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at a certain temperature radius of an air bubble is doubled when it comes to the top from the bottom of a mercury column of of height 'h'. If the pressure at the top is two atmospheres, the value of h is?

at a certain temperature radius of an air bubble is doubled when it comes to the top from the bottom of a mercury column of of height 'h'. If the pressure at the top is two atmospheres, the value of h is?

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Let the depth of lake be h cm
Pressure at the bottom of lake,
P1 = Atmospheric pressure + pressure due to water column in the lake
  = 76 × 13.6 × g + hρg
  = (76 × 13.6 + h × 1) g
Volume of bubble at the bottom, V1 = V
Volume of bubble at the surface, V2 = 2V
Pressure at the surface P2 = Atmospheric pressure
  = 76 cm of Hg
  = 76 × 13.6 × g
From Boyle's law, P1V1 = P2V2
(76 × 13.6 + h × 1) g × V = 76 × 13.6 × g× 2V
or h = (2 ×76 ×13.6) – (76 × 13.6)
  = 76 × 13.6
  = 1034 cm
  = 10.34 m

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