Question

The average barometric pressure at an altitude of \(10 \mathrm{km}\) is \(210 \mathrm{mm}\) Hg. Express this pressure in atmospheres, bars, and kilopascals.

Short answer

210 mm Hg is approximately 0.276 atm, 0.280 bar, and 28.0 kPa.

Step-by-step solution

Convert mm Hg to Atmospheres

To convert from millimeters of mercury (mm Hg) to atmospheres, use the conversion factor: \(1 \text{ atm} = 760 \text{ mm Hg}\). Thus, the pressure in atmospheres is calculated as follows: \(\frac{210\text{ mm Hg}}{760\text{ mm Hg/atm}} \approx 0.2763 \text{ atm}\).

Convert mm Hg to Bars

To convert mm Hg to bars, use the conversion factor: \(1 \text{ bar} = 750.06 \text{ mm Hg}\). Therefore, the pressure in bars is: \(\frac{210\text{ mm Hg}}{750.06\text{ mm Hg/bar}} \approx 0.2800 \text{ bar}\).

Convert mm Hg to Kilopascals

To convert mm Hg to kilopascals (kPa), use the conversion factor: \(1 \text{ mm Hg} = 0.133322 \text{ kPa}\). Thus, the pressure in kilopascals is: \(210 \text{ mm Hg} \times 0.133322 \text{ kPa/mm Hg} \approx 28.0 \text{ kPa}\).

Key concepts

Barometric Pressure

Barometric pressure is the measure of the weight of the air above us in the atmosphere. Often recorded using a barometer, it is expressed in terms of millimeters of mercury (mm Hg). When you hear about weather forecasts mentioning high or low air pressure, they're referring to barometric pressure. It's an important measure used not only in meteorology but also in various scientific fields such as aviation and physiology. Barometric pressure changes with altitude, which is why pressure readings can be quite different when you compare sea-level readings to those taken at higher altitudes, like 10 km above sea level. Understanding how to convert barometric pressure into different units is crucial for applications where precision and consistency across different measures are needed.

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the atmosphere on a surface area. At sea level, average atmospheric pressure is approximately 1 atmosphere (atm). The higher you go above sea level, the lower the atmospheric pressure tends to be. This is because there are fewer air molecules and hence less weight exerted downwards. At a height of 10 km, for example, the atmospheric pressure is significantly reduced compared to the standard atmospheric pressure at sea level. In practical applications, having a way to express this pressure in different units enables scientists and engineers to communicate findings and ensure compatibility with global standards.

Units of Pressure

Pressure can be measured in various units, depending on the region and field of study. The most common units of pressure include:

• Atmospheres (atm): A unit often used in atmospheric sciences and common reference for pressure at sea level.
• Millimeters of Mercury (mm Hg): Commonly used in medicine and weather forecasting.
• Bars: Used in meteorology and engineering. 1 bar is roughly equivalent to atmospheric pressure at sea level.
• Kilopascals (kPa): A standard unit used in many scientific and engineering contexts, part of the metric system familiar across the world.

Each unit has its specific context of use but to communicate universally, conversions between these units are often necessary.

Pressure Conversion Factors

When converting between units of pressure, specific conversion factors are employed to ensure accuracy. For instance, converting from mm Hg to atmospheres uses the factor: 1 atm = 760 mm Hg. This conversion helps standardize pressure readings to the commonly known atmospheric pressure levels. To convert from mm Hg to bars, you use the factor: 1 bar = 750.06 mm Hg. This conversion is helpful in meteorological contexts, as bars are frequently used to express pressure differences in weather systems. For mm Hg to kilopascals (kPa), the factor is: 1 mm Hg = 0.133322 kPa. Since the kilopascal is a SI unit, this conversion is widely adopted in scientific and technical fields that require precision. Knowing these conversion factors allows anyone working with pressure data to adjust and communicate their readings accurately and effectively across diverse fields and disciplines.