Question

The pressure on top of Mount Everest (29,029 ft or 8848 m) averages about 235 mmHg. Convert this pressure to \begin{equation}\begin{array}{ll}{\text { a. torr }} & {\text { b. psi }} \\\ {\text { c. in Hg }} & {\text { d. atm }}\end{array}\end{equation}

Short answer

a. 235 torr, b. 4.54 psi (to two decimal places), c. 9.25 in Hg (to two decimal places), d. 0.31 atm (to two decimal places)

Step-by-step solution

Converting mmHg to torr

Since 1 mmHg is equivalent to 1 torr by definition, 235 mmHg is equal to 235 torr directly without any calculations.

Converting mmHg to psi

Use the conversion factor between mmHg and psi. 1 mmHg is approximately equal to 0.0193368 psi. Therefore, multiply 235 mmHg by the conversion factor: \(235 \times 0.0193368 \text{ psi/mmHg} = 4.54414 \text{ psi}\).

Converting mmHg to in Hg

Use the conversion factor between mmHg and in Hg. 1 inch of mercury (in Hg) is equivalent to 25.4 mmHg. To convert from mmHg to in Hg, divide the pressure value by 25.4: \(235 \div 25.4 = 9.25197 \text{ in Hg}\).

Converting mmHg to atm

Use the conversion factor between mmHg and atm. 1 atm is approximately equal to 760 mmHg. To convert from mmHg to atm, divide the pressure value by 760: \(235 \div 760 = 0.30921 \text{ atm}\).

Key concepts

mmHg to Torr

Understanding the relationship between millimeters of mercury (mmHg) and torr is fundamental in pressure conversion, primarily because they are identical units of pressure. The origin of these units traces back to the use of mercury in barometers, which measure atmospheric pressure. By definition, 1 mmHg is exactly equal to 1 torr, named after the Italian mathematician and physicist Evangelista Torricelli, who is credited with inventing the barometer.
For instance, the atmospheric pressure on top of Mount Everest is given as 235 mmHg. An essential tip for students is recognizing that no calculation is needed when converting mmHg to torr. Thus, 235 mmHg translates directly to 235 torr. When you encounter such conversion problems, always remember that this particular conversion is a simple recognition task rather than a numerical one.

mmHg to Psi

Pressure conversion from mmHg to pounds per square inch (psi) might seem daunting, but it is just a matter of applying the conversion factor correctly. Psi is a unit of pressure that is widely used in the United States, particularly in automotive and industrial applications. One mmHg is approximately equal to 0.0193368 psi.
To convert pressure from mmHg to psi, you multiply the value in mmHg by this conversion factor. As demonstrated with the atmospheric pressure at the summit of Mount Everest, 235 mmHg converts to psi as such: \(235 \times 0.0193368 \text{ psi/mmHg} = 4.54414 \text{ psi}\). Remember, the key is to use the accurate conversion factor and multiply it with your mmHg value to get the pressure in psi. Always double-check your conversion factors for accuracy to prevent errors in your calculations.

mmHg to in Hg

The conversion from millimeters of mercury to inches of mercury (in Hg) incorporates the relationship between the metric system and the imperial system of measurement. Since 1 in Hg is defined as 25.4 mmHg, you'll need to perform a simple division to convert mmHg into in Hg. This is because one inch equals 25.4 millimeters.
For practical application, converting the pressure on Mount Everest from mmHg to in Hg requires the following calculation: \(235 \div 25.4 = 9.25197 \text{ in Hg}\). It is crucial for students to memorize or have access to common conversion factors between systems, as this will streamline the process of converting different units of measure. Always divide the mmHg value by 25.4 to convert it to in Hg.

mmHg to atm

The atmosphere (atm) is another fundamental unit of pressure commonly used in scientific contexts. One atm is defined as the pressure exerted by the Earth's atmosphere at sea level and is approximately equivalent to 760 mmHg. To convert from mmHg to atm, divide the mmHg value by 760.
In our example with the Mount Everest pressure reading, the conversion to atm would be calculated as follows: \(235 \div 760 = 0.30921 \text{ atm}\). Teaching students the importance of understanding the standard atmosphere can help them appreciate the concept of pressure variations at different altitudes. To tackle conversions to atm, always remember to divide by 760, and ensure the comprehension of atmospheric pressure as it relates to real-world phenomena.