An air bubble has a volume of 1.65 cm3 when it is released by a submarine 105 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.
_____cm3
To determine the final volume of the air bubble when it reaches the surface, we can use Boyle's Law, which states that the volume of a gas is inversely proportional to its pressure.
In this scenario, the pressure at the bottom of the lake and the pressure at the surface are different. As the bubble ascends from 105 m below the surface to the surface, the pressure decreases.
We can use the following formula to calculate the final volume:
P1 * V1 = P2 * V2
Where:
P1 = Initial pressure (at the bottom of the lake)
V1 = Initial volume (1.65 cm3)
P2 = Final pressure (at the surface)
V2 = Final volume (what we want to find)
Since the number of air molecules remains constant and the temperature is constant, we can assume that the product of pressure and volume is constant.
The pressure at the bottom of the lake can be calculated as:
P1 = P0 + ρgh
Where:
P0 = Atmospheric pressure (usually taken as 1 atm or 101.325 kPa)
ρ = Density of water (approximately 1000 kg/m3)
g = Acceleration due to gravity (9.8 m/s2)
h = Depth below the surface (105 m)
Plugging in the values, we can calculate P1.
Next, we need to find P2, the final pressure at the surface. Since the bubble reaches the surface, the pressure is equal to atmospheric pressure (P0).
Now we can rearrange the equation:
P1 * V1 = P2 * V2
V2 = (P1 * V1) / P2
Using the known values of P1, V1, and P2 that we calculated, we can substitute them into the equation to find V2, the final volume of the bubble when it reaches the surface.