Answer:
The radius of the bubble when it reaches the surface at 30 ºC is 1.015 centimeters.
Explanation:
Let suppose that air bubble behaves as ideal gas, whose equation of state is:
(Eq. 1)
Where:
- Pressure of the bubble, measured in kilopascals.
- Volume of the bubble, measured in cubic meters.
- Molar amount of the bubble, measured in kilomoles.
- Temperature, measured in Kelvin.
- Ideal gas constant, measured in kilopascal-cubic meter per kilomole-Kelvin.
Then, we eliminate the molar amount and the ideal gas constant by constructing the following relationship:
(Eq. 2)
Where:
, - Pressure of the bubble at bottom and surface, measured in kilopascals.
, - Volume of the bubble at bottom and surface, measured in cubic meters.
, - Temperature of the bubble at bottom and surface, measured in Kelvin.
The pressure experimented by the bubble at bottom and surface are, respectively:
If we know that , , , and , then the volume of the bubble at surface is:
And the volume of the air bubble is determined by this formula:
(Eq. 3)
Where is the radius of the air bubble, measured in centimeters.
If we know that , then the radius of the air bubble is:
The radius of the bubble when it reaches the surface at 30 ºC is 1.015 centimeters.