# Charles' Law

if you're really bored you can examine the relationship between volume and temperature by yourself here's how you can do it what you'll do is you'll want to take a balloon like this and put it in the sunlight so that it gets really hot so that the temperature gets pretty high and you want to keep track of how big it is and then what you'll want to do is you want to put that guy in the freezer so the temperature is low I'm just going to draw an ice cube here not nearly as

good as my son when I put this in the freezer what's going to happen to it it's going to get much smaller the volume of this balloon is going to decrease this makes sense based on what we know about kinetic theory why is that well they're gas particles in these balloons the higher the temperature the higher the kinetic energy of these particles so they're going to be moving around really fast when we take this balloon and we put it in the freezer these particles move slower and

slower so they don't need as much room think about the size of room that we need to contain a whole bunch of totally hyperactive kids who are running around all over the place and then on the other hand we only need a much smaller room to hold the same number of kids that are really sleepy and really tired they're not going to be moving around nearly as much so we see here that the volume relatively speaking is pretty high in this case when the temperature is high but then when we lower

the temperature and these guys have much less kinetic energy they're not moving around as much I'm sorry I wrote T here the volume is going to be much lower so these guys volume and temperature show a direct relationship as one goes up the other follows and goes up two is one goes down the other one goes down to direct relationship let's take a look at again some some math problems that we can do with with what we've learned pressure and volume are related by what we call

Boyle's law it's

## Charles

law another scientist who came up with the idea of relating volume and temperature## Charles

law can be stated like this we can say that v1 over t1 equals v2 divided by t2 just like Boyle's law## charles

law when expressed like this assumes that some sort of change happens in our gas sample and the volume over the temperature before the change equals the volume divided by the temperature after the change now we talk about volume and temperature here in wheneverwe're using temperature with gases I'm going to do this in red because it's so important we must always use the Kelvin temperature must use Kelvin temperature we always have to do this whenever we're using temperature with gases now if you remember earlier the Kelvin temperature is found by taking the degree Celsius temperature and adding 273 to it and then we get our temperature in Kelvin it's not degrees Kelvin it's just Kelvin keeping that in mind let's go ahead

and take a look at this problem we say that a balloon takes up 625 liters at 0 degree Celsius if it's heated to 80 degrees Celsius what will what will its new volume be there are a couple of steps we have to take let's figure out which of these variables we're going to be solving for first or there's a change we change this gas by heating it up so before our volume 625 liters we have that and our temperature zero degrees Celsius but remember we're going to have to change this

to Kelvin temperature before we can use it in the equation if it's heated to 80 degrees Celsius so we know what the new temperature is but remember we have to change this to Kelvin what will its new volume so v2 is going to be what we're trying to solve for first of all though we're going to have to change these Celsius temperatures into Kelvin temperatures so t1 t1 equals zero degrees Celsius plus 273 equals well this one's easy 273 Kelvin that's our t1 t2 is going to be 80

degrees plus 273 which is going to give us 353 Kelvin see these are the 2 Kelvin temperatures that we're going to have to use going into this now let's see how we can rearrange this equation here we know this guy this guy this guy we're solving for v2 so we're just going to move t2 up here as if we're multiplying both sides by t2 so our equation is going to become v1 times t2 divided by t1 equals v2 let's go ahead now and plug these values in v1 our initial value our

initial volume is 625 liters times our t2 which is in kelvins 353 Kelvin divided by t1 which is always using Kelvin temperature 273 Kelvin let's look what happens to our units here the Kelvin cancel out so our final answer is going to be left in liters and the answer to this is going to be 808 liters rounded to three significant figures this is how we solve a problem with volume and temperature with

## Charles

law as before if you need to know more about## Charles

law in depth how how thescientist