Question

Convert \(375 \mathrm{mmHg}\) to atmospheres, bar, torr, and pascals.

Short answer

375 mmHg is 0.493 atm, 0.500 bar, 375 torr, or 49995.75 Pa.

Step-by-step solution

Understanding the Problem

We are given a pressure measurement in millimeters of mercury (mmHg) and need to convert it into different pressure units: atmospheres (atm), bar, torr, and pascals (Pa).

Conversion Factor for mmHg to atm

1 atm is equivalent to 760 mmHg. To convert 375 mmHg to atm, we use the formula: \[ \text{Pressure in atm} = \frac{\text{Pressure in mmHg}}{760} \]Substitute the given value: \[ \text{Pressure in atm} = \frac{375}{760} \approx 0.493 \text{ atm} \]

Conversion Factor for mmHg to bar

1 bar is equivalent to 750.062 mmHg. To convert 375 mmHg to bar, we use the formula: \[ \text{Pressure in bar} = \frac{\text{Pressure in mmHg}}{750.062} \]Substitute the given value: \[ \text{Pressure in bar} = \frac{375}{750.062} \approx 0.500 \text{ bar} \]

Conversion Factor for mmHg to torr

1 mmHg is equivalent to 1 torr. So, 375 mmHg is equal to 375 torr.

Conversion Factor for mmHg to pascal

1 mmHg is equivalent to 133.322 Pa. To convert 375 mmHg to Pa, we use the formula: \[ \text{Pressure in Pa} = \text{Pressure in mmHg} \times 133.322 \]Substitute the given value: \[ \text{Pressure in Pa} = 375 \times 133.322 = 49995.75 \text{ Pa} \]

Final Calculations and Recap

We have converted 375 mmHg into:- Atmospheres: \(\approx 0.493 \text{ atm}\)- Bar: \(\approx 0.500 \text{ bar}\)- Torr: \(375 \text{ torr}\)- Pascals: \(49995.75 \text{ Pa}\)

Key concepts

millimeters of mercury (mmHg)

Millimeters of mercury (mmHg) is a unit of pressure traditionally used in medicine and meteorology. It is based on the height of a column of mercury and is a common unit in the measurement of blood pressure. One mmHg is defined as the pressure exerted by a one-millimeter high column of mercury.

This unit is closely related to atmospheric pressure where 760 mmHg equals one atmosphere (atm). Thus, when dealing with conversions, it's important to remember this equivalence. It provides an intuitive scale for understanding pressure, similar to how a thermometer gauge works. For practical purposes:

• 1 mmHg = 133.322 pascals (Pa)
• 1 mmHg = 0.00133322 bar
• 1 mmHg = 0.00131578947 atm
• 1 mmHg = 1 torr (by definition)

atmospheres (atm)

Atmospheres (atm) is a unit of pressure defined as the pressure exerted by a 760 mmHg column of mercury at sea level. It's commonly used in chemistry and physics, providing a useful measure for expressing the pressure of gases.

One atmosphere is considered standard atmospheric pressure at sea level. Understanding this helps in grasping various scientific concepts, like the behavior of gases under pressure:

• 1 atm = 760 mmHg
• 1 atm = 101325 pascals (Pa)
• 1 atm = 1.01325 bar
• 1 atm = 760 torr

By converting 375 mmHg to atm, as shown in our example, you use the formula \[ \text{Pressure in atm} = \frac{\text{Pressure in mmHg}}{760} \]This formula helps to understand the proportional relationship between pressure in mmHg and atm.

bar

The bar is a metric unit of pressure, slightly less than the atmospheric pressure at sea level. It is not an SI unit but is widely used in various fields, including meteorology, oceanography, and engineering.

One bar is roughly equal to the atmospheric pressure on Earth at sea level, which makes it convenient to use. It's easy to compute with whole numbers:

• 1 bar = 750.062 mmHg
• 1 bar = 100000 pascals (Pa)
• 1 bar = 0.986923 atm
• 1 bar = 750.062 torr

To convert 375 mmHg to bar, use the formula \[ \text{Pressure in bar} = \frac{\text{Pressure in mmHg}}{750.062} \]This straightforward division emphasizes the relationship between mmHg and the bar unit.

torr

Torr is a unit of pressure that is essentially identical to mmHg. Due to this equivalence, many calculations become simpler because the numerical value is the same.

When using torr, you are still referencing the pressure of a mercury column, but it often simplifies mathematical computation since:

• 1 torr = 1 mmHg
• 1 torr = 133.322 pascals (Pa)
• 1 torr = 0.00131578947 atm
• 1 torr = 0.00133322 bar

Since 1 mmHg equates to 1 torr, converting between these units is direct and requires no complex math, as seen in our example.

pascals (Pa)

Pascals (Pa) is the SI unit of pressure and represents the amount of force exerted perpendicularly on a unit area. Named after Blaise Pascal, it is fundamental in physics and engineering fields.

The use of pascals facilitates precise scientific calculations, providing consistency in measuring pressures under different conditions:

• 1 Pa = 1 Newton per square meter
• 1 Pa = 0.00750062 mmHg
• 1 Pa = 9.86923×10^-6 atm
• 1 Pa = 10^-5 bar
• 1 Pa = 0.00750062 torr

To convert 375 mmHg to pascals, use the formula \[ \text{Pressure in Pa} = \text{Pressure in mmHg} \times 133.322 \]By applying this multiplication, we achieve the accurate pressure in pascals, highlighting the direct conversion method required.