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 543 kPa into atmospheres (atm) and millimeters of mercury (mmHg), we will use standard 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
Pressure (atm)=543 kPa101.325 kPa/atm=5.36 atm\text{Pressure (atm)} = \frac{543 \, \text{kPa}}{101.325 \, \text{kPa/atm}} = 5.36 \, \text{atm}
Step 2: Convert 543 kPa to mmHg
First, convert kPa to atm (as above), then use: Pressure (mmHg)=5.36 atm×760 mmHg/atm=4073.6 mmHg\text{Pressure (mmHg)} = 5.36 \, \text{atm} \times 760 \, \text{mmHg/atm} = 4073.6 \, \text{mmHg}
Final Answers:
- 5.36 atm
- 4073.6 mmHg
300-Word Explanation:
Pressure is the force applied per unit area and is commonly measured in several units depending on the context—kilopascals (kPa), atmospheres (atm), and millimeters of mercury (mmHg or torr) are standard units in physics and chemistry.
At a depth of 45.0 meters under water, the pressure increases due to the weight of the water above. The total pressure at this depth includes atmospheric pressure plus the pressure from the water column. Here, you are given the absolute pressure as 543 kPa. To make meaningful comparisons, it’s often necessary to convert this value into other units.
The kilopascal (kPa) is a metric unit of pressure. The atmosphere (atm) is a unit based on the average atmospheric pressure at sea level, defined as 101.325 kPa. To convert kPa to atm, divide the given pressure by 101.325. This gives: 543101.325=5.36 atm\frac{543}{101.325} = 5.36 \, \text{atm}
This means the pressure 45 meters underwater is over 5 times the atmospheric pressure at sea level.
The millimeter of mercury (mmHg) is another unit used especially in medicine and meteorology. It reflects the pressure exerted by a column of mercury 1 millimeter high. Since 1 atm equals 760 mmHg, we multiply the atm value (5.36) by 760: 5.36×760=4073.6 mmHg5.36 \times 760 = 4073.6 \, \text{mmHg}
Thus, the pressure at 45 meters depth is 5.36 atm or 4073.6 mmHg—a value that illustrates the immense effect of water depth on pressure.