To calculate the pressure at a depth of 12 kilometers below sea level, we can use the formula for hydrostatic pressure, which is given by:
\[ P = P_0 + \rho g h \]
Where:
- \( P \) is the total pressure at depth,
- \( P_0 \) is the atmospheric pressure at sea level (approximately 101,325 Pa or 1 atmosphere),
- \( \rho \) is the density of seawater (approximately 1025 kg/m³),
- \( g \) is the acceleration due to gravity (approximately 9.81 m/s²),
- \( h \) is the depth in meters (12,000 m for 12 km).
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Calculate the hydrostatic pressure due to the water column:
\[ P_{water} = \rho g h = (1025 , \text{kg/m}^3)(9.81 , \text{m/s}^2)(12000 , \text{m}) \]
\[ P_{water} = 1025 \times 9.81 \times 12000 \approx 120,000,000 , \text{Pa} \quad (\text{or } 120 , \text{MPa}) \]
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Convert the pressure from pascals to atmospheres:
To convert pascals to atmospheres, we use the conversion \( 1 , \text{atm} = 101325 , \text{Pa} \):
\[ P_{water} \text{ (in atm)} = \frac{P_{water}}{101325} \approx \frac{120,000,000 , \text{Pa}}{101325 , \text{Pa/atm}} \approx 1184.5 , \text{atm} \]
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Add the atmospheric pressure at sea level to get the total pressure:
\[ P_{total} = P_{0} + P_{water} = 1 , \text{atm} + 1184.5 , \text{atm} \approx 1185.5 , \text{atm} \]
Thus, the total pressure at a depth of 12 kilometers below sea level is approximately 1185.5 atmospheres.