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$\bullet$ $\bullet$ A diver observes a bubble of air rising from the bottom ofa lake (where the absolute pressure is 3.50 atm ) to the surface (where the pressure is 1.00 atm). The temperature at the bottom is $4.0^{\circ} \mathrm{C}$ and the temperature at the surface is $23.0^{\circ} \mathrm{C}$ .$$\begin{array}{l}{\text { (a) What is the ratio of the volume of the bubble as it reaches }} \\ {\text { the surface to its volume at the bottom? (b) Would it be safe }} \\ {\text { for the diver to hold his breath while ascending from the bottom of the lake to the surface? Why or why not? }}\end{array}$$

3.74

Physics 101 Mechanics

Chapter 15

Thermal Properties of Matter

Temperature and Heat

The First Law of Thermodynamics

The Second Law of Thermodynamics

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Lectures

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this's Chapter 15 problem. One twelve 12. We have a diver that that was observing a bubble of here rising from the bottom of the lake, where we have the pressure living Use Hellman theme to see me to refer to the bottom. It's 3.5 ATM atmosphere, right, and the temperature at the bottom is given to us is for Celsius, and the pressure on the surface is one atmosphere. Hand the temperature on the surface. This is 23 south seas. Now we're asked the ratio of the volume on the surface we respected about in party. So we're asked the surface over the body of frustration. So in order to address this question, since we have the pressure and the temperature in the bottom and the pressure and temperature on the surface and in the meantime being inside the bubble, there is always the same amount of our air as it's descending from the bottom to towards the surface of the lake. If you write the ideal gas law, release two cases on the bottom and at the surface that would do PB B equals and our tea be right. This is for the bottom. So let's try it. Seen what remains constant here. Like we said, the model here is constant inside the vault, right? So then number of Moses constant and is, you know, the ideal gas Constant is constant. So if you do, I both sides find a temperature at the bottom. We get on the left hand side of the equation equals to end. Times are then if you're right, you'll guess law for the for When we're on this love When the bubble is on the surface of the lake, then he would be peace are closely, sir. Was over the temperature at the service, right. They have to be equal to each other from here. If you want to know what the space show is of the wilding on the surface, there's perspective while at the bottom. Then we just isolate this term, right diffraction. However, we're going to do it If you want The by both sides by t s over P s. The bee would see what happens to us. Yes, maybe so. The's air going to cancel of these argument cancels on the right hand side, we're gonna have what we're looking for. And on the right hand side. The's volumes were going to cancel. And then we're gonna have They may be right. What we have on the left hand side, in the left hand side. We have guests for real, baby. On the right hand side, we have the TV times. Yes, right over. He s turns TV, right? I'm just rewriting this portion then. Well, we confined ratio because we know each pair of Albright inside. So the pressure at the bottom is 3.5 atmospheres, and then the temperature on the surface is 23 Celsius I've ever remember. We need to convert that to Calvin. So that's what we have Divided by the treasure of surface is one. At most fear times. The temperature of the bottom is force else's recommended a conversion to Kelvin. Wait, There we go. Now, if you will get this racial where you see that it's 3.7 and four, this means be on the surface, right? So the ratio of the volume as the bubble is ascending off words from the bottom, right. This is the bottom of the lake to the surface. The volume of the surface is 3.74 times bigger then then the volume at the bottom. Right? So in part, be best something related to this. So were asked whether or not he would be safe for the diver toe. Hold his breath. You hurt his or her breath when ascending from the bottom of the lake to the surface. Well, the lungs are going to have to expand 3.74 times for that to happen. And that is dangerous, right? That is not that is not healthy. So if you mean she hum holes their breath, this increase in volume 3.74 times increase in volume in the loans would be very dangerous. So you don't want to do that, right? You don't wanna hold your breath is you're doing

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