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 at 45.0 m underwater (543 kPa) into different units, we need the following conversion factors:
- 1 atm = 101.325 kPa
- 1 atm = 760 mmHg
1. Convert 543 kPa to atm:
[
P_{\text{atm}} = \frac{543\ \text{kPa}}{101.325\ \text{kPa/atm}} \approx 5.36\ \text{atm}
]
2. Convert 543 kPa to mmHg:
[
P_{\text{mmHg}} = \frac{543\ \text{kPa}}{101.325\ \text{kPa/atm}} \times 760\ \text{mmHg/atm}
]
[
P_{\text{mmHg}} \approx 5.36\ \text{atm} \times 760\ \text{mmHg/atm} \approx 4072\ \text{mmHg}
]
Final Answers:
- Pressure in atm: ≈ 5.36 atm
- Pressure in mmHg: ≈ 4072 mmHg
300-word Explanation:
Pressure is defined as force per unit area. When you go underwater, the deeper you go, the more water is above you, which increases the pressure. At a depth of 45.0 meters, the total pressure includes both atmospheric pressure at the surface and the pressure due to the weight of the water above.
In this case, the pressure is given in kilopascals (kPa), a standard metric unit. But often in science and medicine, pressure is also expressed in atmospheres (atm) and millimeters of mercury (mmHg). Converting between these units requires knowing the relationships among them.
One atmosphere is the average pressure at sea level and equals 101.325 kPa. To convert from kPa to atm, divide the pressure in kPa by 101.325. So, 543 kPa ÷ 101.325 = 5.36 atm. This means the pressure at 45.0 m depth is over five times the normal atmospheric pressure.
To get pressure in mmHg, which is commonly used in medicine (like blood pressure readings), we use another conversion. Since 1 atm = 760 mmHg, we multiply 5.36 atm by 760, which gives about 4072 mmHg.
Understanding how pressure changes with depth is important in diving, engineering, and medical fields. If divers or submarines go too deep without proper pressure compensation, they can be at serious risk. Also, equipment used in these conditions must be designed to withstand such high pressures.