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 and E xplanation is:
To convert the given pressure at 45.0 m under water (543 kPa) into different units:
Final Answers:
- Pressure in atm:
$\boxed{5.36 \, \text{atm}}$ - Pressure in mmHg:
$\boxed{4,073 \, \text{mmHg}}$
Detailed Explanation (300+ words):
In physics and chemistry, pressure is often measured in different units depending on the context. The pressure under water is commonly measured in kilopascals (kPa), but it is also useful to express it in atmospheres (atm) and millimeters of mercury (mmHg) for scientific and medical applications.
Step 1: Understand the Given Pressure
You are told that the pressure at a depth of 45.0 meters under water is 543 kPa.
This includes both the atmospheric pressure and the hydrostatic pressure due to the water column.
Step 2: Convert kPa to atm
The standard conversion factor is:
$$
1 \, \text{atm} = 101.325 \, \text{kPa}
$$
So to convert 543 kPa into atm:
$$
\frac{543 \, \text{kPa}}{101.325 \, \text{kPa/atm}} \approx 5.36 \, \text{atm}
$$
This means the pressure at that depth is about 5.36 times the pressure of the atmosphere at sea level.
Step 3: Convert kPa to mmHg
Another standard pressure unit is mmHg, which is often used in medicine (like blood pressure readings). The conversion factor is:
$$
1 \, \text{kPa} = 7.50062 \, \text{mmHg}
$$
So,
$$
543 \, \text{kPa} \times 7.50062 \, \text{mmHg/kPa} \approx 4073 \, \text{mmHg}
$$
Why These Conversions Matter:
Understanding pressure conversions is important in diving, medicine, and atmospheric sciences. For example:
- Divers need to monitor pressure to avoid decompression sickness.
- Clinicians need to relate mmHg to understand respiratory or circulatory pressures.
- Engineers and scientists use atm or kPa depending on their industry standards.
By knowing how to convert between units, one can interpret and apply pressure data accurately across disciplines