Can Boyle's Law Determine How Far a Submerged Bottle Must Be Sunk?

[kriegera]

My physics teacher recently assigned this challenge and I have no clue where to begin. I think the ideal gas law might apply but I'm not sure. Any insight?

A bottle, full of air at atmospheric pressure, whose volume is 500 cubic centimeters, is sunken mouth downwards below the surface of a pond. How far must it be sunk for 100 cubic centimeters of water to run up into the bottle?

 

[Doc Al]

Sure, use the ideal gas law.

 

[kriegera]

Not quite sure how to use the gas law though on this specific problem. Since the Ideal Gas Law is:

pV=nRT

where p is the absolute pressure of the gas; V is the volume of the gas; n is the amount of substance of the gas, usually measured in moles; R is the gas constant and T is the absolute temperature.

All we're given in the problem is the volume of gas and the amount of liquid we want to replace the gas. None of the other elements are available to us. I recognize this as an ideal gas law problem but don't know how to get started.

 

[Andrew Mason]

Not quite sure how to use the gas law though on this specific problem. Since the Ideal Gas Law is:

pV=nRT

where p is the absolute pressure of the gas; V is the volume of the gas; n is the amount of substance of the gas, usually measured in moles; R is the gas constant and T is the absolute temperature.

All we're given in the problem is the volume of gas and the amount of liquid we want to replace the gas. None of the other elements are available to us. I recognize this as an ideal gas law problem but don't know how to get started.

If 100 ml of water is in the bottle, what is the volume of air? What is the pressure of the air (this is where you use the ideal gas law to find the pressure of the compressed air in the bottle). How does this pressure compare to the pressure of the water at that point? What depth gives that water pressure?

AM

 

[Doc Al]

A couple of hints:
(1) Assume the temperature is constant.
(2) How does the water pressure depend upon depth below the surface?

 

[hawkmaster]

Due to limited data given in the question I would assume your instructor is looking for a simple solution such as Boyle's law where P1 x V1 = P2 X V2. Once you account for the pressure then calculate the change in pressure as the bottle is submerged.