An air bubble rises from the bottom of a water tank of height 5 m . If the initial volume of the bubble is 3 mm 3 . What will be its volume as it reaches the surface. Assume that its temperature does not change. [ g = 9 . 8 m s - 2 , 1 atm = 10 5 Pa , density of water = 1 gm cc - 1 ]

Question

An air bubble rises from the bottom of a water tank of height 5 m . If the initial volume of the bubble is 3 mm 3 . What will be its volume as it reaches the surface. Assume that its temperature does not change. [ g = 9 . 8 m s - 2 , 1 atm = 10 5 Pa , density of water = 1 gm cc - 1 ], 1 . 5 mm 3, 4 . 5 mm 3, 9 mm 3, 6 mm 3

MARKS App · Accepted Answer

Given that, V 1 = 3 mm 3 , = d = 5 m Pressure on surface of water tank, P 2 = 1 atm = 10 5 p a Pressure at depth of 5 m P 1 = 1 atm + d p g = 10 5 + 1 gm cc - 1 + 5 × 10 3 × 9 . 8 P 1 = 149 × 10 3 V 2 = P 1 V 1 T 2 T 1 P 2 = P 1 V 1 P 2 ( ∵ Temperature is constant) = 149 × 10 3 × 3 10 5 = 4 . 47 mm 3 = 4 . 5 mm 3

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