If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:8:07

okay so we just finished talking about Boyle's law and the experiments that led to the PV part of the ideal gas equation and now I want to talk about the experiments that led to the V equals T part of the equation so about a hundred years after Robert Boyle there came a French physicist named Jacques Charlet and if I didn't look at the pronunciation for this man's name I probably would have said Jack's Charles but it's Akshar delay and and this French physicist also liked experimenting with gas and actually turns out he was the first person to fill up a hot air balloon with hydrogen gas and fly solo but in jocks experiments with gas and temperature he found that if you heat a gas in a closed container say like a piston so I've got a piston here and I'll fill it with with gas it'll be green gas and this piston will be under constant pressure because as that atmosphere is pushing down on top of the piston and then the pressure of the gas pushing up is going to equal the atmosphere but under constant pressure with the same amount of particles as you heat this piston so let me apply some heat here and what we'll see is that the volume of the gas will also increase so if I showed the same piston after the heat was applied we'd see that the gas was taking that more volume even though there's the same number of particles here we still have six green particles of gas so this is what the piston would look like after the heat was applied and so as you heat a system of gas the volume will also increase and in fact the volume increases directly with it with the temperature or the volume increases proportionally to the increase in temperature and I think I can show this a little bit more clearly if I use a plot of gasses increasing with temperature and so this is what a plot of volume expansion would look like for for different gases as we're increasing the temperature this this pink gas would be helium and so at about 300 degrees Celsius this helium we can see is taking up a volume of about five liters right here and and as we decrease this temperature the volume is going to do proportionally this this straight line is is showing this down to at zero degrees Celsius we've got just a little over three liters and that this helium is taking that and then we've got this green gas and this might be methane and and we're seeing the same thing as we increase the temperature we're increasing proportionately the volume that the methane is taking taking up and this blue line might indicate water vapor water gas steam and this yellow line would would indicate hydrogen gas but all of these gases can be plotted in a straight line so in y-intercept form that would look like y equals MX plus B and if we if we substitute the values that we're using in this graph our Y is our volume so we would see that Y is equal to V and our X is our temperature so so if we fill that all the way in here we'd have V is equal to M T plus B now if you're wondering why the slopes are different it's because the different gas samples in this example would have different number of moles and you can also see that the lines are coming to a stopping point at different places and that's because that all of these gases turn into liquid at different temperatures they all have different boiling points so with methane the boiling point would be about negative 100 degrees Celsius but we could kind of extrapolate this line down and with with water vapor the boiling point is 100 degrees Celsius so that's kind of why this straight line stopped but we can we can extrapolate this this line all the way down as well and the same thing with hydrogen and if we extrapolate these values out to find their y-intercepts or their B values we would see something really interesting and that's that all of them have a volume of 0 at the exact same temperature which is negative 273 0.15 degrees Celsius which is also a zero Kelvin and so Charles law is actually another proof that zero Kelvin is absolute zero because we can't have a negative volume for gas all of these gases have to take up some volume so the lowest temperature that we could theoretically achieve for any of these gases is negative 273 0.15 degrees Celsius or zero Kelvin now if we take our equation which is V equals MT and now we don't need to be because our y-intercept is zero and if we move some variables around we'll see that V / T is equal to M or in other words the quotient of our volume divided by our temperature is constant it's the same volume as long as the sample size is the same so the same number of moles and the pressure doesn't change and this is exactly the concept that we've applied to our ideal gas equation so let's try to use this concept in a problem if the volume of the piston filled with gas is four point three one liters at 25 degrees Celsius then what is the volume of the gas after it's heated to 50 degrees Celsius assuming that the system doesn't experience a change in pressure and well what would what we're looking at is a change in volume related to a change in temperature assuming constant pressure and assuming a closed system with constant moles so this is a perfect opportunity to apply charles law so we need to start with v1 over t1 is equal to v2 over t2 and again we're just saying that the initial quotient of the volume and temperature is equal to the final quotient of the volume and temperature because volume divided by temperature is constant so our initial volume is four point three one liters and our initial temperature is 25 degrees Celsius but when we're using the ideal gas law we really need to be operating in Kelvin because Kelvin allows us to not use negative values for temperature so let's convert 25 degrees Celsius to Kelvin and all we would do is take 25 and add 273 which would give us 298 Kelvin so our initial temperature 298 Kelvin and we're looking for the final volume so v2 and then our our final temperature is 50 degrees Celsius and and we need to convert that to Kelvin so 50 plus 273 is going to give us 323 Kelvin and so that's the value that will input for our final temperature I noticed that I put t1 here that's actually t2 our final temperature is 323 Kelvin so to continue solving this and we need to multiply both sides by 323 Kelvin to isolate our final volume so times 323 Kelvin and that's going to allow us to completely cancel out the value on this side and we'll cancel out our units of Kelvin on this side and so what we have is 323 times four point three one divided by 298 and we're retaining our value or our unit of liters and that's going to give us a final volume of four point six seven liters and so thanks to Jacques Charlet we know that if we're looking at a closed closed system under constant pressure then we can predict the change in volume related to the change in temperature or vice versa