Question

A gauge on a compressed gas cylinder reads 2200 psi (pounds per square inch; 1 atm \(=14.7\) psi). Express this pressure in each of the following units. a. standard atmospheres b. megapascals (MPa) c. torr

Short answer

The pressure of 2200 psi is approximately equal to 149.66 atm, 15.167 MPa, and 113,713 torr.

Step-by-step solution

Convert psi to atmospheres

Given the pressure gauge reading as 2200 psi, we will first convert it to standard atmospheres using the given conversion factor (1 atm = 14.7 psi). \(Number\ of\ atmospheres = \frac{Pressure\ in\ psi}{Conversion\ factor}\)

Calculate atmospheres

Now we will plug in the values and find the number of atmospheres. \(Number\ of\ atmospheres = \frac{2200}{14.7}\) \(Number\ of\ atmospheres ≈ 149.66\) Therefore, the pressure in standard atmospheres is approximately 149.66 atm.

Convert psi to megapascals (MPa)

Next, we need to convert the pressure in psi to megapascals (MPa). To do this, we will use the conversion factor 1 psi = 0.00689476 MPa. \(Pressure\ in\ MPa = Pressure\ in\ psi × Conversion\ factor\)

Calculate megapascals

Now we will plug in the values and find the pressure in MPa. \(Pressure\ in\ MPa = 2200 × 0.00689476\) \(Pressure\ in\ MPa ≈ 15.167\) Therefore, the pressure in megapascals is approximately 15.167 MPa.

Convert psi to torr

Lastly, we need to convert the pressure in psi to torr. To do this, we will use the conversion factor 1 psi = 51.7149 torr. \(Pressure\ in\ torr = Pressure\ in\ psi × Conversion\ factor\)

Calculate torr

Now we will plug in the values and find the pressure in torr. \(Pressure\ in\ torr = 2200 × 51.7149\) \(Pressure\ in\ torr ≈ 113713\) Therefore, the pressure in torr is approximately 113,713 torr.

Key concepts

Standard Atmospheres

Pressure can be expressed in various units, but one common unit is the standard atmosphere, abbreviated as atm. A standard atmosphere is a unit of pressure defined as being precisely equivalent to 101,325 pascals. It's a convenient unit because it roughly matches atmospheric pressure at sea level. When working with pressures in everyday chemical and physical applications, converting to atmospheres can simplify calculations and help us think about pressure in familiar terms.
To convert pressure measurements to standard atmospheres, we commonly use psi (pounds per square inch) as the starting unit in the United States. One approach is to use the conversion ratio:

• 1 atm = 14.7 psi.

This means that if you have a measurement in psi, you simply divide by 14.7 to convert to atmospheres. Let's look at an example: a pressure reading of 2200 psi would be converted as follows:
\[ Number\ of\ atmospheres = \frac{2200}{14.7} \approx 149.66 \]
This means that 2200 psi is approximately 149.66 standard atmospheres.

Megapascals

The megapascal (MPa) is another unit frequently used, especially in engineering contexts. It is part of the metric system and is equal to a million pascals (1 MPa = 1,000,000 Pa), which makes it handy for expressing large pressures. Scientists and engineers alike prefer megapascals when dealing with pressures in mechanical systems, material properties, or fluid dynamics.
When converting from psi to MPa, the conversion factor is:

• 1 psi = 0.00689476 MPa.

This factor helps translate the force applied over a square inch into metric units, making international collaboration easier. Let's convert 2200 psi to MPa:
\[ Pressure\ in\ MPa = 2200 \times 0.00689476 \approx 15.167 \]
So, 2200 psi translates to approximately 15.167 MPa. This unit conversion demonstrates how the same physical quantity can be represented in different scientific contexts.

Torr

The torr, named after Evangelista Torricelli, is an older unit of pressure, closely related to atmospheres. One complete standard atmosphere is equivalent to 760 torr, which aligns with the millimeter of mercury scale used in barometers.
In certain scientific fields, especially those related to vacuum pressures and old laboratory standards, torr is still used alongside the more modern units. To convert from psi to torr, the well-accepted conversion is:

• 1 psi = 51.7149 torr.

This relationship allows for the rapid conversion of a psi measurement to a measurement in torr. For a pressure of 2200 psi, the equivalent in torr is calculated as follows:
\[ Pressure\ in\ torr = 2200 \times 51.7149 \approx 113713 \]
Thus, 2200 psi is around 113,713 torr. Converting to torr is particularly useful in fields like vacuum science where very low-pressure readings are common.