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 :
Let’s solve the problem step-by-step and then provide a detailed explanation.
Given:
- Pressure at 45.0 m under water = 543 kPa
- Convert pressure to atmospheres (atm)
- Convert pressure to millimeters of mercury (mmHg)
Step 1: Convert kPa to atm
The conversion factor between kilopascals (kPa) and atmospheres (atm) is: 1 atm=101.325 kPa1 \text{ atm} = 101.325 \text{ kPa}
To convert 543 kPa to atm: Patm=543 kPa101.325 kPa/atm=5.36 atmP_{atm} = \frac{543 \text{ kPa}}{101.325 \text{ kPa/atm}} = 5.36 \text{ atm}
Step 2: Convert kPa to mmHg
The conversion factor between kPa and mmHg is: 1 atm=760 mmHg=101.325 kPa1 \text{ atm} = 760 \text{ mmHg} = 101.325 \text{ kPa}
From this, 1 kPa equals: 1 kPa=760 mmHg101.325≈7.5 mmHg1 \text{ kPa} = \frac{760 \text{ mmHg}}{101.325} \approx 7.5 \text{ mmHg}
Therefore, to convert 543 kPa to mmHg: PmmHg=543 kPa×7.5 mmHgkPa=4072.5 mmHgP_{mmHg} = 543 \text{ kPa} \times 7.5 \frac{\text{ mmHg}}{\text{kPa}} = 4072.5 \text{ mmHg}
Final answers:
- Pressure in atmospheres (atm): 5.36 atm
- Pressure in millimeters of mercury (mmHg): 4072.5 mmHg
Detailed Explanation (300+ words):
Pressure is a physical quantity that expresses the force exerted on a unit area. When underwater, pressure increases with depth due to the weight of the water above. This pressure is often measured in different units depending on the context: kilopascals (kPa), atmospheres (atm), and millimeters of mercury (mmHg) are common units in physics and chemistry.
In this problem, the pressure is given as 543 kPa at a depth of 45.0 meters underwater. To understand this value in more familiar terms, such as atmospheres and mmHg, unit conversion is necessary.
First, converting from kPa to atmospheres is straightforward because the standard atmospheric pressure at sea level is defined as 1 atm = 101.325 kPa. By dividing the given pressure (543 kPa) by 101.325 kPa/atm, we find the equivalent pressure in atmospheres. This gives approximately 5.36 atm, which means the pressure at 45 meters underwater is about 5.36 times the normal atmospheric pressure at sea level.
Next, converting from kPa to mmHg involves understanding that 1 atm corresponds to 760 mmHg. Since 1 atm = 101.325 kPa, dividing 760 mmHg by 101.325 kPa provides the conversion factor of roughly 7.5 mmHg per kPa. Multiplying the pressure in kPa by 7.5 yields the pressure in mmHg. So, 543 kPa converts to approximately 4072.5 mmHg.
These conversions are essential in many scientific fields, including physics, chemistry, and engineering, because different units are preferred for different applications. For example, mmHg is commonly used in medicine to measure blood pressure, while atm and kPa are more common in physics and engineering contexts.
Understanding these conversions helps interpret and compare pressure values accurately across disciplines, ensuring clarity and consistency in communication and analysis.