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

• Mo
In summary, the volume of the bubble increases as it rises to the surface of the lake due to a decrease in pressure and a constant temperature. The second part of the question involves finding the depth of the lake using the given pressure and bubble volumes. Fish being cold-blooded is also noted as a possible factor.
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.

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

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.

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: $P_1 V_1 = P_2 V_2$.

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.

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

1. How does pressure affect the volume of a fish's swim bladder?

The swim bladder of a fish is a gas-filled organ that helps the fish regulate its buoyancy. As the fish swims to different depths in the water, the surrounding pressure changes. This pressure change causes the gas in the swim bladder to compress or expand, therefore changing the volume of the bladder and helping the fish maintain its desired buoyancy.

2. Why do fish need to regulate their swim bladder volume?

Fish need to regulate their swim bladder volume in order to control their vertical position in the water. If the swim bladder is too full, the fish will float to the surface, making it difficult for them to swim down. On the other hand, if the swim bladder is too empty, the fish will sink to the bottom of the water, making it difficult for them to swim up.

3. How does the depth of the water affect the pressure on a fish's swim bladder?

The deeper a fish swims, the higher the water pressure will be. This increased pressure causes the gas in the swim bladder to compress, making the bladder smaller. As the fish swims back up to shallower depths, the pressure decreases and the swim bladder expands.

4. What happens if a fish's swim bladder is damaged or not functioning properly?

If a fish's swim bladder is damaged or not functioning properly, it can lead to buoyancy issues and difficulty swimming. The fish may not be able to control its position in the water and may struggle to maintain its desired depth. In some cases, this can also affect the fish's ability to feed and reproduce.

5. Can a fish's swim bladder volume be affected by factors other than pressure?

Yes, the volume of a fish's swim bladder can also be affected by factors such as body temperature and the amount of gas produced by the fish's metabolism. Changes in these factors can also impact the fish's buoyancy and ability to swim effectively.

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