Final answer:
Using Boyle's Law, the absolute pressure at depth h for the underwater bubble is calculated to be approximately 549,545 Pascals.
Step-by-step explanation:
The question asks to calculate the absolute pressure at a certain depth in water when an air bubble increases in radius from 4 mm to 7 mm, assuming the temperature remains constant. We can use Boyle's Law, which states that the pressure of a given mass of an ideal gas is inversely proportional to its volume when the temperature stays constant (P1V1 = P2V2). The air bubble's volume at depth is (4/3)π(0.004 m)³ and at the surface is (4/3)π(0.007 m)³. The absolute pressure at the surface is 1 atmosphere, which can also be expressed as 101,325 Pa.
To find the pressure at depth, we'll set up the equation as follows: P1 * (4/3)π(0.004 m)³ = P2 * (4/3)π(0.007 m)³. Because we know P2 (absolute pressure at the surface), we can solve for P1 (absolute pressure at depth).
Substituting the given values and solving for P1 yields:
P1 * (4/3)π(0.004 m)³ = 101,325 Pa * (4/3)π(0.007 m)³
P1 = 101,325 Pa * ((0.007 m)³ /(0.004 m)³)
P1 = 101,325 Pa * (7/4)³
P1 = 101,325 Pa * (343/64)
P1 = 549,545 Pa
Therefore, the absolute pressure at depth h is 549,545 Pascals.