Perform each conversion. (a) \(2.3 \mathrm{~atm}\) to torr (b) \(4.7 \times 10^{-2}\) atm to millimeters of mercury (c) \(24.8\) psi to millimeters of mercury (d) \(32.84 \mathrm{in}\). Hg to torr

Understanding how to convert atmospheres to torr is crucial in various scientific disciplines, especially when dealing with pressure measurements. An atmosphere (\texttt{atm}) is a unit of pressure defined as the pressure exerted by the weight of the Earth's atmosphere at sea level, while the torr is a unit of pressure named after Evangelista Torricelli, an Italian physicist and mathematician. The relationship between these units is linear and uncomplicated: 1 \texttt{atm} is equivalent to 760 torr.

To perform a conversion, simply multiply the value in atmospheres by 760. For instance, if you have a pressure of 2.3 \texttt{atm}, the conversion to torr is calculated as follows: \(2.3 \texttt{ atm} \times 760 \texttt{ torr/atm} = 1748 \texttt{ torr}\). This straightforward calculation is essential for tasks ranging from calibrating laboratory instruments to setting correct pressures in industrial systems.

Converting atmospheres to millimeters of mercury (mm Hg) is a common practice in science, particularly in fields that involve fluid dynamics and weather prediction. Like the torr, the millimeters of mercury unit is derived from the height of a column of mercury that can be supported by a given pressure. The conversion factor between atmospheres and millimeters of mercury is the same as with torr, since 1 torr is equal to 1 mm Hg.

To convert a pressure in atmospheres to millimeters of mercury, you multiply by 760. For example, taking a small pressure of 0.047 \texttt{atm}: \(4.7 \times 10^{-2} \texttt{ atm} \times 760 \texttt{ mm Hg/atm} = 35.72 \texttt{ mm Hg}\).

This conversion is frequently needed for medical applications such as blood pressure measurements, as well as in the calibration of altimeters used in aviation.

The pound per square inch (psi) is another widely used unit for measuring pressure, especially in the United States and in the fields of mechanics and hydraulics. In order to convert psi to millimeters of mercury, a specific conversion factor is used: 1 psi is equivalent to approximately 51.715 mm Hg.

When faced with the task of converting 24.8 psi to mm Hg, the calculation is as follows: \(24.8 \texttt{ psi} \times 51.715 \texttt{ mm Hg/psi} = 1282.532 \texttt{ mm Hg}\).

This relationship allows technicians to convert between measurements taken in different systems without losing accuracy, ensuring that systems are functioning correctly and safely within their designed parameters.

In some instances, pressure is measured in inches of mercury (in. Hg), particularly in meteorology when reporting barometric pressures. To convert inches of mercury to torr, one must first convert in. Hg to mm Hg using the factor 1 in. Hg equals 25.4 mm Hg, as millimeters of mercury and torr are directly equivalent.

For example, the conversion for 32.84 in. Hg to torr includes two steps. First, convert inches to millimeters: \(32.84 \texttt{ in. Hg} \times 25.4 \texttt{ mm Hg/in. Hg} = 834.136 \texttt{ mm Hg}\). Then, recognize that 1 mm Hg is equal to 1 torr: 834.136 \texttt{ mm Hg} = 834.136 \texttt{ torr}.

This conversion is particularly helpful for aviation where aircraft altimeter settings are based on inches of mercury but may need conversion for compatibility with international standards.