How Does Water Pressure Change with Depth?

[brad sue]

Hi,
I am lost with this problem.

A bottle containig air is closed with a watertight yet smoothly moving piston. The bottle with its air has a total mass of 0.30kg. At the surface of a body of water whose temperature is a uniform 285 K throughout, the volume of air contained in the bottle is 1.5L.
Recall that the pressure of water increases with depth below the surface, D, as p=p_o+ρ *g*D, where p_o is the surface pressure and ρ=1.0 kg/L.
The bottle is submerged.
a- What is the volume of the air in the bottle as a function of depth?
b- Calculate the buoyant force on the bottle as a function of depth?

There are other questions but I need to understand these ones first.
There a picture but if you need it , I will try to draw it.
thank you

 

[Doc Al]

a- What is the volume of the air in the bottle as a function of depth?

Treat the air as an ideal gas. Start by figuring out the volume of air as function of pressure.

b- Calculate the buoyant force on the bottle as a function of depth?

How does the buoyant force on an object depend on the object's volume? (What is Archimedes' principle?)

 

[lightgrav]

This starting situation is at the surface of Earth,
with Pressure = 1 atm = 101,000 N/m^2 .
You'll have to find out how much of this 0.3 kg is air,
and how much of it is glass (the glass does not compress).

 

[Doc Al]

You'll have to find out how much of this 0.3 kg is air,
and how much of it is glass

I wouldn't bother trying to do that: It will be easier to just treat the air in terms of its volume (which is given at the surface), and assume that the volume of the bottle itself can be neglected.

 

[brad sue]

Treat the air as an ideal gas. Start by figuring out the volume of air as function of pressure.
How does the buoyant force on an object depend on the object's volume? (What is Archimedes' principle?)

OK, If I use :
PV=nRT and P_o*V_o=nRT.
then I take the ratio PV/P_o*V_o which is 1
I found:
V=V_o*P_o/P
Am I right?

 

[Doc Al]

Looks good to me.