There is an air bubble of radius 1 . 0 mm in a liquid of surface tension 0 . 075 N m – 1 and density 1000 kg m – 3 at a depth of 10 cm below the free surface. The amount by which the pressure inside t

Question

There is an air bubble of radius 1 . 0 mm in a liquid of surface tension 0 . 075 N m – 1 and density 1000 kg m – 3 at a depth of 10 cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _______ P a g = 10 m s - 2 .

TestHub · Accepted Answer

The pressure inside the bubble is given by
$Δ P = P - P_{0} = ρ g h + \frac{2 T}{r}$
The data given is
$r = 10^{- 3} m T = 0.075 N m^{- 1} ρ = 1000 kg m^{- 3} h = 10 cm$
Therefore, the pressure in the bubble is
$Δ P = (1000 \times 10 \times 10 \times 10^{- 2}) + \frac{2 \times 0.075}{10^{- 3}} = 1000 + 150 = 1150 P a$

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