An air bubble has a volume of 1.50 cm3 when it is released by a submarine 1.00 x 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.

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Asked Dec 24, 2019
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An air bubble has a volume of 1.50 cm3 when it is released by a submarine 1.00 x 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.

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Expert Answer

Step 1

Given,

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Volume of air bubble,V, =1.50 cm² =1.50×10-6 m³ Height,h=100 m Pressure acting on top surface,P, = P, =1.01x10° Pa %3D

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Step 2

By using Boyle’s equation between submarine and water surface and denoting submarine level as 1 and surface level as 2 then calculation can be done as follows,

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RV, = P,V, V, =v, P, At submarine level, P = P, + pgh where, Gauge Pressure = pgh At surface level, P = P, (P, +pgh). V, = P. pgh V, =| 1+ P

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Step 3

Since submarine is placed at 100 m below the above surface due to its situation the...

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pgh = 1+ |И V2 P. (1000)(9.8)(100) 1.01×10 V, =| 1+ |(1.50×10*) V; = (10.70)(1.50×10*) V, =1.61×10 m³ =16.1×10- m³ V, =16.1 cm³

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