Step 1: Find Surface Area Relationship
The bubble's surface area at the top is
125% more than at the bottom. This means:
Atop =Abottom +1.25Abottom =2.25Abottom Step 2: Connect Surface Area and Volume
The volume
(V) of a bubble is related to its surface area
(A) by:
V∝A3∕2Step 3: Express Volume Change
Let
V1 be the volume at the bottom, and
V2 at the top. Then,
=()3∕2=(2.25)3∕2=3.375Step 4: Use Boyle's Law for Pressure and Volume
Since the water temperature is the same, Boyle's law applies:
p1V1=p2V2==3.375Step 5: Write Out Pressure at Bottom and Top
At the bottom, pressure is
p1= atmospheric pressure + pressure from water column with height
h Atmospheric pressure is equal to water pressure from 10 m column. So:
p1=10+h At the top, the pressure is just the atmospheric pressure:
p2=10Step 6: Set Up the Equation and Solve for
hSo,
= Set equal to
3.375:=3.37510+h=33.75h=23.75m
