[Rimi]

On the bottom of a sea (depth 50 m) a bubble of methane gas is formed (diameter dbottom = 1 cm).
What is the diameter of the bubble when it reaches the sea surface? The temperature rises from 5
°C at the bottom of the sea to 25 °C on the surface. The hydrostatic pressure is given by pH = ρ g
h, where h is the height of the water column. The density, ρ, is assumed to be independent of
temperature between 5 °C and 25 °C.

I'm not really sure how to approach this..I want to use P1V1/T1 = P2V2/T2, but I don't know what to do about P2 because wouldn't h be zero?

[Borek]

Pressure on the surface is already 1 atm, so the pressure at depth is 1 atm PLUS ρgh.

[Rimi]

Ohhh that's the key that I was missing huh? The rest of the approach is fine?

Is rho meant to be the density of water or the density of methane? I'm assuming water and since it doesn't change it'll just be 1 throughout. Is this correct?

Thanks.

[Borek]

Is rho meant to be the density of water or the density of methane? I'm assuming water and since it doesn't change it'll just be 1 throughout. Is this correct?

Water, yes.