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 :
Correct Answers:
- Pressure in atmospheres (atm): 5.36 atm
- Pressure in millimeters of mercury (mmHg): 4073 mmHg
Explanation (300+ words):
When dealing with fluid pressure, such as pressure at a certain depth underwater, we often measure it in kilopascals (kPa). However, other common pressure units include atmospheres (atm) and millimeters of mercury (mmHg), especially in scientific, meteorological, and medical contexts. Let’s walk through the conversion process and understand how it works.
Given:
- Pressure = 543 kPa
- Depth = 45.0 meters (though it’s given, we don’t need it for the conversions here)
Step 1: Convert kPa to atm
1 atmosphere (atm) is defined as exactly 101.325 kPa.
To convert from kPa to atm:
[
\text{Pressure (atm)} = \frac{\text{Pressure (kPa)}}{101.325}
]
[
\text{Pressure (atm)} = \frac{543}{101.325} ≈ 5.36 \, \text{atm}
]
So, the pressure at 45.0 meters underwater is approximately 5.36 atm.
Step 2: Convert kPa to mmHg
1 atmosphere is also equivalent to 760 mmHg (millimeters of mercury), so:
[
\text{Pressure (mmHg)} = \frac{760}{101.325} × \text{Pressure (kPa)}
]
[
\text{Pressure (mmHg)} ≈ 7.4989 × 543 ≈ 4073 \, \text{mmHg}
]
Thus, 543 kPa is approximately 4073 mmHg.
Why These Units Matter:
- kPa is common in engineering and physics.
- atm is useful for comparing pressure to atmospheric pressure at sea level.
- mmHg is often used in medicine (like blood pressure readings).
