Question

The diameters of a bubble at the surface of a lake is 4 mm and at the bottom of the lake is 1 mm. If atmospheric pressure is 1 atm and the temperature of the lake-water and the atmosphere are equal, what is the depth of the lake ? (The density of lake-water and Hg are 1 gm/ml and 13.6 gm/ml respectively. Also neglect the contribution of pressure due to surface tension)​

Answer 1

We know from the Charles Law that the pressure is directly proportional to the temperature at a given volume.

So, we get that

T1.P1.V1 = T2P2V2

Case1- When the bubble is at surface.

The pressure is P1 =1atm

And the volume is V1 =4π×(4)^2

Case2- When the bubble is at the bottom then we will get that.

The pressure will be P2=1atm+ρgh which will be (1+ 10 51000×9.8×h)atm

The volume is V2 =4π12

Since, the temperature is same given in the question, so on substituting the values in the equation we will get.

16=1+0.098h

On solving we will get h=153.03m

Answer 2

Refer to the attachment .....❤️