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 pressure at 45.0 meters under water (543 kPa) into atmospheres (atm) and millimeters of mercury (mmHg), we use the following conversion factors:
- 1 atm=101.325 kPa1 \text{ atm} = 101.325 \text{ kPa}
- 1 atm=760 mmHg1 \text{ atm} = 760 \text{ mmHg}
Step 1: Convert 543 kPa to atm
Patm=543 kPa101.325 kPa/atm≈5.36 atmP_{\text{atm}} = \frac{543\ \text{kPa}}{101.325\ \text{kPa/atm}} \approx 5.36\ \text{atm}
Step 2: Convert 543 kPa to mmHg
PmmHg=543 kPa101.325 kPa/atm×760 mmHg/atmP_{\text{mmHg}} = \frac{543\ \text{kPa}}{101.325\ \text{kPa/atm}} \times 760\ \text{mmHg/atm} PmmHg≈5.36×760≈4073.6 mmHgP_{\text{mmHg}} \approx 5.36 \times 760 \approx 4073.6\ \text{mmHg}
Final Answers:
- Pressure in atm: ≈ 5.36 atm
- Pressure in mmHg: ≈ 4074 mmHg
Pressure is a measure of force applied per unit area. Under water, pressure increases with depth due to the weight of the water above. At a depth of 45.0 meters, the given pressure is 543 kilopascals (kPa). However, this value may need to be converted to other common pressure units—atmospheres (atm) and millimeters of mercury (mmHg)—for clarity or to match the units used in various scientific and engineering fields.
To convert kPa to atm, we use the fact that 1 atm equals 101.325 kPa. Dividing 543 kPa by 101.325 kPa/atm gives approximately 5.36 atm. This means that the pressure at that depth is about 5.36 times the standard atmospheric pressure at sea level.
For mmHg, which is a unit derived from the height of a mercury column that can be supported by atmospheric pressure, we convert using the relationship between atmospheres and mmHg. Since 1 atm equals 760 mmHg, multiplying 5.36 atm by 760 mmHg/atm gives us roughly 4074 mmHg.
These conversions are essential in various scientific applications such as diving physics, fluid mechanics, and medical contexts like measuring blood pressure. Knowing how pressure varies in different units helps professionals make appropriate calculations and safety considerations when working with pressurized systems or environments like underwater or high-altitude settings.
