Air Bubbles in water, or lake temperature, lake depth, related Questions.

(1) The diameters of a buble 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 respectively. Also neglect the contribution of pressure due to surface tension)

(2) Radius of bubble X-1 is 0.32 cm and X-2 is 0.48 cm. What is the temperature of of pond at the position of bubble X-2. If presure of the Bottom of the pond is 2.8 atm and at the top is 1 atm.

(3) A bubble of gas released at bottom. of the lake increase to four time its original volume when it reach the surface. assuming that atmosphere ic pressure is equivalent to the exerted by a column of water 10 m height. What is the depth of the lake.

(4) An air bubble starts rising from the bottom of lake, it diameter is 3.6 mm at bottom and 4 mm at the surface. The depth of lake is 250 cm and temperature at surface is 40℃ . What is the temperature at the bottom of lake? (Given atmospheric pressure = 76 cm of Hg and g= 980 cm sec-1 neglect surface tension effect).