Question

Put the following in order of increasing pressure: \(363 \mathrm{mm} \mathrm{Hg}, 363 \mathrm{kPa}, 0.256 \mathrm{atm},\) and \(0.523 \mathrm{bar}\)

Short answer

In order of increasing pressure: 0.256 atm, 363 mmHg, 0.523 bar, 363 kPa.

Step-by-step solution

Understand Pressure Units

The problem provides pressure values in different units: mmHg, kPa, atm, and bar. To compare these values, we need to convert them to a common unit.

Conversion Factors

Identify the conversion factors for each unit: - 1 atm = 760 mmHg - 1 atm = 101.325 kPa - 1 atm = 1.01325 bar - 1 bar = 100 kPa. These will be used to convert all pressures to atm.

Convert mmHg to atm

For 363 mmHg, use the conversion factor 1 atm = 760 mmHg: \[ 363 \text{ mmHg} \times \frac{1 \text{ atm}}{760 \text{ mmHg}} = 0.4776 \text{ atm} \]

Convert kPa to atm

For 363 kPa, use the conversion factor 1 atm = 101.325 kPa: \[ 363 \text{ kPa} \times \frac{1 \text{ atm}}{101.325 \text{ kPa}} = 3.5838 \text{ atm} \]

Convert bar to atm

For 0.523 bar, use the conversion factor 1 atm = 1.01325 bar: \[ 0.523 \text{ bar} \times \frac{1 \text{ atm}}{1.01325 \text{ bar}} = 0.5161 \text{ atm} \]

Compare Pressures in atm

Now compare the values in atm: - 0.256 atm - 0.4776 atm (363 mmHg) - 0.5161 atm (0.523 bar) - 3.5838 atm (363 kPa) Arrange them in increasing order based on these values.

Key concepts

Pressure Units

Pressure involves the force applied over an area. Different situations and industries use differing units to measure pressure. Understanding these units is essential:

• **Millimeters of Mercury (mmHg)**: Often used in medical settings such as measuring blood pressure.
• **Kilopascals (kPa)**: Commonly used in scientific calculations and engineering.
• **Atmospheres (atm)**: This unit relates directly to pressure from Earth's atmosphere at sea level.
• **Bar**: Used in meteorology and air pressure systems, as it is close to atm, but slightly more.

Each unit has its own typical application, but they all measure the same physical quantity, pressure. Understanding their context helps in making accurate conversions.

Conversion Factors

Conversion factors are key tools in translating one set of units to another. They establish the relationship between different measurement systems: - **Converting to Atmospheres**: Since 1 atm is a standard reference, we use it frequently.

• 1 atm = 760 mmHg
• 1 atm = 101.325 kPa
• 1 atm = 1.01325 bar
• 1 bar = 100 kPa

To make a comparison of pressures given in different units, convert them into one common unit system. Let's say you have a value in kPa, using the conversion factor will help switch it to atm. This simplifies complex problem-solving processes in physics and engineering.

Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the weight of the atmosphere. It is typically represented in atmospheres (atm). Understanding this helps in comprehending relative pressure changes:

• At sea level, standard atmospheric pressure is 1 atm. This serves as a baseline.
• A deviation from 1 atm signifies a difference in pressure relative to the atmosphere.

Knowing how to interpret atmospheric pressure can help in predicting weather patterns, diagnosing lung capacities in medicine, and designing systems like aircraft cabins that depend on pressure.

Order of Magnitude

The 'order of magnitude' is a way to see how different values compare by examining exponential scales. This is crucial when handling large or small numbers related to pressure. By scaling all values to a common unit, such as atm, differences become apparent:

• Comparing pressures: When converted into the same unit, like atm, you easily list values in a logical sequence.
• Example: Given values might differ by several orders of magnitude as pressure can vary vastly in different systems.

Understanding the order of magnitude helps prioritize which pressures are significantly greater or lesser. This can guide decision-making, for instance, in selecting materials that can withstand high pressure.