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

[6021023]

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

 

[naresh]

How would you solve the problem if the temperature was given to you in Fahrenheit?

 

[6021023]

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?

 

[naresh]

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?