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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

An air bubble has a volume of 1.50 cm3 when it is released by a submarine 1.00 × 102 m below the surface of a lake. What is the volume of the bubble when it reaches the surface? Assume the temperature and the number of air molecules in the bubble remain constant during its ascent.

To determine
The volume of the bubble when it reaches the surface ( V2 ).

Explanation

Given Info: The initial volume of the bubble is V1=1.50cm3 . The depth is h=1.00×102m .

At constant temperature,

V2V1=P2P1 (I)

  • P1 is the atmospheric pressure.
  • P2 is the pressure at depth ‘h’.

The formula to calculate the pressure at depth ‘h’ is,

P2=P1+hρg (II)

  • ρ is the density of water.
  • g is the acceleration due to gravity.

From Equations (I) and (II),

V2=V1(1+hρgP1)

Substitute 1.50cm3 for V1 , 1.00×102m for h, 1000kgm3 for ρ , 9

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