Final answer:
To calculate the final volume of an air bubble before it breaks the sea surface, we must apply the combined gas law, taking into account the changes in both pressure and temperature as the bubble rises from 18 m below the surface, where the sea density is 1606 kg/m³ and the temperature is 8°C, to the surface with a temperature of 25°C.
Step-by-step explanation:
The student is asking about the behavior of a gas bubble under changing pressure conditions as it rises from the depths of a sea to the surface, which involves the combined gas law in physics. The bubble's volume at the surface can be determined by using the combined gas law, which relates pressure, volume, and temperature changes of a gas. We assume that the amount of gas in the bubble (number of moles n) is constant, and we can ignore any solubility effects of the gas in water given the short time span of a bubble's ascent.
At a depth of 18 m below the surface, the absolute pressure can be calculated by adding the atmospheric pressure (1 atm) to the pressure due to the weight of the seawater above the diver (calculated using the depth, the density of seawater, and the acceleration due to gravity). The volume of the bubble at the surface can be found by applying Boyle's Law (for pressure-volume changes at constant temperature) and Charles's Law (for volume-temperature changes at constant pressure). These principles are combined since both the pressure and temperature of the bubble change during the ascent.
First, we need to convert the initial volume given in cm³ to L for consistency with typical gas law applications:
0.8 cm³ = 0.0008 L
Then, we would calculate the initial pressure at 18 m depth and the final pressure at the surface (assuming it's 1 atm), convert the temperatures from Celsius to Kelvin, and apply the combined gas law as follows:
P1 * V1 / T1 = P2 * V2 / T2
Where P1 is the initial pressure, V1 is the initial volume, T1 is the initial temperature, P2 is the final pressure (1 atm), V2 is the final volume, and T2 is the final temperature. After rearranging the equation and inserting the respective values, we can solve for V2, the final volume of the bubble before it breaks the surface.