To solve this problem, we will first find the pressure exerted by the water column and the air inside the bubble. Then, we will use Boyle's Law to find the volume of the bubble just above the water surface.
Calculate the pressure exerted by the water column:
The atmospheric pressure is equivalent to 8 cm of water, which is 8000 Pa (Pascals) using the conversion 1 cm of water = 100 Pa. The height of the beaker is 40 cm, so the pressure exerted by the water column (Pw) is:
Pw = 8000 Pa/cm * 40 cm = 320,000 Pa
Calculate the pressure exerted by the air inside the bubble:
The initial volume of the bubble is 7 cm³, and it is at the bottom of the beaker. We can assume that the pressure inside the bubble (Pa) is equal to the atmospheric pressure (8 cm of water) since the bubble is in contact with the water at the bottom of the beaker.
Pa = 8000 Pa/cm * 7 cm³ = 56,000 Pa
Use Boyle's Law to find the volume of the bubble just above the water surface:
Boyle's Law states that the product of pressure (P) and volume (V) of a gas is constant, provided that the temperature remains constant:
P1 * V1 = P2 * V2
In our case, we have two states:
State 1: Bubble at the bottom of the beaker (P1 = Pa, V1 = 7 cm³)
State 2: Bubble just above the water surface (P2 = Pw, V2 = x cm³)
Now, we can plug in the values and solve for x:
Pa * 7 = Pw * x
56,000 Pa * 7 cm³ = 320,000 Pa * x
372,000,000 Pa cm³ = 320,000 Pa * x
x = 372,000,000 Pa cm³ / 320,000 Pa ≈ 1,162.5 cm³
