of the particles within the, within the five litre container, it's increasing as well. And they're heating the gas at the sides of the container at high speeds. And so what's going to happen, as long as the temperature, sorry. As long as the volume remains constant which it is, the pressure inside the container is going to increase dramatically depending on how much the temperature is increasing. So let's talk about this relationship. We know it's a direct relationship. As temperature increases, so does pressure. And conversely, as temperature decreases, so does pressure. So temperature and pressure have a good relationship as long as the volume remains constant.

Okay. So let's put this in mathematical formula. Pressure one over temperature one equals to pressure two over temperature two. Because this is direct relationship, they are divided by each other. The temperature we're going to make sure it's in kelvin and the reason we make sure it's in kelvin is because we want to make sure that there's no negative numbers on the denominator and kelvin's the only temperature scale that actually only has positive numbers. So we're going to make sure this is in kelvin and this is our, this is Gay Lussac's law mathematically.

Graphically we can put the temperature on the x axis and pressure on the y axis. We know that as we increase temperature, we also increase pressure creating a positive slope.

Okay. Let's actually look at this in demonstration. So what I have right here, I'm going to put my goggles on. Make sure we're safe. Safety comes first. We have what I'm having on this hot plate is a coke can as you can see. And I'm heating it up. Let's say the gas particles inside the container are heating up also and they're heating the pressure of the soda can at high speed. But it actually it's open so it has a place to escape so the pressure inside the container is equal to the pressure outside here and so everything is all good. What I'm going to do is I'm going to flipping the can over into this ice water bath sealing the container. And what's that, what's going to happen is the temperature is going to drop and the pressure inside the container is also going to drop. And but the pressure outside is going to remain the same. so what is going to happen? Let's see.

So, as you can see it actually didn't take much at all. What happened was the pressure outside was so much greater than the pressure inside because we had dropped the temperature so dramatically that it actually pushed on the can and crashed it as you can see. Completely crashed it.

Okay. Don't try that home. Alright. Let's turn this off and let's go solve a problem together. Okay. So the pressure in a car tyre is 1.88 atmospheres. That's our first pressure at 25 degrees celsius, there's our first temperature. What will be the pressure if the temperature warms up to 37 degrees celsius? Okay. So first I want to make sure these temperatures are in kelvin not in celsius. I'm going to change them. 25 degrees celsius plus 273 is equal to 298 kelvin. 37 degrees celsius, it should be degrees celsius plus 273 is equal to 310 kelvin. Okay, so my first pressure when I woke up, I put the tyre pressure at 1.88 atmospheres. And the temperature outside was 298 kelvin. We don't know pressure at the end of the day when it's 37 degrees celsius. We don't know it. So we're going to say x over 310 kelvin. We cross multiply 1.88 times 310 divided by 298 and it's going to give me 1.96 atmospheres.

The pressure inside the tyre is actually going to increase as expected because temperature also increased. So this is an example of Gay Lussac's law in an everyday application.

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