Finding the volume of air in a box when it's lowered into water?

[PhyIsOhSoHard]

Homework Statement

A box that is open at the bottom is lowered into the sea (density like water). The outer volume of the box and the air inside it is [itex]V_{out}=3 m^3[/itex].
The moment the box touches the sea surface the air inside it gets trapped and has a volume at [itex]V_0=2.5 m^3[/itex] and a pressure at [itex]p_0=101 kPa[/itex]. As the box is lowered the temperature is constant and the mass of the box and air is [itex]m=4000 kg[/itex].
Calculate the volume of the air in the box as it is lowered to [itex]h=19 m[/itex] below the sea surface.

Homework Equations

[itex]p=p_0+ρgh[/itex]

[itex]pV=nRT[/itex]

The Attempt at a Solution

I was thinking about using the first equation to calculate the pressure at 19 m below the sea surface since I know the pressure at the sea surface and I know the density of water:
[itex]p=101000 Pa+9.8\frac{m}{s^2}\cdot 19 m=287000 Pa[/itex]

I'm supposed to use the ideal-gas equation to calcuate the volume of the air trapped in the box at 19 m below the sea surface... So I just calculated the pressure at this level but I'm completely lost on what else to do now.

 

[paisiello2]

The thing unclear to me is the volume of air in the box is stated as 3.0 and then re-stated again as 2.5. But perhaps it doesn't change the answer.

At any rate, you can apply the ideal gas law since you know the final pressure P1 and the initial pressure p0 and volume V0.

 

[PhyIsOhSoHard]

The thing unclear to me is the volume of air in the box is stated as 3.0 and then re-stated again as 2.5. But perhaps it doesn't change the answer.

At any rate, you can apply the ideal gas law since you know the final pressure P1 and the initial pressure p0 and volume V0.

The 3.0 is the volume for the air and the box. The 2.5 is only for the air.

In the ideal gas law what do I use for n and T?

 

[paisiello2]

Yes, of course, that would make the most sense. It's confusing since Vout is then irrelevant.

n and T are constant, therefore nRT is also constant. So you can assume any value you like.

 

[PhyIsOhSoHard]

Yes, of course, that would make the most sense. It's confusing since Vout is then irrelevant.

n and T are constant, therefore nRT is also constant. So you can assume any value you like.

But what about [itex]V_0=2.5[/itex]? Am I not supposed to use that for anything?

 

[NascentOxygen]

But what about [itex]V_0=2.5[/itex]? Am I not supposed to use that for anything?

You are using Boyle's Law, ## PV=constant##
where you are given ##V_0## and required to find ##V_1##