Ideal Gas Expansion: Finding Depth of Tank

[Tardis Traveller]

Homework Statement

A bubble comes from the bottom of the tank of water to the surface and triples in its volume. If the temperature of the tank of water doesn't deppend on the depth what is the depth of the tank that the bubble was at?

Homework Equations

$PV=nRT$

The Attempt at a Solution

Since the temperature stays constant i guessed
$P_bV_b=P_uV_u$
$P_bV_b=P_u3V_b$
and i get 30m but the answer states 20m. What is wrong?

 

[SteamKing]

What's the pressure at the surface of the water?

 

[Tardis Traveller]

What's the pressure at the surface of the water?

The atmospheric pressure 1000 kg/m3

 

[SteamKing]

The atmospheric pressure 1000 kg/m3

That's not right; it's not even wrong.

Pressure has units of force per unit area. 1000 kg/m³ is the density of fresh water (approximately).

You should look up what the value of a standard atmosphere is.

 

[Tardis Traveller]

That's not right; it's not even wrong.

Pressure has units of force per unit area. 1000 kg/m³ is the density of fresh water (approximately).

You should look up what the value of a standard atmosphere is.

Oops, your absolutely right i gave you the density, its 100kPa actually at the surface

 

[SteamKing]

Oops, your absolutely right i gave you the density, its 100kPa actually at the surface

You should draw a sketch to help you focus.

Since the top of the tank is presumably open to the atmosphere, the pressure at the water's surface will be atmospheric.

What's the pressure acting on the bubble when it is submerged and starts to rise?

 

[ogg]

P1V1=P2V2 is correct, of course. In order for V2 = 3*V1 it must be P2 = P1÷3
So, you know at depth X, P is 3 times atmospheric. Since you haven't shown any further work about how pressure increases with water depth, I'll stop here.