 In this video, I want to talk a little bit about one of the gas laws, that being Gay-Lusac's law. Gay-Lusac's law states that the pressure of a gas is directly related to the Kelvin temperature of the gas when there is no change in the volume or the amount of gas. So this indicates that there's a direct relationship between pressure and temperature. What do we mean when we have a direct relationship? That means that whenever pressure increases, temperature will also decrease. If we decrease temperature, then we would expect pressure to also decrease. Graphically, we can demonstrate this with p on our y-axis, pressure and temperature on our x-axis as temperature increases, pressure also increases. The formula for Gay-Lusac's law is p1 over t1 is equal to p2 over t2. What we mean by this is the same gas under two separate conditions. So p1 and t1 indicate the gas under condition number one. p2 and t2 are the gas under condition number two. How can we use this formula in a problem? Look at this problem right here. We have a gas that has a pressure of two atmospheres and a temperature of 18 degrees Celsius. We want to find the new pressure when the temperature is increased to 62 degrees Celsius and we're going to keep the volume and the amount of gas constant. So we have to look at what variables is given to us in the problem. So we are given the pressure of the gas is two atmospheres. We are also told in the problem that the temperature of the gas is 18 degrees Celsius under condition number one. But you will notice back here in the definition that the temperature must be in Kelvin before we can use it in this formula. So in order to convert a temperature that is measured in Celsius to Kelvin we must add 273. Now what else does the problem give us? It tells us that the temperature of this gas in condition number two has been increased to 62 degrees Celsius. Once again the Celsius temperature has to be converted to Kelvin before we can use it. So that gives us a temperature of 291 Kelvin for our temperature of our gas in condition one and 335 Kelvin is the temperature of our gas under condition number two. So the one variable that we need to solve for is pressure at condition number two. So in order to solve for P2 we first need to insert all of the values that were given in the problem into our formula. Now by algebraic means we can solve for P2. The first step is we need to move our 335 Kelvin over to the left side of the equal sign. In order to do that we multiply by the inverse. By doing this on the right side of the equal sign we can now cancel out these temperature variables. But what we do to one side of the equal sign we have to do to the other side. So our formula now looks like P2 is going to be equal to 335 Kelvin multiplied by two atmospheres. And then we're going to divide that by 291 Kelvin. Now how do we know that we've set up the equation in the correct way? Well we can look at the units and which units cancel out in order to do that. You see here that we have Kelvin in our numerator. We also have Kelvin in our denominator. Those can cancel out. The only unit that we're left with is that of atmospheres. Turns out pressure has a unit of atmospheres. So whenever we input this we find that P2 is equal to 2.3 atmospheres. And that's what we would expect. Because if you look here we increase the temperature of our gas. According to Gay-Lucic's law it states that there's a direct relationship. So when our temperature increases our pressure should also increase. And that's what occurred.