The pressure 45.0 m under water is 543 kPa. What is this pressure in atmospheres (atm)? P atm
What is this pressure in millimeters of mercury (mmHg)? PE mmHg
The correct answer and explanation is :
The given pressure of 543 kPa is equivalent to:
- 5.36 atm (atmospheres)
- 4072.83 mmHg (millimeters of mercury)
Explanation:
Pressure is a measure of force exerted per unit area. In this case, we are given the pressure 45.0 m underwater as 543 kPa, and we need to convert it into different units.
Conversion to Atmospheres (atm):
The atmospheric pressure at sea level is defined as 1 atm = 101.325 kPa. To convert from kPa to atm:
[
P_{\text{atm}} = \frac{P_{\text{kPa}}}{101.325}
]
[
P_{\text{atm}} = \frac{543}{101.325} = 5.36 \, \text{atm}
]
This means the pressure at 45 meters underwater is about 5.36 times the atmospheric pressure at sea level.
Conversion to Millimeters of Mercury (mmHg):
The unit mmHg is often used in medical and meteorological applications. The conversion factor is 1 atm = 760 mmHg, and since 1 atm = 101.325 kPa, we use:
[
P_{\text{mmHg}} = P_{\text{kPa}} \times \frac{760}{101.325}
]
[
P_{\text{mmHg}} = 543 \times \frac{760}{101.325} = 4072.83 \, \text{mmHg}
]
Thus, a pressure of 543 kPa corresponds to 4072.83 mmHg.
This calculation is crucial in engineering, diving, and atmospheric studies, where understanding pressure variations is necessary for safety and operational efficiency.
