Why Does a Bubble Expand as It Rises to the Surface?

[Mo]

I have attempted the first part of this question.I am hoping someone will be able to check if they think my reasoning is ok.The second part however, has me stumped A push in the right direction would be quite nice --thank you!--

The Question
"A fish resting on the bottom of a lake releases a small air bubble from its mouth.The bubble increases in volume as it journeys to the surface through water known to be at a constan temperature.Explain why the volume of the bubble increases as it rises to the surface.The volume of the realeased bubble was 4mm^3 but had increased to 20mm^3 (cubed) by the time it had reached the surface.Given that the atmosphjeric pressure acting on the surface of the lake is equivalent to an additional 10m of water, calculate the depth of the lake at the point where the fish is resting.Explain all your working.

My Answer
a) "The volume of the bubble increases as it rises to the surface, this can be because of:

The pressure being decreased
The temperature decreasing

Since both are related to each other, we can only assume that the temperature of the bubble decreased (to that of the sea level constan), wghich led to a a decrease in pressure and hence, an increase in volume"

b) Have not got a clue.

I hope someone will be able to check my first answer, and maybe give me a little push in the right direction for part b. Thanks very much,

Regards,
Mo

 

[Gamma]

My Answer
a) "The volume of the bubble increases as it rises to the surface, this can be because of:

The pressure being decreased
The temperature decreasing

Since both are related to each other, we can only assume that the temperature of the bubble decreased (to that of the sea level constan), wghich led to a a decrease in pressure and hence, an increase in volume"

It is given that the temparature of the water remains constant. So
$$P*V = Constant$$

As one moves up from the bottom of the lake, there is a drop of pressure.
P decreased means V should increase.

For the second part, if what is given as the additional pressure (10 m water) is the pressure difference between lake bottom and the surface, then the answer is very straight forward.

Gamma.

 

[Doc Al]

As Gamma explained, treat the temperature of the water as constant throughout, so:
$$P*V = Constant$$

For part 2, you need to figure out the pressure difference between the surface and bottom of the lake. Use the given bubble volumes and the pressure at the surface (= 10 m of water!) to solve for the pressure at the bottom. Set up a ratio like this: $P_1 V_1 = P_2 V_2$.

 

[HallsofIvy]

Fish are cold blooded. There would be no reason for the initial temperture of the bubble to be different from the temperature of the water which we are told is a constant.

The pressure on the bubble is equal to the atmospheric pressure plus the weight of water above (which decreases as it rises) divided by the surface area of the bubble.

 

[Mo]

Thank you for your help, all. It has helped me realize the answer (and the fact i got to revise this stuff a lot more!)

Reagrds,
Mo