Question

A Canadian newscast states that the barometer reads \(104 \mathrm{kPa}\). Express the atmospheric pressure in each of the following units: (a) psi (b) \(\mathrm{cm} \mathrm{Hg}\)

Short answer

104 kPa is equivalent to 15.08 psi and 78.01 cm Hg.

Step-by-step solution

Convert kPa to psi

The conversion factor from kilopascals to pounds per square inch (psi) is 1 kPa = 0.145038 psi. To convert 104 kPa to psi, use the formula:\[\text{Pressure in psi} = 104 \times 0.145038\]Calculating this gives:\[\text{Pressure in psi} = 15.083952\]Rounding to a reasonable number of significant figures, we have:\[\text{Pressure in psi} = 15.08 \, \text{psi}\]

Convert kPa to cm Hg

The conversion factor from kilopascals to centimeters of mercury (cm Hg) is 1 kPa = 0.750062 cm Hg. To convert 104 kPa to cm Hg, use the formula:\[\text{Pressure in cm Hg} = 104 \times 0.750062\]Calculating this gives:\[\text{Pressure in cm Hg} = 78.007448\]Rounding to a reasonable number of significant figures, we have:\[\text{Pressure in cm Hg} = 78.01 \, \text{cm Hg}\]

Key concepts

Atmospheric Pressure

Atmospheric pressure is the weight exerted by the atmosphere at a given point. This pressure is a result of the mass of air above us in the earth's atmosphere. It is a crucial concept in meteorology and everyday weather reporting. Although we typically don't feel it, atmospheric pressure can influence everything from weather patterns to our ability to breathe. Understanding atmospheric pressure is essential for various fields, including aviation and meteorology. It affects how aircraft fly and plays a role in determining weather conditions. For meteorological purposes, atmospheric pressure is often measured using a barometer. The most common units to represent atmospheric pressure include kilopascals (kPa), millibars, and inches or centimeters of mercury (Hg). The standard atmospheric pressure at sea level is approximately 101.325 kilopascals (kPa). When converting to other units as seen in the exercise, recognizing these relationships helps:

• 1 atmosphere is approximately 101.325 kPa
• Common instruments used to measure atmospheric pressure include barometers

Kilopascals

Kilopascals (kPa) are part of the metric system and are used to measure pressure. It's a convenient and widely used unit, especially in countries that use the International System of Units (SI). One pascal (Pa) is defined as one newton per square meter. However, since a pascal is quite small, kilopascals are often used—where 1 kPa equals 1,000 pascals. They provide a more manageable number for expression when it comes to measuring atmospheric pressure. In most weather reports globally, you will find pressure expressed in kilopascals. The reason is that it matches well with other metric system units, making scientific calculations and conversions more straightforward. For example, in our exercise, pressure is given as 104 kPa. Using relationships between units helps to easily convert this pressure into other units such as psi and cm Hg.

• 1 kPa = 1,000 Pa
• 104 kPa is a typical atmospheric pressure reported in Canadian weather forecasts

Pounds per Square Inch

Pounds per square inch (psi) is a unit of pressure commonly used in the United States and the UK. It indicates how many pounds of force are applied per square inch of area. This unit is prevalent in various applications, such as in car tires, where pressure is typically measured in psi. In the context of atmospheric pressure, psi provides another way to express pressure values, especially for those accustomed to the imperial system. Converting from kilopascals (a metric unit) to psi (an imperial unit) involves understanding the conversion factor. For instance, 1 kPa is equivalent to approximately 0.145038 psi. Applying this, as in the exercise, allows conversion of 104 kPa to roughly 15.08 psi. This knowledge assists individuals in diverse fields, like engineering and meteorology, to appreciate atmospheric pressure and its variations from one unit to another.

• 1 psi = 6.89476 kPa
• Used extensively in tire pressure measurements and pressure gauges

Centimeters of Mercury

Centimeters of mercury (cm Hg) is another unit to express pressure. This measure relates to the height of a column of mercury the atmospheric pressure can support. Historically, mercury barometers were one of the first tools used to measure atmospheric pressure. Here, pressure causes mercury to rise in a tube; the height of this column then directly correlates to atmospheric pressure. In the exercise, converting from kilopascals to centimeters of mercury involves using the conversion factor that states 1 kPa is approximately 0.750062 cm Hg. Thus, 104 kPa converts to roughly 78.01 cm Hg. Understanding cm Hg is essential, especially for interpreting data from older, traditional mercury-based pressure instruments still used in certain applications.

• 1 cm Hg = approximately 13.5951 mm Hg
• Typically used in older barometers and some medical equipment for blood pressure measurement