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
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.