Question

Convert the following pressures into atmospheres. a. \(109.2 \mathrm{kPa}\) c. \(781 \mathrm{mm} \mathrm{Hg}\) b. 781 torr d. 15.2 psi

Short answer

The converted pressures in atmospheres are as follows: a. 1.078 atm, c. 1.028 atm, b. 1.028 atm, d. 1.034 atm.

Step-by-step solution

Identify the conversion factor

We know that \(1 \mathrm{atm} = 101.325 \mathrm{kPa}\). We will use this conversion factor to convert the given pressure in kPa to atm.

Conversion calculation

Divide the given pressure value by the value of the conversion factor: \[ \frac{109.2 \mathrm{kPa}}{101.325 \mathrm{kPa/atm}} = 1.078 \mathrm{atm} \] So, 109.2 kPa is approximately equal to 1.078 atm. #c. Convert mm Hg to atm#

Identify the conversion factor

We know that \(1 \mathrm{atm} = 760 \mathrm{mm} \mathrm{Hg}\). We will use this conversion factor to convert the given pressure in mm Hg to atm.

Conversion calculation

Divide the given pressure value by the value of the conversion factor: \[ \frac{781 \mathrm{mm} \mathrm{Hg}}{760 \mathrm{mm} \mathrm{Hg/atm}} = 1.028 \mathrm{atm} \] So, 781 mm Hg is approximately equal to 1.028 atm. #b. Convert torr to atm# Note: torr is the same unit as mm Hg, so the process will be the same as in the previous step.

Identify the conversion factor

We know that \(1 \mathrm{atm} = 760 \mathrm{torr}\). We will use this conversion factor to convert the given pressure in torr to atm.

Conversion calculation

Divide the given pressure value by the value of the conversion factor: \[ \frac{781 \mathrm{torr}}{760 \mathrm{torr/atm}} = 1.028 \mathrm{atm} \] So, 781 torr is approximately equal to 1.028 atm. #d. Convert psi to atm#

Identify the conversion factor

We know that \(1 \mathrm{atm} = 14.696 \mathrm{psi}\). We will use this conversion factor to convert the given pressure in psi to atm.

Conversion calculation

Divide the given pressure value by the value of the conversion factor: \[ \frac{15.2 \mathrm{psi}}{14.696 \mathrm{psi/atm}} = 1.034 \mathrm{atm} \] So, 15.2 psi is approximately equal to 1.034 atm.

Key concepts

Converting kPa to atm

When working with pressure units, it is often necessary to convert between different systems of measurement. One common conversion is from kilopascals (kPa) to atmospheres (atm), which are both units of pressure. To convert from kPa to atm, we need to use a conversion factor. The conversion factor is based on the equivalence of 101.325 kPa to 1 atm, which is the standard atmospheric pressure at sea level.

To perform the conversion:

• First, remember the conversion factor, which is: 1 atm = 101.325 kPa.
• To convert kPa to atm, you divide the pressure value in kPa by 101.325.
• So, if you have 109.2 kPa and you want to know how many atmospheres that is, you divide 109.2 by 101.325 to get approximately 1.078 atm.

This process provides a straightforward way to transition between these two pressure units, allowing us to understand and compare pressures in different scientific and engineering contexts.

Converting mm Hg to atm

Millimeters of mercury (mm Hg) is another unit used to measure pressure, particularly in meteorology and medicine. At sea level, standard atmospheric pressure is 760 mm Hg, which equals 1 atm.

Here is how you convert mm Hg to atm:

• Start with the conversion factor: 1 atm = 760 mm Hg.
• To find out how many atmospheres a certain pressure in mm Hg is, divide the mm Hg value by 760.
• For example, to convert 781 mm Hg to atm, you perform the calculation 781 ÷ 760, resulting in approximately 1.028 atm.

This conversion is frequently used in fields like aviation and medical where pressure readings in mm Hg are common, but comparisons or calculations may require pressure in atmospheres.

Converting torr to atm

The torr is a unit of pressure named after the Italian physicist Evangelista Torricelli. It is a non-SI unit but is still used in various scientific fields. Since 1 torr is exactly equivalent to 1 mm Hg, their conversion to atm is the same.

To convert from torr to atm:

• Remember the equivalent conversion factor: 1 atm = 760 torr.
• Divide the number of torr by 760 to find its equivalent in atmospheres.
• For instance, to convert 781 torr to atm, the calculation is the same as for mm Hg and gives you 781 ÷ 760 or about 1.028 atm.

Understanding this conversion is particularly useful in vacuum technology and blood pressure measurements, where torr is commonly used.

Converting psi to atm

Pound-force per square inch (psi) is predominantly used in the United States and in engineering fields to measure pressure. Converting psi to atm allows for comparison between American engineering readings and the metric system.

The following steps outline the conversion process:

• The established conversion factor is 1 atm = 14.696 psi.
• To convert psi to atm, simply divide the psi value by 14.696.
• For example, a pressure of 15.2 psi is equivalent to 15.2 ÷ 14.696, which equals approximately 1.034 atm.

This conversion is essential for many applications including automotive tire pressures, diving equipment, and aerospace engineering, where understanding pressure in atmospheres can be critical for safety and design.