Lucy is going skin diving to see coral off the coast of Mexico in sea water with a density of 1025 kg/m^3.
If she were to hold her breath as she ascends to the waters surface a)by how many times would the volume of her lungs change assuming the water temperature remain constant? b)would her lungs be crushed or would they blow up like a balloon? c)What is the best way to ascend after diving?
By the way, for pressure submerged add the surface pressure to the pressure due to water depth.
a) To calculate the change in volume of Lucy's lungs as she ascends to the water's surface, we need to use Boyle's Law, which states that the volume of a gas is inversely proportional to its pressure, as long as the temperature remains constant.
Boyle's Law equation: P1 * V1 = P2 * V2
Since Lucy is going skin diving, we can assume that the initial pressure is atmospheric pressure (101325 Pa) at sea level. Let's denote this as P1 and the initial volume of her lungs as V1.
As Lucy ascends to the surface, the pressure decreases due to the decrease in hydrostatic pressure from the water column above her.
Let's assume the final pressure at the water surface is also atmospheric pressure (P2 = 101325 Pa). We need to find the final volume of her lungs, denoted as V2.
Using Boyle's Law: P1 * V1 = P2 * V2
Since P1 = P2 (both are atmospheric pressure), the equation simplifies to: V1 = V2
This means the volume of Lucy's lungs remains the same as she ascends to the water surface. Therefore, the volume of her lungs does not change by any factor.
b) Since the volume of Lucy's lungs does not change as she ascends, her lungs would not be crushed or blow up like a balloon. They would remain at their original volume.
c) The best way to ascend after diving is to follow proper decompression procedures. Ascending too quickly can lead to decompression sickness, also known as "the bends," which is caused by the formation of nitrogen bubbles in the body.
To ascend safely, divers should make decompression stops at specified depths to allow their bodies to gradually release excess nitrogen. The specific procedures and depths for decompression stops depend on the dive profile and diving certification level.
It is important to follow these procedures, ascend slowly, and maintain an appropriate ascent rate to ensure gas bubbles are safely eliminated from the body. Additionally, ensuring proper training, equipment, and supervision by experienced divers or instructors is essential for a safe ascent after diving.
To answer these questions, we'll need to use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature is held constant.
a) Let's assume that the initial volume of Lucy's lungs is V1, and the volume when she reaches the surface is V2. According to Boyle's Law, we have the equation: P1 ∙ V1 = P2 ∙ V2. Since she's holding her breath, the pressure inside her lungs remains constant. The pressure at the water surface (P2) is atmospheric pressure or approximately 1 atm. The pressure at the diving depth (P1) is the sum of the atmospheric pressure and the pressure due to the water column above her. We can calculate P1 using the equation P1 = P2 + ρ ∙ g ∙ h, where ρ is the density of water, g is the acceleration due to gravity, and h is the depth of the dive.
b) To determine whether her lungs would be crushed or blow up like a balloon, we need to compare the initial lung volume to the final lung volume. If the final lung volume (V2) is much smaller than the initial lung volume (V1), her lungs would be crushed. On the other hand, if the final lung volume is significantly larger than the initial volume, her lungs would expand, risking rupture.
c) The best way to ascend after diving is to practice a controlled ascent known as "decompression." Ascending too quickly can lead to decompression sickness or "the bends." The standard practice is to ascend slowly, making decompression stops at specific depths for a certain amount of time, during which excess nitrogen can be safely released from the body.
To obtain specific values for these calculations, we'll need the diving depth and the corresponding data.
She went SCUBA diving, NOT skin diving!
Skin diving you do not breathe air at high pressure when submerged and are therefore not in danger of blowing your lungs up upon ascent.
You did not say how deep.
surface pressure = 10^5 Pascals
pressure at depth = rho g d
= 1025*9.81*depth in meters
P1V1 = P2 V2
V1/V2 = P2/P1
The air expands during ascent as the pressure goes down. Lungs blow up, called "air embolism" by divers.
YOU MUST breathe out while ascending. Navy submarine escape training requires ascending in test tank yelling HO HO HO so instructor is sure trainee is breathing out.