Gas Laws - A-level Physics

now what makes gas is different from liquids and solids is that they can be compressed so you apply pressure to a gas you can actually make the space that it takes up smaller so we have a few gas laws that describe what happens gas is when we change something about them now when you push on a gas and you apply a pressure and we're going to give that the letter P now you might see this as a capital P or a little P doesn't really matter and we have the volume as well our volume and pressure of a gas proportional unless I think if you increase the pressure the force on a gas you're squashing it so you're actually going to make the volume smaller likewise if we let off pressure then the volume is going to increase the space that the gas takes up is gonna increase they're actually inversely proportional what we end up is with this graph here and that is P is inversely proportional to the volume of the gas this is called Boyle's law the way I like to remember this is that if you want to pop a boil on your face then you need to increase the pressure on it gross but it will help you remember it by the way if you have a gas that follows Boyle's law like this and you have this graph how would the graph change if you measure pressure and volume at a higher temperature and this curve would move away from the origin there's another term that you might need to know about and that is adiabatic all this word means is that if you have energy being transferred then no energy is lost to the surroundings in the same way no energy is gained from the surroundings so the system is closed what else can we change for a gas we also have temperature if we increase the temperature of a gas then you probably know that you're actually making the particles vibrate faster and they're knocking off each other more and so they'll actually try to take up more room more space so if you increase temperature you increase volume volume and temperature of a gas are proportional to each other this is called Charles's law if we increase the temperature again what's going to happen to the pressure you'll probably guess that if you increase the temperature again the pressures going to increase just like the volume because the particles are bouncing off each other harder because they have more energy so pressure is proportional to temperature now this is sometimes called the gay-lussac law sometimes just called the pressure law now there's a couple of things that we need to take into account here Boyle's law is theoretically possible but in the real world things start going a little bit weird if we increase the pressure too much so an ideal gas will obey Boyle's law perfectly but actually that can't happen what do we have in the real world though well we have gases that nearly obey Boyle's law perfectly kind of ironically we call those perfect gases so put it this way perfect is as perfect as it's going to get but it's still not ideal but a perfect gas we can still apply Boyle's law as a near enough approximation now in order for these two graphs to be true these two relationships we need temperature to be zero there and zero there too but hang on a minute if we use degrees Celsius we know that zero degrees isn't actually the lowest temperature that you can get so when it comes to gases Celsius isn't good enough why is that well because because basically it doesn't start at zero it's a relative scale we need something better don't forget that Celsius is based on water zero degrees being the freezing point of water and 100 being the boiling point so we need something better something that does actually start at zero and that is the Kelvin scale and that is a scale where the lowest temperature is zero Kelvin that doesn't say okay that says zero Kelvin we don't need to put the little degrees circle for Kelvin we can just write the number and then a capital K now because Kelvin didn't want to rock the boat too much he started his scale at zero but he decided to keep a temperature difference of one Kelvin the same as a temperature difference of 1 degrees C if the temperature of something goes up by one Kelvin that is exactly the same as plus one degree Celsius by the way we call zero degrees Kelvin Absolute Zero lowest possible temperature that you can get now we haven't actually managed to get every now we haven't actually managed to get something to Absolute Zero very close but not to absolute zero that's when particles have no energy at all so whenever we do calculations with gases we need to use the Kelvin scale instead and I can tell you that zero degrees Kelvin is equals to minus 273 degrees Celsius so absolute zero in Celsius is minus 273 you won't really have to convert Kelvin into Celsius it's usually the other way around so all you have to do to go from degrees Celsius to Kelvin is add 273 so you could get given a temperature of five degrees Celsius how many Kelvin is that add 273 278 Kelvin so we have to use the Kelvin scale because it is an absolute scale where it starts at zero so we now have three laws but now we need one law to rule them all so we have P is inversely proportional to the volume volume proportional to temperature and pressure proportional to temperature another way that we can reconcile all of these laws into one is by taking the volume or over to the other side so we have P V proportional to and we can see that V is proportional to T and P is proportional to T and there we have it PV pressure times volume is proportional to the temperature now there's another thing that this ultimately depends on and that is the number of molecules that we have in a certain amount of gas if we double the number of molecules even if they're the same temperature well we're going to have twice the pressure aren't we so we actually need to put capital n in there as well capital N and it's very important that it's a capital N is the number of molecules number of gas molecules no that's not a hashtag that means number then to turn this into an equation a proper equation we end up with PV equals n T I don't need a constant in there and we call that K this is our ideal gas equation or one form of it anyway K is the Boltzmann constant and it's a very small number that you'll always be given capital n the number of molecules is obviously going to be absurdly big we need something else that tells us how many molecules we have so instead we look to moles and that's a little n it's the number of moles now 1 mole equals 6.02 times 10 to the 23 molecules can you see why we actually deal with moles instead of molecules now this number here is called the Avogadro constant the Avogadro constant gives you the number of molecules in one mole of something specifically in this case a gas sometimes given the symbol an a so to go from moles to molecules all you have to do is times by Avogadro's constant and then to go backwards to go from molecules to moles divided by Avogadro's constant so if we have PV equals n KT and we instead go to number of moles we still want P V and T to stay intact so if we're dividing by Avogadro's constant to get from molecules to moles and whatever we do with K we have to compensate and times by Avogadro's constant instead so we have a new constant we give that the letter R R is just the gas constant and it's equals to 8.31 so instead of dealing with massive numbers of molecules and tiny numbers with the Boltzmann constant instead we've got number of moles and we have a gas constant which is 8.3 one as well much easier numbers to deal with so you can probably see the NK he calls n are just different ends more often than not we're going to be dealing with moles and the gas constant but sometimes you might have to convert a number of molecules into moles first so this is our final form of the ideal gas law and it tells us what is happening with the pressure volume number of moles and temperature of a gas moles by the way doesn't have a unit temperature is obviously going to be in Kelvin not degree see pressure is in Pascal's thus Newton's per meter squared and volume is going to be in meters cubed now here we have our gas law here what about if you rearrange to find are we in there with PV over NT and we know R is a constant so if we have a change in a gas we know that PV over NT is going to be the same before as afterwards so we can say that PV before so little subscript 1 over N 1 T 1 is equals to P 2 V 2 over n 2 T 2 before and after if you don't know how to deal with proportionality if you don't know how to deal with proportionality questions like this have a look at my proportionality video first from there it's just a matter of finding out what is staying the same now we have a couple of definitions that we need to know if a change in a gas is isothermic it means that the temperature is constant ISO means same thermic temperature isobaric and guess what this is berrak barometers they are she'd detect change in Russia so that's actually a constant pressure and more often than not n is constant not always but usually if we've got a certain amount of gas and then we're changing the temperature volume or pressure then we're still going to have the same number of molecules same number of moles the exception to this is when we have maybe a canister and we're letting out some gas or we're putting more gas in in that case yes n is going to change so the trick is once you've got this is to remove everything that's staying the same so let's say that I have a question that says that I'm compressing a gas from 100 kiloPascals to 500 kilopascals but I can tell you that the temperature is staying the same so it's actually ISO thermic so let's get our whole equation for before and afterwards but it's isothermic so I know the temperature staying the same so I can literally cross out the temperature on both sides and I haven't been told that I'm letting out any gas or putting any more Rinne so I can assume that the number of moles are staying the same as well so I left with PV before equals PV afterwards all that I have to do then is rearrange to find the new volume let's say that before my volume was 30 meters cubed let's rearrange this just to find v2 this ends up being p1 v1 divided by PT it gives me the new volume and that's going to give me 100 divided by 500 I haven't bothered putting times 10 to the 3 or killer in there because well it's just a ratio so we can just use a hundred followed by 500 times that by the volume before that gives us a fifth of this and a 6 meters cubed if I had a question which is isobaric and the temperature was changing then I'd have to remove the pressures and I'd end up with v1 over t1 equals v2 over t2 and then I'll rearrange to find the new temperature probably just remember that whenever you see a temperature for gases we are talking kelvin not too greasy so you will have to convert from degree C to Kelvin if that's what you're given and that's how you use the ideal gas law it seems rather simple but just like sh and sh see the problems arise when you come across some really quite complicated questions where you really have to think hard about what's changing on what's staying the same so as per usual where you just have to practice practice practice to come across as many different scenarios as possible I hope that helps if it did then please leave a like and if you have any comments or questions then please put a comment down below and I'll see you next time

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Id: QhnlyHV8evY

Length: 12min 47sec (767 seconds)

Published: Thu Mar 16 2017