If a scuba diver fills his lungs to full capacity of 4.8 L whe...

Question

If a scuba diver fills his lungs to full capacity of 4.8 L when 9.0 m below the surface of sea water, to what volume would his lungs expand if he quickly rose to the surface? Is this advisable?

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem during an underwater expedition, an explorer inhales oxygen from her tank, filling her lungs to their maximum capacity of 5.5 L while she is located 10 m below the sea surface. If she quickly ascends to the surface, what would be the volume of her lungs? Would this be a good idea to attempt? Hint the density of seawater is 1025 kg per cubic meter and one atmosphere equals 101,325 pascals. OK. So that's our angle. Our angle is we're trying to solve for two separate answers. Our first answer is we're trying to figure out what would be the volume of this diver's lungs as she quickly ascends to the surface, given the provided conditions in the prom itself. And our second answer is we're trying to determine whether or not this would be a good idea for her to quickly ascend to the surface as stated in the prom itself. So with that in mind, let's read off our multiple choice answers and see which answer might be our final answer. And let us note that for all of our answers, for the volume of our lungs, they're all gonna be in units of liters. So A is 7.0 and it would not be a good idea. B is 9.0 and it would be a good idea. C is 11 and it would not be a good idea and D is 13 and it does not matter. OK. So our first step is we need to calculate the initial pressure, which we're gonna call P I by recalling and using the following equation which states that P I, our initial pressure is equal to the pressure of the atmosphere plus the density multiplied by the acceleration due to gravity multiplied by the height. Awesome. So let's take a moment here really fast and let's write this as a side note in blue. So let us quickly note that the pressure of the atmosphere, this is equal to 101,325 palls. And we know that the density, which specifically this is the density of seawater is equal to 1025 kilograms per meter cubed. And then we know that the acceleration due to gravity is equal to 9.81 m per second squared. And then we know the depth which is the depth that she dived down to in meters is equal to 10 m. OK. Thus, we can now plug in all of our known variables and sulfur. The numerical value for P I. So let's do that. So P I is equal to 101,325 past scales plus 1 1025 kg per cubic meter multiplied by our acceleration due to gravity which is 9.81 m per second squared multiplied by our height, which is 10 m. So let me plug that into our calculator. We will find that P I is equal to 201 877 point five pascals. So it's 201,877 0.5 pascals. So now let's take a moment here to quickly note that V I will be the initial volume of the lungs underwater and VF will be the final volume of the lungs at the surface. So now our second step is that we need to calculate the final volume. VF by recalling and using Boyle's Law equation which states that P multiplied by V I is equal to PF multiplied by VF Awesome. So essentially what this equation is saying is that the initial pressure multiplied by the initial volume is equal to the final pressure multiplied by the final volume. And we could quickly note here in blue that we know that V I which once again V I is the initial volume of the lungs under water, which is equal to 5.5 L as given to us by the problem itself. And we note, we need to note now that PF is the final pressure at the surface level, which the pressure at the surface level will be equal to atmospheric pressure. Thus, we could write that PF is equal to 101,325 has skills. Awesome. So moving right along here. So now we can rearrange our Boyles Law equation to isolate and solve for VF. So when we isolate and solve for VF, we will find that VF is equal to P multiplied by V I divided by P F. So we can plug in our known variables and sulfur the numerical value of VF. And when we do that, we will find that P I which we determine to be 201,877 0.5 scales multiplied by V I which is 5.5 L divided by PF which we know that PF is 101,325 as scales. So let me plug that into our calculator. We will find that it is equal to 10.958 liters, which is approximately equal to 11 L when we round to the nearest hole number. And that is one of our answers. Hooray, we did it And now for our second answer, whether or not it's a good idea to do this or not, we need to note and recall that since the volume of the lungs expands to twice the volume underwater, if they explore suddenly, very quickly, swims up to the surface ascends to the surface. Therefore, this is very dangerous because the lungs will be expanding so rapidly that this will not be a good idea. So not a good idea. So not a good idea. Awesome. So with that in mind, let's look at our multiple choice answers to see what our final answer has to be. And it appears the correct answer has to be the multiple choice answer letter C which states that it's 11 L and it would not be a good idea. Thank you so much for watching. Hopefully that helped and I can't wait to see in the next video. Bye.

If a scuba diver fills his lungs to full capacity of 4.8 L when 9.0 m below the surface of sea water, to what volume would his lungs expand if he quickly rose to the surface? Is this advisable?

Key Concepts

Boyle's Law

Gas Laws and Diving

Decompression Sickness

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