How Does a Rising Bubble's Volume Change with Pressure and Temperature?

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Homework Help Overview

The discussion revolves around the behavior of a rising air bubble in a lake, specifically how its volume changes with varying pressure and temperature as it ascends from the bottom to the surface. The problem involves applying the ideal gas law to determine the volume ratio of the bubble at two different depths.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the application of the ideal gas law and the implications of temperature changes on volume. There is a question about how to handle temperature conversions, particularly from Fahrenheit to Kelvin. Additionally, the safety of a diver holding their breath during ascent is questioned, with considerations of volume expansion and temperature stability.

Discussion Status

The discussion is active, with participants exploring different approaches to the problem, including temperature conversion methods and the implications of volume expansion for divers. Some guidance has been offered regarding assumptions about temperature changes, but there is no explicit consensus on the safety of holding one's breath during ascent.

Contextual Notes

Participants are considering the effects of temperature and pressure on gas volume, and there is an ongoing debate about the assumptions regarding temperature stability for the diver compared to the bubble. The problem context includes specific pressures and temperatures at two depths in the lake.

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Homework Statement


A diver observes a bubble of air rising from the bottom of a 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 C, and the temperature at the surface is 23.0 C}.

What is the ratio of the volume of the bubble as it reaches the surface to its volume at the bottom, V2/V1?


Homework Equations


p1V1/T1 = p2V2/T2

V2/V1 = p1/p2 * T2/T1

The Attempt at a Solution



V2/V1 = (3.5)/1 * 23/4

V2/V1 = 20.125
 
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How would you solve the problem if the temperature was given to you in Fahrenheit?
 
I would convert to K. That gave me the correct answer. Thanks!

Also, there's a second part to this question:

"Would it be safe for the diver to hold his breath while ascending from the bottom of the lake to the surface?"

My first answer would be no, because the solution V2/V1 = 3.74 shows that the volume of air expands more than three times, but I think that the temperature inside the diver should stay the same, and so it won't expand like this. What's the answer?
 
Last edited:
Well, you could assume that the temperature doesn't change from the bottom to the top - you will still get a factor of more than three. What other difference is there between a diver and a bubble? :smile:
 

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