Final answer:
The maximum depth a diver can snorkel differs between freshwater and Dead Sea water due to the varying densities. By equating the maximum pressure that human lungs can withstand in both environments, we can calculate the respective maximum depths and determine their difference based on density. The saltier and denser Dead Sea water results in a shallower maximum depth for safe snorkeling compared to freshwater.
Step-by-step explanation:
To understand the maximum depth at which a diver can snorkel in freshwater versus the saltier water of the Dead Sea, we must consider the impact of the water density and the maximum pressure difference human lungs can withstand. The scenario presented assumes a diver creating a negative gauge pressure of 3.00 cm H2O by snorkeling at 60.0 cm below the surface in freshwater. Pressure difference in the lungs is manageable within the body's maximum capacity of 0.056 atm to function properly.
To find the maximum depth (dmax) difference between freshwater and Dead Sea water, we use the relationship between pressure, depth, and density as follows: P = h
g, where P is pressure, h is depth, ρ (rho) is the density of the liquid, and g is the acceleration due to gravity. Since the maximum pressure is consistent for the diver's lung functionality, setting the pressures equal allows us to find the depths in each fluid by using the respective densities.
For freshwater (ρ = 1000 kg/m3):
dmax, fresh = (0.056 atm) / (1000 kg/m3 × 9.81 m/s2)
For Dead Sea water (ρ = 1.40×103 kg/m3):
dmax, Dead Sea = (0.056 atm) / (1.40×103 kg/m3 × 9.81 m/s2)
The difference in depths will be the subtraction of dmax, Dead Sea from dmax, fresh. Since Dead Sea water is denser, the depth at which the same pressure difference is experienced will be shallower compared to freshwater.