The pressure 45.0 m under water is 543 kPa. What is this pressure in atmospheres (atm)?
The correct answer and explanation is :
To convert the pressure from kilopascals (kPa) to atmospheres (atm), we need to use the conversion factor between these two units. The relationship is:
[
1 \, \text{atm} = 101.325 \, \text{kPa}
]
Given that the pressure at 45.0 meters underwater is 543 kPa, we can use the following formula to convert this pressure to atmospheres:
[
\text{Pressure in atm} = \frac{\text{Pressure in kPa}}{101.325 \, \text{kPa/atm}}
]
Now, substituting the given pressure of 543 kPa into this formula:
[
\text{Pressure in atm} = \frac{543 \, \text{kPa}}{101.325 \, \text{kPa/atm}} \approx 5.36 \, \text{atm}
]
Explanation:
The problem states that the pressure at a depth of 45.0 meters underwater is 543 kPa. When we are underwater, pressure increases due to the weight of the water above us. This is because the water exerts additional pressure on everything below the surface, increasing the total pressure experienced as we go deeper. The pressure at any depth under water consists of two components:
- Atmospheric Pressure: The pressure exerted by the air above the water. At sea level, this pressure is 1 atmosphere (atm), equivalent to 101.325 kPa.
- Hydrostatic Pressure: The pressure exerted by the water column above the point in question. This increases with depth. The total pressure at a depth is the sum of atmospheric pressure and hydrostatic pressure.
To convert the pressure from kPa to atmospheres, we simply use the conversion factor between these two units. The result tells us that the total pressure at 45 meters underwater is approximately 5.36 atm, which includes both the atmospheric pressure and the pressure from the water column.