Question

An American newscast states that the barometer reads 30.8 in. Hg. Express the atmospheric pressure in each of the following units: (a) \(k P a\) (b) torr

Short answer

The atmospheric pressure is 104.33 kPa and 782.32 torr.

Step-by-step solution

Understanding the Problem

We need to convert a barometer reading from inches of mercury (in. Hg) to both kilopascals (kPa) and torr. Given the barometer reading is 30.8 in. Hg.

Conversion to Pascal (Pa)

Firstly, understand that 1 in. Hg is equal to 3386 Pa. So, we multiply 30.8 in. Hg by 3386 Pa/in. Hg to get the pressure in pascals.\[ 30.8 \times 3386 = 104328.8 \, \text{Pa} \]

Conversion to Kilopascal (kPa)

Since 1 kPa equals 1000 Pa, divide the pressure in pascals by 1000 to convert it to kilopascals.\[ \frac{104328.8}{1000} = 104.3288 \, \text{kPa} \]

Conversion to Torr

1 in. Hg is equivalent to 25.4 torr (approximately). Multiply 30.8 in. Hg by 25.4 to get the pressure in torr.\[ 30.8 \times 25.4 = 782.32 \, \text{torr} \]

Key concepts

Barometer Reading

A barometer reading is essentially a measurement of atmospheric pressure using a barometer, an instrument designed specifically for this purpose. Barometers come in various forms, but the two most common are the mercury barometer and the aneroid barometer. In our discussion here, we focus on the mercury barometer, which uses a column of mercury to measure pressure. When atmospheric pressure is measured in inches of mercury (in. Hg), it tells us how high the mercury column rises due to the air pressure exerted outside. The higher the column, the greater the atmospheric pressure. This measurement is quite intuitive, as it directly shows the physical impact of atmospheric pressure on the mercury column in the barometer.

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of air in the atmosphere on the surface of the Earth. It is a crucial concept in many fields, including meteorology and aviation. Atmospheric pressure can vary depending on altitude, temperature, and weather patterns. At sea level, the average atmospheric pressure is about 101.3 kPa (kilopascals) or 760 torr. Understanding atmospheric pressure is essential for predicting weather changes, as it influences wind, precipitation, and temperature. It also affects various biological and mechanical processes, such as breathing and engine performance. Thus, having the ability to convert atmospheric pressure into different units helps in international applications and science communication.

Units of Pressure

Pressure is a fundamental physical quantity, and its units are important for expressing measurements. Some common units of pressure include:

• Pascal (Pa): the standard SI unit of pressure.
• Kilopascal (kPa): often used in meteorology, equal to 1000 pascals.
• Millimeter of Mercury (mm Hg): a traditional unit often used in medicine.
• Inch of Mercury (in. Hg): commonly used in weather reports in the United States.
• Atmosphere (atm): a unit of pressure defined as 101325 Pa.
• Torr: a unit approximately equal to the pressure exerted by a 1-mm high column of mercury.

Being familiar with these units ensures accurate communication and conversion of pressure readings in different contexts, enhancing comprehension across diverse regions and disciplines.

Inches of Mercury

Inches of mercury (in. Hg) is a unit of pressure measurement based on the height of a mercury column under atmospheric pressure conditions. This unit originated with the mercury barometer and remains common in meteorological reports, especially in the United States. One inch of mercury is approximately equal to 3386 pascals, demonstrating quite a significant amount of pressure. Using in. Hg is especially practical when referring to atmospheric pressure because it provides an intuitive visual reference: the higher the column of mercury, the higher the pressure. However, international scientific communities and various technical fields prefer the use of SI units, like pascals or kilopascals, for precision and consistency.

Kilopascal

The kilopascal (kPa) is a metric unit of pressure and part of the International System of Units (SI). It represents 1000 pascals (Pa). The kPa unit is widely used in different scientific fields, weather forecasting, and engineering. It offers a more convenient way to discuss everyday pressures as compared to the pascal because it reduces the number of digits in use, making it easier to read and interpret. In weather contexts, for instance, atmospheric pressure at sea level is typically around 101.3 kPa. By converting pressure measurements, such as barometer readings, into kPa, scientists and forecasters can more readily describe and predict weather conditions with a standardized format that eases the comparison of data globally.

Torr

The torr is a non-SI unit of pressure named after Evangelista Torricelli, an Italian physicist and mathematician credited with inventing the barometer. It defines the pressure exerted by a 1-mm high column of mercury at 0 degrees Celsius under gravity equivalent to 1 atm. One torr is equivalent to precisely 1/760 of an atmosphere (atm), making it almost equivalent to 133.322 pascals. The historical significance and widespread scientific usage of the torr make it a popular choice in fields like vacuum technology and medicine, especially when discussing blood pressure. Torr units simplify the process of comparing atmospheric pressure in different conditions without the complexity of converting entirely to SI units, making it a practical alternative in specific scientific situations.