# problem

Joined Dec 29, 2004
83
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=po+ρ *g*D, where po 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 thoses first.

B

#### CoulombMagician

Joined Jan 10, 2006
37
a) Boyle's law P*V/T = constant. T is constant here so at a depth D the pressure is p and the piston compresses the gas inside until the internal pressure is also p. At this point the new volume V is

V = V0*p0/p = (p0/p)*1.5L

B) The bouyant force is the weight of the displaced water less the weight of the bottle

F = 1.0kg/L * 1.5L * (p0/p) -0.3kg

When Archimedes discovered this principle while he was bathing he was reportedly so excited that he ran naked thorough the city streets.

Joined Dec 29, 2004
83
Originally posted by CoulombMagician@Jan 21 2006, 04:12 AM
a) Boyle's law P*V/T = constant. T is constant here so at a depth D the pressure is p and the piston compresses the gas inside until the internal pressure is also p. At this point the new volume V is

V = V0*p0/p = (p0/p)*1.5L
B) The bouyant force is the weight of the displaced water less the weight of the bottle

F = 1.0kg/L * 1.5L * (p0/p) -0.3kg

When Archimedes discovered this principle while he was bathing he was reportedly so excited that he ran naked thorough the city streets.
[post=13305]Quoted post[/post]​
Thank you,
I understand your reasonning but how can we find the p0??

#### CoulombMagician

Joined Jan 10, 2006
37
It is one atmosphere, ~15 psi if my memory is working.