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Thermal expansion in liquids

How do we quantify expansion coefficient in liquids? Unlike solids, liquids don't have a definite shape or size, so we need to be careful while thinking of expansion coefficients. In this video, we will see what's the best way to quantify expansion coefficients fo liquids. Created by Mahesh Shenoy.

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Video transcript

when you heat up liquids they expand so let's talk a little bit about thermal expansion in liquids in particular what we'll do in this video is we'll compare the properties of liquids with that of a solid from thermal expansion point of view now if we go back to solids we'll already defined a number called as alpha L the linear expansion coefficient this number just tells us how much is the change in length of any given solid per unit length per unit temperature change and similarly if you want to calculate the changes in area we define a very similar quantity called as alpha a this tells you how much is the change in area per unit area per Keeper temperature change per unit temperature change and similarly volume expansion coefficient alpha V so we have three numbers that we can define for solids one for length one for area and one for volume and if you require more clarity on this then we have spoken a lot about this in previous videos so it would be a great idea to go back there watch them and then come back over here however when it comes to liquids when it comes to liquids we don't have alpha L we don't have alpha a we only have off of V we can only define volume expansion coefficient and here's the reason why suppose you have some container with water let's say it already has some water in it and if you were to pour this water pour this water in say another container say say mmm test tube let's say the same one put another container then notice that this shape changes you may have already learned this the shape of a liquid depends on the shape of the container which means the length of the liquid or the height of the liquid or maybe the radius of the cross-section or maybe the area of cross section or total surface area anything you take it turns out it depends on the shape of the container none of these are fixed values and therefore you can change the area or the length of a liquid even without changing the temperature even by keeping temperature fixed you can just change the container and these things change so it makes no sense to talk about linear expansion or area expansion coefficients because the length or area is not a fixed value at all but what is fixed for a liquid is its volume even if you change the shape even if you change the container the volume is something that never changes if you want to change the volume of a liquid there's only one way to do that that is by changing the temperature and therefore for liquids the only number we're going to talk about is the volume expansion coefficient so let's just write that down that's an important difference we can see so for liquids liquids only have only have volume expansion coefficient volume expansion coefficient coefficient and the way we define this number is identical to how we do it for solids the way we do it for solids is we define alpha V as change in volume per unit volume per unit temperature change identical again if you require more clarity on this if this seems a little bit confusing to you again go back and watch videos on volume expansions in solid and then you can come back over here all right let me show you a table now here it is now if you've seen previous videos and you may have seen these values before these are awful and alpha v values of some solids but now we have also added in liquids alcohol mercury water and look they don't have any linear expansion coefficient values just now we discussed they only have volume expansion coefficients we also have a gas and you can see a couple of question marks over here that's because gases are extremely interesting they have their own story and so we will do that in another video so let's not worry about them over here but I don't think which we can see from this table is that look at the values of alpha v they are incredibly large compared to that of solids they are huge so that's another thing we can note this means that when you heat liquids they expand much more in volume compared to compared to solids so we could say liquids it's okay liquids expand more expand more than solids then solids alright so let's look at water for example it tells us the expansion coefficient is 200 times 10 to the minus 6 Kelvin inverse what does that mean what that means is if you take say 1 liter of water visualize this take 1 liter of water and you increase this temperature by one Kelvin that's why the Perkins with one Kelvin then the Delta be the change in volume would be 200 times 10 power minus 6 liters and if you convert that that's about 0.2 milliliters so one little water increase temperature by one Kelvin it will expand by 0.2 milliliters which doesn't seem like it doesn't seem like a lot it is very tiny but it's much bigger than what solids would give you and therefore if you want to build a thermometer the best way to do that is to take a liquid and put it inside glass because notice glass doesn't expand much on heating and therefore when temperature changes the glass hardly expands but say the mercury which we usually use expands a lot and so we can easily calculate the temperature by using mercury inside a glass but but look at the value of alpha V for alcohol it's significantly higher than that of mercury which means if you were to put alcohol inside glass that would be even better thermometers and we use that chances are that the term that you may have used in your school about a tourist are indeed alcohol thermometers and there are many reasons for that one is that alcohol is it's much cheaper to make an alcohol thermometer compared to mercury so it's readily available another reason could be could be that since alcohol expands more it's more thermally sensitive and so you can reach temperatures better with alcohol but I think the most important reason for me would be that mercury is poisonous so if if the thermometer were to leak out or maybe it were to break and you know labardi thermometers are bound to break I mean I as a kid would you should break them all the time so anyways if they were to break and if you were to inhale the mercury vapors that could be very poisonous and so the safest option for labardi thermometers would be alcohol thermometers alcohol has one disadvantages as a thermometer alcohol boils at 80 degrees Celsius so if you need a thermometer that can measure very high temperatures we usually go for mercury thermometers but for low temperature measurement alcohol thermometers are the best options and so even the clinical thermometers the one that you stick into your mouth to check your body temperature when you are running a fever I'm not I'm not talking about the digital thermometers not those I'm talking you're still talking about the liquid thermometers that we used to use before those thermometers are also alcohol and not mercury it makes sense right I mean who would want to have a glass tube filled with poisonous liquid in their mouth especially when they're sick