Question

A typical automobile tire is inflated with air to a pressure of 32 psi. Convert this pressure to \(\mathrm{atm}, \mathrm{mmHg},\) and pascals.

Short answer

32 psi = 2.177 atm = 1653 mmHg = 220636 Pa.

Step-by-step solution

Understand the Problem

You are given a pressure of 32 psi (pounds per square inch) and need to convert it to three different units: atm (atmospheres), mmHg (millimeters of mercury), and pascals (Pa).

Conversion Factors

Identify the conversion factors needed: - 1 atm = 14.696 psi - 1 atm = 760 mmHg - 1 atm = 101325 Pa These will help in converting psi to the desired units.

Convert psi to atm

Use the conversion factor for psi to atm:\[ \text{Pressure in } \text{atm} = \frac{32 \, \text{psi}}{14.696 \, \text{psi/atm}} \approx 2.177 \text{ atm} \]

Convert psi to mmHg

First, convert psi to atm as in Step 3, and then use the conversion factor from atm to mmHg:\[ \text{Pressure in atm} = 2.177 \text{ atm} \]\[ \text{Pressure in } \text{mmHg} = 2.177 \, \text{atm} \times 760 \, \text{mmHg/atm} \approx 1653 \text{ mmHg} \]

Convert psi to Pascals

Again, start by converting psi to atm (Step 3), then use the conversion from atm to Pa:\[ \text{Pressure in } \text{Pa} = 2.177 \, \text{atm} \times 101325 \, \text{Pa/atm} \approx 220636 \text{ Pa} \]

Key concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air in the Earth's atmosphere. Imagine being at sea level; the air above you, extending all the way into space, presses down with a specific force. This is what we measure as atmospheric pressure. It is important as a reference point for many scientific calculations and is typically measured in units of atmospheres (atm). For example, 1 atmosphere is defined as the pressure exerted by a column of mercury exactly 760 millimeters high. This relationship allows for conversions between different pressure units such as mmHg, which is another standard unit for pressure calculations.
Understanding atmospheric pressure is crucial in fields like meteorology and aviation, where pressure changes are indicators of weather patterns and flight stability.

Unit Conversion

Unit conversion is the process of changing a value from one unit of measurement to another. When working with pressure, conversions help us understand and compare variances in measurements. Some common units for pressure include psi (pounds per square inch), atm (atmospheres), mmHg (millimeters of mercury), and pascals (Pa).
Consider converting 32 psi to other units using conversion factors:

• 1 atm = 14.696 psi
• 1 atm = 760 mmHg
• 1 atm = 101325 Pa

Performing each conversion step-by-step involves dividing or multiplying by these factors, ensuring accuracy and clarity when shifting between different units. This skill is fundamental in science and engineering for accurate data analysis and reporting.

Pressure Measurement

Pressure measurement involves determining the force applied per unit area. It's fundamental in various scientific and industrial applications, including atmospheric studies and the design of pressure-sensitive devices. To measure pressure accurately, one must consider both the method and the units used.
Pressure can be static, like the atmospheric pressure, or dynamic, as in situations involving fluid flow. In laboratory settings and industrial environments, various instruments such as barometers, manometers, and pressure sensors are used. These instruments translate the physical pressure into a readable output, often in units like atm or mmHg, allowing precise control and monitoring of physical processes.

Pascals

Pascals (Pa) are the SI unit of pressure. Named after Blaise Pascal, a renowned French mathematician and physicist, this unit is widely used in scientific fields for its simplicity and acceptance in the International System of Units. One pascal is defined as one newton per square meter, providing a clear understanding of how force relates to area.
To convert pressure from psi to pascals, for instance, we first convert psi to atm and then use the conversion factor where 1 atm equals 101325 pascals. This systematic approach ensures the precision necessary for scientific accuracy.

• Pascals are convenient for expressing small pressure differences.
• They allow compatibility with other SI units in research and development.

mmHg

The unit mmHg, or millimeters of mercury, is a traditional metric unit used to measure pressure. It originated from mercury barometers, where the height of a mercury column in millimeters directly corresponded to atmospheric pressure. One millimeter of mercury is defined precisely as the pressure exerted by a column of mercury 1 millimeter high, at 1 standard atmosphere pressure level at the Earth’s surface.
In the medical field, mmHg is commonly applied when measuring blood pressure, providing an intuitive and historical framework for understanding bodily pressures. Converting 32 psi to mmHg requires calculating through atmospheres using the factor of 760 mmHg per atm, bridging traditional and modern measurement techniques. Using mmHg remains significant in areas where historical data necessitate unit consistency.