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 of 543 kPa at a depth of 45.0 meters underwater to atmospheres (atm) and millimeters of mercury (mmHg), we need to use appropriate conversion factors. Let’s go through the calculations step by step.
Step 1: Converting kPa to atm
1 atmosphere (atm) is defined as 101.325 kPa. To convert the pressure in kilopascals (kPa) to atmospheres (atm), we divide the pressure in kPa by the standard pressure of 1 atm (101.325 kPa):
[
P_{\text{atm}} = \frac{543 \, \text{kPa}}{101.325 \, \text{kPa/atm}}
]
[
P_{\text{atm}} = 5.36 \, \text{atm}
]
Thus, the pressure at a depth of 45.0 meters underwater is approximately 5.36 atm.
Step 2: Converting kPa to mmHg
1 millimeter of mercury (mmHg) is equivalent to 133.322 Pa (pascals), and since 1 kPa = 1,000 Pa, this means:
[
1 \, \text{kPa} = \frac{1000}{133.322} \, \text{mmHg} \approx 7.50062 \, \text{mmHg}
]
Now, to convert the pressure of 543 kPa to mmHg, we multiply by the conversion factor:
[
P_{\text{mmHg}} = 543 \, \text{kPa} \times 7.50062 \, \text{mmHg/kPa}
]
[
P_{\text{mmHg}} = 4072.8 \, \text{mmHg}
]
Thus, the pressure at a depth of 45.0 meters underwater is approximately 4072.8 mmHg.
Summary of Results:
- The pressure is 5.36 atm.
- The pressure is 4072.8 mmHg.
Explanation:
The pressure underwater increases with depth due to the weight of the water above. At 45.0 meters, the water exerts a pressure of 543 kPa. This pressure is converted to other units using known conversion factors. Converting to atmospheres gives us a value of 5.36 atm, which is over five times the pressure at sea level. Similarly, converting to millimeters of mercury (mmHg) gives a value of 4072.8 mmHg, reflecting how much more pressure is exerted at this depth compared to the standard atmospheric pressure at sea level. These conversions are useful for understanding how pressure changes with depth in different units, and they show how significant the pressure is at underwater depths.