Question

A diver observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 2.50 atm ) to the surface (where the pressure is 1.00 atm). The temperature at the bottom is 4.0 ∘C and the temperature at the surface is 23.0 ∘C. What is the ratio of the volume of the bubble as it reaches the surface to its volume at the bottom?

Answer 1

Using the universal gas equation, we have

P1V1 = nRT1 ...........(1)

P2V2 = nRT2 .............(2)

Dividing (1) by 2 we have

V1/V2 = P2T1 / P1T2

V1/V2 = 2.5 *277 / 1 * 297

V1/V2 = 2.33

So the ratio of the volume at the surface and at the bottom is 2.33