20. Heat and Temperature
Volume Thermal Expansion
Struggling with Physics?
Join thousands of students who trust us to help them ace their exams!Watch the first video
Video duration:
4mRelated Videos
Related Practice
Skip to main content
Hey, guys. We've got an interesting problem here for you. So we've got a glass flask that is completely filled with mercury. Then, we're gonna increase the temperature of both the flask and the mercury, and we're gonna try to figure out how much mercury is sort of overflowing and spilling out of the flask. Let me just draw this out for you just to make this really clear for you. So I have this sort of glass flask like this. Right? It's filled with mercury at 0 degrees Celsius. Then what happens is you increase the temperature to 100 degrees Celsius. You have an increase of temperature and things start expanding. Now we have a three-dimensional expansion because we have a three-dimensional object like a glass that holds some liquid in it. So what happens here is that the glass and the mercury both expand. So the question is do they expand the same amount? And the answer is no, because remember the expansion depends on these beta coefficients, the coefficients of volumetric expansion, you'll notice that the one for mercury is actually bigger than the one for the glass. So here's what's going on here. You're increasing from 0 to a100, and what happens is the glass changes in volume by some amount. I'm gonna call that delta v glass. Now for the same change, 0 to a100, you also have the mercury that starts to change in volume. What happens is this delta v is gonna be greater than the delta v for the glass. So what happens is if this thing is already completely filled with mercury, if it expands in more volume, basically you're gonna have mercury that starts to leak out of this container and it starts to spill out over the edges. This is really what we wanna find here. So I'm gonna call this v spill. That's really what we're looking at here. And what happens is if the the volume for the mercury changes more than the volume for the glass, then v spill is just gonna be the subtraction of those 2. It's gonna be the delta v for the mercury minus the delta v for the glass. So really simply here, if the mercury increases by 15 but the glass increases by 10 then the amount that spills over is just the difference between them. It's 5. Right? So that's what spills out of the container. So that's really what we've got going on here and because we're looking at these delta v equations, these delta v variables, we're gonna be using our delta v equation for volumetric thermal expansion. So basically, what I have to do is just replace these equations here with, the correct substance. Right? So I've got delta v for the mercury. So this is gonna be the beta for the mercury times the initial volume of the mercury. I'm just gonna use hg. That's the chemical symbol for mercury, times the change in temperature of the mercury, minus the beta for the glass, mine times the v initial for the glass, times delta t for the glass. Right? So we just got the, the coefficients there. Alright. So basically, what I've got here is I've got the 2 coefficients like this. Now what happens is I need to figure out the initial volumes of the glass and also the change in the temperatures. Now if you think about what's going on here is that both of these were initially at 0 degrees and then they both end up at 100 degrees. So these two delta t's are gonna be the same. This delta t that we're working with here is just gonna be 100. Now what about the initial volume? Well, the initial volume here is just gonna be 250 for both. If the glass holds 250 centimeters cubed and it's completely filled with mercury, the mercury also is 250 centimeters cubed. So basically, what happens is these two variables on both of the terms here are actually gonna be the same. And because of that, actually just makes the equation a little bit simpler here. So v spill, which is what I'm looking for here, is actually just going to be v initial times delta t, remember it's gonna be the same for both, times, and this is gonna be beta for h g minus beta for the glass. All I've done here is I've sort of just grouped together these two variables which are the same and then these 2 sort of, get combined into a parenthesis. Alright. So this v spill here Alright. So now it's time to just go ahead and start plugging in. Now, normally, what I would do is I would convert this, to meters cubed, but it actually asks us to keep it in centimeters cubed, so I don't have to do any converting. So the volume initial is gonna be 250 centimeters cubed times the delta t, which is just 100, and now the beta coefficients. The one for Mercury is 1.8 times 10 to the minus 4 minus 1.2 times 10 to the minus 5. Alright. So you go ahead and work this out and what you're gonna get here is that the v spill is just equal to 4.2 centimeters. So we got a positive number, which just means that we were right. Some amount of mercury is gonna spill out of the container and the amount that spills out is just this amount, 4.2 centimeters cubed. So hopefully, that makes sense guys. Let me know if you have any questions.
05:21
