Balloon underwater

[Eye Cue]

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As a balloon descends underwater at constant rate, I can figure out as much as that the volume decreases. However, I can't seem to grasp why the volume doesn't decrease linearly. It actually changes the most near the surface, and less as it descends.

My thought process:

P=density*g*y
as depth increases, P increases proportionally.
P is proportional to 1/V, so as P increases, V decreases proportionally.

I am either applying these equations incorrectly or am making a stupid mathematical error. Would anyone care to elaborate? Thanks.

 

[Eye Cue]

Wait, I actually think I might understand it now... but it would still be nice to have someone clarify to make sure I am reasoning correctly..

 

[G1SG2]

As a balloon descends underwater at constant rate, I can figure out as much as that the volume decreases. However, I can't seem to grasp why the volume doesn't decrease linearly. It actually changes the most near the surface, and less as it descends.

My thought process:

P=density*g*y
as depth increases, P increases proportionally.
P is proportional to 1/V, so as P increases, V decreases proportionally.

I am either applying these equations incorrectly or am making a stupid mathematical error. Would anyone care to elaborate? Thanks.

Is this from TBR CBT 1? I just took it yesterday and I hated that passage with the balloons on the belt lol. I think what they're trying to say is that the volume changes the most at the beginning because the balloon already has a pressure of 1 atm at the surface and then when it goes 10 m below the surface it incurs another 1 atm of pressure, so now it is subject to 2 atm of pressure. To double that to 4 atm of pressure, it'll have to reach 30 m below the surface. In other words, it'll have to travel a relatively larger distance to double the pressure whereas before when it was at the surface, it only had to go 10 m below the surface to double the pressure from 1 atm to 2 atm. Thus, the decrease is not linear.

 

[Eye Cue]

Is this from TBR CBT 1? I just took it yesterday and I hated that passage with the balloons on the belt lol. I think what they're trying to say is that the volume changes the most at the beginning because the balloon already has a pressure of 1 atm at the surface and then when it goes 10 m below the surface it incurs another 1 atm of pressure, so now it is subject to 2 atm of pressure. To double that to 4 atm of pressure, it'll have to reach 30 m below the surface. In other words, it'll have to travel a relatively larger distance to double the pressure whereas before when it was at the surface, it only had to go 10 m below the surface to double the pressure from 1 atm to 2 atm. Thus, the decrease is not linear.

TBR indeed. Tried to rephrase it, though, because I didn't want to give it away to those who haven't taken it. heh
That's kind of the logic I was getting at, but still don't feel as strong with it as I wish I did.

 

[G1SG2]

TBR indeed. Tried to rephrase it, though, because I didn't want to give it away to those who haven't taken it. heh
That's kind of the logic I was getting at, but still don't feel as strong with it as I wish I did.

Whoops, haha. Yeah, I didn't feel that comfortable with it as well. TBR is tricky! Great practice, though. Alright, time for TBR CBT 2 🙂

 

[Akarat]

Since V is proportional to 1/P, would it help to think of it as a graph of y = 1/x?

With the graph, you can see that it is not a linear slope.

 

[Eye Cue]

Whoops, haha. Yeah, I didn't feel that comfortable with it as well. TBR is tricky! Great practice, though. Alright, time for TBR CBT 2 🙂

TBR CBT 2 on Monday for me, good luck!

Since V is proportional to 1/P, would it help to think of it as a graph of y = 1/x?

With the graph, you can see that it is not a linear slope.

That actually makes PERFECT sense. Thanks for the insight!

 

[loveoforganic]

And to think about it logically, if volume decreased linearly with pressure, you'd reach zero volume (and negative volume, which is??) very quickly.

 

[Eye Cue]

And to think about it logically, if volume decreased linearly with pressure, you'd reach zero volume (and negative volume, which is??) very quickly.

To answer your question, negative volume is what I have left in my Nutella jar after about the second break during an AAMC 😉