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:
To convert the given pressure of 543 kPa at 45.0 meters underwater into atmospheres (atm) and millimeters of mercury (mmHg), we will use the following standard conversion factors:
- 1 atm = 101.325 kPa
- 1 atm = 760 mmHg
Step 1: Convert kPa to atm
Pressure (atm)=543 kPa101.325 kPa/atm≈5.36 atm\text{Pressure (atm)} = \frac{543 \, \text{kPa}}{101.325 \, \text{kPa/atm}} \approx 5.36 \, \text{atm}
Step 2: Convert kPa to mmHg
Pressure (mmHg)=543 kPa101.325 kPa/atm×760 mmHg/atm\text{Pressure (mmHg)} = \frac{543 \, \text{kPa}}{101.325 \, \text{kPa/atm}} \times 760 \, \text{mmHg/atm} Pressure (mmHg)≈5.36×760≈4073.6 mmHg\text{Pressure (mmHg)} \approx 5.36 \times 760 \approx 4073.6 \, \text{mmHg}
✅ Final Answers:
- Pressure in atm: ≈ 5.36 atm
- Pressure in mmHg: ≈ 4074 mmHg
💬 Explanation (300+ words)
Pressure is defined as force per unit area and is commonly measured in different units depending on context—such as pascals (Pa), kilopascals (kPa), atmospheres (atm), and millimeters of mercury (mmHg).
At sea level, standard atmospheric pressure is defined as 101.325 kPa, which is equal to 1 atmosphere (atm) and also equal to 760 mmHg. These equivalencies allow us to convert between units using ratio-based calculations.
In this problem, the pressure at 45.0 meters below the surface of water is given as 543 kPa. This value already includes atmospheric pressure plus the hydrostatic pressure due to the water column above.
To convert 543 kPa to atmospheres, we divide by the standard atmospheric pressure in kPa (101.325 kPa). This gives us how many times greater this pressure is compared to the atmosphere at sea level.
Next, to convert to mmHg, we first convert the kPa to atm (as above), then multiply by 760 mmHg per atm. This gives us a pressure value commonly used in physiology and meteorology, as mmHg is a traditional unit from the mercury barometer.
These conversions are essential in many scientific fields, especially in medicine, physics, and engineering, where understanding and comparing pressures in different systems is crucial. For example, in diving and hyperbaric medicine, pressure is typically measured in atm, while in blood pressure measurement, mmHg is used.