An air bubble of volume 1 cm 3 rises from the bottom of a lake 40 m deep to the surface at a temperature of 12 ° C . The atmospheric pressure is 1 × 10 5 Pa , the density of water is 1000 kg m - 3 and g = 10 m s - 2 . There is no difference of the temperature of water at the depth of 40 m and on the surface. The volume of air bubble when it reaches the surface will be

Step-by-step solution

The pressure at the bottom of the lake can be calculated as follows: P b o t t o m =   P 0   +   ρ g h = 10 5 + 1000   ×   10   ×   40   Pa = 5 × 10 5   Pa   As the temperature of water remains constant, it can be written that P bottom V bottom = P top V top       . . . ( 1 ) Substitute the values of the known parameters into equation (1) to calculate the required volume of the bubble when it reaches the surface. 5 × 10 5 &#21