Calculate the pressure in atmospheres in the ocean at a depth of 3.20 km assuming the constant density of sea water in the water column is 1.10 g/mL. The atmospheric pressure is 1.00 atm.
To calculate the pressure in atmospheres in the ocean at a depth of 3.20 km, you can use the formula for hydrostatic pressure:
P = P₀ + ρgh,
where:
P is the pressure at the given depth,
P₀ is the atmospheric pressure at the surface (1.00 atm),
ρ is the density of sea water (1.10 g/mL),
g is the acceleration due to gravity (9.8 m/s²),
and h is the depth (3.20 km).
First, convert the depth from kilometers to meters:
3.20 km = 3.20 × 1000 m = 3200 m.
Next, convert the density of sea water from grams per milliliter (g/mL) to kilograms per cubic meter (kg/m³):
1.10 g/mL = 1.10 × 1000 kg/m³ = 1100 kg/m³.
Now, substitute the values into the formula:
P = 1.00 atm + (1100 kg/m³) × (9.8 m/s²) × (3200 m).
Calculating this equation will give us the pressure in units of pascals (Pa). To convert to atmospheres, you can use the conversion factor:
1 atm = 101325 Pa.
So, divide the result by 101325 to get the pressure in atmospheres.
P = (1.00 atm + (1100 kg/m³) × (9.8 m/s²) × (3200 m)) / 101325.