Question

The atmospheric pressure at the summit of \(\mathrm{Mt}\). McKinley is \(581 \mathrm{mmHg}\) on a certain day. What is the pressure in atmospheres and in kilopascals?

Short answer

Pressure is approximately 0.764 atm and 77.437 kPa.

Step-by-step solution

Understanding the Problem

We need to convert the given atmospheric pressure from millimeters of mercury (mmHg) to two different units: atmospheres (atm) and kilopascals (kPa). Given pressure is 581 mmHg.

Convert mmHg to Atmospheres

The conversion factor between mmHg and atm is 1 atm = 760 mmHg. To convert 581 mmHg to atm, we use the formula: \[ \text{pressure in atm} = \frac{\text{pressure in mmHg}}{760} \] Plugging in the values, we get: \[ \text{pressure in atm} = \frac{581}{760} \approx 0.764 \text{ atm} \]

Convert mmHg to Kilopascals

The conversion factor between mmHg and kPa is 1 mmHg ≈ 0.133322 kPa. To convert 581 mmHg to kPa, we use the formula: \[ \text{pressure in kPa} = \text{pressure in mmHg} \times 0.133322 \] Plugging in the values, we get: \[ \text{pressure in kPa} = 581 \times 0.133322 \approx 77.437 \text{ kPa} \]

Key concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air above us in the atmosphere. At sea level, this pressure is typically standard, measuring around 101.3 kilopascals (kPa), 760 millimeters of mercury (mmHg), or 1 atmosphere (atm). However, as you move to higher altitudes, like the summit of Mt. McKinley, the atmospheric pressure decreases because there is less air above. Atmospheric pressure is crucial for many aspects of weather forecasting and scientific measurements. It influences weather patterns, boiling points of liquids, and even breathing at high altitudes. To understand changes in atmospheric pressure, it's often necessary to convert pressure measurements into various units, as these provide different perspectives on the quantity being measured.

Millimeters of Mercury (mmHg)

Millimeters of mercury, commonly abbreviated as mmHg, is a unit of pressure that originated from the measurement of atmospheric pressure using a mercury barometer. The unit 'millimeter of mercury' physically represents the pressure exerted by a 1 mm high column of mercury. Historically, mmHg was the most common unit for measuring blood pressure in medicine. It continues to be used in various scientific fields due to its ease of understanding and measurement. To convert mmHg to other pressure units, such as atmospheres (atm) or kilopascals (kPa), specific conversion factors based on the density of mercury and gravitational pull must be used.

Kilopascals (kPa)

Kilopascals, or kPa, is another common unit for measuring pressure. It is part of the metric system and is equivalent to 1,000 pascals (Pa). Because it is part of the SI (International System of Units), it is widely used in scientific research and engineering. The kPa unit is convenient for expressing atmospheric pressure in a way that is easy to understand and relate to physical concepts. For example, 1 kPa equals 0.145 psi (pounds per square inch) or about 0.01 atm. Converting from mmHg to kPa involves multiplying the pressure in mmHg by the factor 0.133322. Understanding these conversions is essential when interpreting data across different scientific contexts.

Atmospheres (atm)

Atmospheres (atm) is a unit of pressure that is based on the average atmospheric pressure at sea level, precisely defined as 101,325 pascals (Pa). Using atmospheres as a unit simplifies many calculations because it relates directly to the pressure we experience in everyday life. When performing conversions, you should know that 1 atm equals 760 mmHg. This makes it convenient to convert measurements taken with traditional barometers or in laboratories where mercury columns are used. This unit is commonly used in physics and chemistry, especially when discussing gas laws and other principles relating to the pressure and volume of gases.