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 543 kPa into atmospheres (atm) and millimeters of mercury (mmHg), we use the following conversion factors:
- $1\ \text{atm} = 101.325\ \text{kPa}$
- $1\ \text{atm} = 760\ \text{mmHg}$
Step 1: Convert kPa to atm
$$
\text{Pressure in atm} = \frac{543\ \text{kPa}}{101.325\ \text{kPa/atm}} \approx 5.36\ \text{atm}
$$
Step 2: Convert atm to mmHg
$$
\text{Pressure in mmHg} = 5.36\ \text{atm} \times 760\ \text{mmHg/atm} = 4073.6\ \text{mmHg}
$$
Final Answers:
- 5.36 atm
- 4073.6 mmHg
Pressure is a fundamental concept in physics and chemistry, especially when dealing with fluids and gases. It is defined as force per unit area and can be measured in several units, including kilopascals (kPa), atmospheres (atm), and millimeters of mercury (mmHg).
In this case, the pressure measured at 45.0 meters under water is given as 543 kilopascals (kPa). This includes atmospheric pressure and the added hydrostatic pressure due to the water above.
To convert from kilopascals to atmospheres, we use the known conversion factor:
1 atmosphere = 101.325 kilopascals.
By dividing 543 kPa by 101.325, we find that the pressure equals approximately 5.36 atmospheres. This means the pressure 45 meters underwater is over five times the pressure we experience at sea level.
To convert this pressure into millimeters of mercury (mmHg), which is a unit commonly used in medicine and meteorology (especially for blood pressure or atmospheric pressure), we use another conversion:
1 atmosphere = 760 mmHg.
Multiplying 5.36 atm by 760 mmHg/atm gives a result of 4073.6 mmHg. This value gives a more relatable sense of the pressure, especially in contexts where mmHg is the preferred unit.
Understanding these conversions is essential in many scientific fields. For example, scuba divers must know pressure in atm to calculate how gas volumes change with depth, and healthcare workers often use mmHg to monitor cardiovascular health.
