Question

A gauge on a compressed gas cylinder reads \(2200 \mathrm{psi}\) (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

a: The pressure in standard atmospheres is approximately \(149.66 \mathrm{atm}\). b: The pressure in megapascals is approximately \(15.16 \mathrm{MPa}\). c: The pressure in torr is approximately \(113,723.60 \mathrm{torr}\).

Step-by-step solution

Converting psi to atm

Using the conversion factor 1 atm = 14.7 psi, we can calculate the pressure in atmospheres: pressure (atm) = pressure (psi) / 14.7 pressure (atm) = 2200 / 14.7 Calculate the value. pressure (atm) ≈ 149.66 So, the pressure in atmospheres is approximately 149.66 atm.

a. Expressing pressure in standard atmospheres

The pressure in standard atmospheres is already calculated in step 1, which is: pressure (atm) ≈ 149.66 Answer a: The pressure in standard atmospheres is approximately 149.66 atm.

Converting atm to kPa

Now, let's convert the pressure in atm to kPa using the conversion factor 1 atm = 101.325 kPa: pressure (kPa) = pressure (atm) * 101.325 pressure (kPa) = 149.66 * 101.325 Calculate the value. pressure (kPa) ≈ 15161.13

b. Expressing pressure in megapascals (MPa)

Now that we have the pressure in kPa, we can convert it to MPa using the conversion factor 1 MPa = 1000 kPa: pressure (MPa) = pressure (kPa) / 1000 pressure (MPa) = 15161.13 / 1000 Calculate the value. pressure (MPa) ≈ 15.16 Answer b: The pressure in megapascals is approximately 15.16 MPa.

Converting atm to torr

Finally, we'll convert the pressure in atm to torr using the conversion factor 1 atm = 760 torr: pressure (torr) = pressure (atm) * 760 pressure (torr) = 149.66 * 760 Calculate the value. pressure (torr) ≈ 113723.60 Answer c: The pressure in torr is approximately 113,723.60 torr.

Key concepts

Standard Atmospheres

Understanding the concept of standard atmospheres (atm) is essential when dealing with various scientific and engineering calculations related to pressure. Atmospheric pressure is the force per unit area exerted on a surface by the weight of the air above that surface in the Earth's atmosphere. One standard atmosphere is defined as the pressure equivalent to that exerted by a 760 mm column of mercury at standard gravity and at a temperature of 0 degrees Celsius. It is standardized at exactly 101,325 pascals or about 14.696 psi.

When you encounter a problem stating a pressure in psi, like the 2200 psi from a gas cylinder gauge in our exercise, converting to standard atmospheres allows you to compare this pressure to the average atmospheric pressure at sea level. This can be crucial for applications in meteorology, aviation, and even scuba diving, where ambient pressure greatly affects calculations and safety measures. As in our example, the conversion to approximately 149.66 atm from the exercise showcases a significant pressure, vastly exceeding normal atmospheric conditions.

Megapascals (MPa)

Megapascals (MPa) are a unit of pressure in the metric system and are widely used in material science and engineering to express tensile strengths, elastic moduli, and compressive stresses. One megapascal is equivalent to one million pascals, where a Pascal is the SI unit for pressure defined as one newton per square meter. It is important to understand that pressure indicates the force applied over a certain area; therefore, different units can express the same physical concept at various magnitudes. For example, in the given problem, the pressure of a gas cylinder was converted to MPa after finding its equivalent in kPa. The resultant pressure was found to be approximately 15.16 MPa, indicating a high-pressure system – common in industrial gas cylinders. In engineering contexts, MPa helps in approaching problems where large pressure values are involved by providing a scaled unit that is easier to handle and interpret.

Torr

The unit 'torr' is another important and frequently used unit in the field of pressure measurement. Named after Evangelista Torricelli, an Italian physicist and mathematician, one torr is defined as 1/760th of an atmosphere. Because standard atmospheric pressure is equal to approximately 760 mmHg (millimeters of mercury), the torr is a convenient unit when working with instruments like barometers and manometers that measure pressure in terms of the displacement of a column of mercury.

In the context of the exercise, pressure expressed in torr gives a significant figure, around 113,723.60 torr, which provides insight into highly precise measurements needed in scientific research and industrial processes where even small differences in pressure can lead to vastly different outcomes. Understanding the relationship between torr and atmospheres is key in fields ranging from physics to medical technologies where vacuum conditions or controlled pressures are imperative.

PSI to ATM Conversion

When converting pressures from pounds per square inch (psi) to standard atmospheres (atm), it's essential to utilize the correct conversion factor. As shown in the problem, 1 atm is equal to 14.7 psi, which provides the basis for the conversion. The psi is a common unit of pressure in the United States, used for measuring tire pressure, engine manifold vacuum, and much more. Transparency in conversion to atm is particularly relevant for international collaboration and standardization where the metric system and SI units are predominantly used. Therefore, being able to accurately convert between these units is an essential skill in a globally connected world. While many manual conversions, such as the psi to atm calculation seen in our example with a pressure of around 149.66 atm from 2200 psi, can be done with a simple calculator or conversion chart, understanding the principles behind these conversions fosters better comprehension and reduces the chances of error in practical scenarios.