In this problem, we are told we have a diving bell, which is basically usually it's kind of a jar like thing. Um and it is It's a way for to kind of store oxygen or air down underneath the water for divers. And so we have this diving bell here. We are told that s so Here's the bottom, and this is at 100 m, So H is 100 m above below the surface of the water. Um, we told that the surface appear temperatures 20 degrees C. But down here, it's 10 degrees C. Um, this diving bell is has a length of 3 m, and so we want to figure out what the how much what The height of the water is in here. So obviously, as we push this down, we're going to get down to so that the pressure, the pressure, um, of this air needs to be equated with the pressure at this level of the at this level of the ah of the the fluid pressure. Right. So we know P one V one over t one equals p two V two over t to So again, um P one when it was initially at the top was just at atmospheric pressure. P two. Now we have atmospheric pressure, plus the pressure from the fluid above us, which is a row g h. Again. There's there's there's a little bit of ah, simplification I used here because this should be actually h minus. Why? But h is you know, we know that that why is going to be no larger than three and a check is 100. So I'm basically assuming here that this is just eight. This level here is very close to H to make things a little simpler. Um, so we know the volume. The initial volume of the air was just the control volume of the bell jar. And the final volume is, um, basically is a the cross sectional area times l minus. Why so just whatever's left in here. So when can plug all this stuff into here? And we noticed that AIDS cancel out. And that's good, because we weren't told what that waas and then we can solve for l minus. Why? And so l minus, Why is t two over t one times atmospheric pressure times the, um length of the bell jar divided by atmospheric pressure pressure, atmospheric pressure plus the pressure from the water, the hydra hydrostatic pressure of the water. Now we can again then solve for y. And so that's just l minus this whole quantity here and now if we plug in our values, we get something that is extremely different from what the textbook answer says, um or the again. I've been given the answers, but I don't know how they got the answer. Um, and they got an answer of 26 centimeters, and I'm assuming that's from some solution manual or something. Um, 26 centimeters just doesn't seem right. And I don't know, I haven't really tried to back out what that would be. Maybe they used 10 m. Um, the thing is, is that, you know, at 100 m, um, you and so if you're if you're if you're scuba diver And I used to, um, you gain an atmosphere of pressure every time meters, you go down. So at this that this 100 m down, you know, you're at about 10 atmospheres of pressure, so you know that that's quite a bit of pressure. Eso What? What That says is that you know this. This number here, this number here is going to be very small, right? So, you know, we're got basically one divided by 11. So, you know, this is close toe 1/10 and this close. This is post the one. I mean, the temperature didn't change much. So one minus 1/10 roughly you know is nine. You know, 0.9. And eso, that's, you know, about 2.7 m is why, um and so you know, the volume of the air is, you know, they got 20 0.26 m, which basically says that, you know, you just have a little bit a little bit of water in the bottom of this. In reality, I'm pretty sure you actually have a lot of water in this. Oh, I know what that I just looked at. I just noticed what it is because they asked the wrong question. How high does the water rise in after? See that? That's, uh what? That 26 centimeters is actually the the height of the air in here, right, because it was 3 m and now it's 2.76 m. So the difference is 0.26 m. So we have just that little bit of air in here. That's not the height of the water. Um, So they asked him the question. How high does the water rise in the bell jar? Um, it didn't ask how much air was left, what the height of the air was, anyway. I think that's where the 26 I just realized that I think that's where the 26 centimeters came from again. And then the second part of the question is a compressed air hose from the surface is used to expel all the water from the bill. Uh, and they ask, What does the men on pressure is needed? And again they get about 10 Mega Pascal's, which is, you know, 100 atmospheres. Um, so but there's no way that you need 100 atmosphere. Obviously, 100 atmospheres would work, although you probably wind up just floating this thing back up. Um, well, obviously, I mean, it's gonna want to float up. There's some weight. It needs to be weighted down. Obviously. Um, but yeah, I don't know how they get about 10 mega Pascal's, because basically, if you set y equal to zero. So what you want is you want the pressure of the air to be the same as the pressure of the water. There's level, which is roughly, you know, um, 10 atmospheres, which is roughly, you know, one point, um, one point, you know, one mega pascal. So I don't know how they get a factor of 10. Um, because the temperature again doesn't change that much. Right. Um, And again, though, you could say, Well, there's, you know, the weight of the air because the hose is going down. Well, the weight of the air is very small because, you know, the density of air is, you know, very was about 1000 of that of the water. So, you know, that's going to be a very small effect. So I don't know how they get get 10, roughly attend, make a pass. Guy answered, because again, it should be roughly the pressure that is at the bottom. You know, you need the pressure. You need to get this pressure up to, um, 1.15 mega Pascal's. And so you need, um you know the pressure to get that water down or to get the air down that far you need, you know, about 10 atmospheres. And then, you know, he then need about 10 atmospheres in here in the end to get the thing feel the jar bell jar with era. So I That doesn't make sense to me how you get, um ah, 100 atmospheres. Um, that's just that's a lot of pressure. So, anyway, I believe the answer is roughly 10 atmospheres.