Measuring the depth of a lake using a bottle

[lep11]

Homework Statement

To measure the depth of a lake, an empty bottle (V=1dm^3) is lowered to the bottom of the freshwater lake. There is a weight attached to the bottom of the bottle to keep it upright. When the bottle is recovered it is filled with 0,58dm^3 of water. Determine the depth of the lake. Assume constant temperature and standard atmospheric conditions.

Homework Equations

Boyle's law says pV=constant
pressure at height h is p(atm)+density of water*g*h
V2=0,42dm3[/B]

The Attempt at a Solution

p2=(p1V1)/V2=p(atm)+density of water*g*h
I solve for h and i got h=14,3m after substituting numbers in. Am I right?

 

[Orodruin]

It is not entirely clear what the procedure for recovering the bottle is. Is it closed at the bottom of the lake such that its contents are fixed to those at that depth? Otherwise the air will just expand again when the bottle is lifted up. This is assuming the opening of the bottle is facing down, if it is facing up the air will simply escape the bottle.

Assuming that the bottle is closed at the bottom and then taken up, your approach seems viable, but it is difficult to tell exactly without you filling in the details of your computation. A good rule of thumb is that the pressure increases by approximately 1 atmosphere per 10 m of depth.

 

[lep11]

It is not entirely clear what the procedure for recovering the bottle is. Is it closed at the bottom of the lake such that its contents are fixed to those at that depth? Otherwise the air will just expand again when the bottle is lifted up. This is assuming the opening of the bottle is facing down, if it is facing up the air will simply escape the bottle.

Assuming that the bottle is closed at the bottom and then taken up, your approach seems viable, but it is difficult to tell exactly without you filling in the details of your computation. A good rule of thumb is that the pressure increases by approximately 1 atmosphere per 10 m of depth.

Thanks for replying. The opening of the bottle is facing up according to the picture. The bottle is not closed at the depth h. However, it is said in the problem statement that the opening of the bottle is very very narrow (so that the air cannot escape).