Question

Make the indicated pressure conversions. a. \(699 \mathrm{~mm} \mathrm{Hg}\) to atmospheres b. 18.2 psi to \(\mathrm{mm} \mathrm{Hg}\) c. \(862 \mathrm{~mm} \mathrm{Hg}\) to torr d. \(795 \mathrm{~mm} \mathrm{Hg}\) to psi

Short answer

a. \(699 \mathrm{~mm} \mathrm{Hg} \approx 0.919 \mathrm{~atm}\) b. \(18.2 \mathrm{~psi} \approx 941.4 \mathrm{~mm} \mathrm{Hg}\) c. \(862 \mathrm{~mm} \mathrm{Hg} = 862 \mathrm{~torr}\) d. \(795 \mathrm{~mm} \mathrm{Hg} \approx 15.37 \mathrm{~psi}\)

Step-by-step solution

a. 699 mm Hg to atmospheres

To convert 699 mm Hg to atmospheres, use the conversion factor of 1 atmosphere = 760 mm Hg. \(699 \mathrm{~mm} \mathrm{Hg} \times \frac{1 \mathrm{~atm}}{760 \mathrm{~mm} \mathrm{Hg}} = \frac{699}{760} \mathrm{~atm} \approx 0.919 \mathrm{~atm}\) So, 699 mm Hg is approximately 0.919 atmospheres.

b. 18.2 psi to mm Hg

To convert 18.2 psi to mm Hg, use the conversion factor of 1 psi = 51.715 mm Hg. \(18.2 \mathrm{~psi} \times \frac{51.715 \mathrm{~mm} \mathrm{Hg}}{1 \mathrm{~psi}} = 18.2 \times 51.715 \mathrm{~mm} \mathrm{Hg} \approx 941.4 \mathrm{~mm} \mathrm{Hg}\) So, 18.2 psi is approximately 941.4 mm Hg.

c. 862 mm Hg to torr

To convert 862 mm Hg to torr, use the conversion factor of 1 torr = 1 mm Hg. \(862 \mathrm{~mm} \mathrm{Hg} \times \frac{1 \mathrm{~torr}}{1 \mathrm{~mm} \mathrm{Hg}} = 862 \mathrm{~torr}\) So, 862 mm Hg is equal to 862 torr.

d. 795 mm Hg to psi

To convert 795 mm Hg to psi, use the conversion factor of 1 psi = 51.715 mm Hg. \(795 \mathrm{~mm} \mathrm{Hg} \times \frac{1 \mathrm{~psi}}{51.715 \mathrm{~mm} \mathrm{Hg}} = \frac{795}{51.715} \mathrm{~psi} \approx 15.37 \mathrm{~psi}\) So, 795 mm Hg is approximately 15.37 psi.

Key concepts

Atmospheres

The term 'atmosphere' or 'atm' is a unit of pressure that is based on the average atmospheric pressure at sea level. It is a reference point used to measure how much pressure is exerted by the atmosphere on a given area. Historically, this was defined as being equal to the pressure exerted by 760 mm of mercury (mm Hg) at sea level and at 0 °C. Let's break it down:

• 1 atmosphere is equivalent to 101,325 Pascals (Pa) in the metric system.
• 1 atm is also approximately equal to 14.696 pounds per square inch (psi) in the imperial system.
• In terms of the original exercise, when converting from mm Hg to atm, you use the conversion: 1 atm = 760 mm Hg.

So, understanding atmospheres is crucial for converting pressures to other units accurately. It's especially useful in various scientific and meteorological applications.

mm Hg

The unit 'mm Hg' stands for millimeters of mercury. It is a traditional unit of pressure measurement that originated from the use of mercury in barometers. This unit measures how high mercury rises in a tube under atmospheric pressure. Key factors about mm Hg:

• 1 mm Hg equals 133.322 Pa.
• This unit is commonly used in medical settings, such as measuring blood pressure.
• It is interchangeable with the unit 'torr', as both represent the same pressure measurement scale. For example, 1 mm Hg = 1 torr.

By understanding and employing conversions like these, you can switch between mm Hg and other pressure units like atmospheres (atm) or psi more efficiently.

Torr

The 'torr' is another unit of pressure named after the Italian physicist Evangelista Torricelli, who invented the barometer. Essentially, the torr is identical to mm Hg, as both are used to measure pressure in the same manner. Noteworthy points about torr:

• 1 torr equals exactly 1 mm Hg.
• Therefore, converting between mm Hg and torr is simple: they are equal in value.

Consequently, exercises or situations involving pressure readings often interchange torr and mm Hg. It's vital for students and professionals to recognize they are the same for clarity and accuracy in calculations.

Psi

Psi stands for "pounds per square inch" and is a common unit of pressure used primarily in the United States. This unit measures the force exerted on one square inch of area. Important aspects of psi include:

• 1 psi equals 6,894.76 Pa.
• To convert from psi to other units like mm Hg, you can use the relation: 1 psi = 51.715 mm Hg.
• Conversely, converting from mm Hg to psi uses the same conversion factor in reverse.

Psi is particularly popular in automotive, chemical, and mechanical industries to specify tire pressure, fluid dynamics, and mechanical stress levels. Understanding how to convert psi to other pressure units is essential for students who might encounter these applications.