Question

Indicate which represents the higher pressure in each of the following pairs: (a) 534 mm Hg or 0.754 bar (b) 534 mm Hg or 650 kPa (c) 1.34 bar or \(934 \mathrm{kPa}\)

Short answer

(a) 0.754 bar, (b) 650 kPa, (c) 934 kPa.

Step-by-step solution

Convert 534 mm Hg to Bar

To compare the pressures, all units need to be converted to the same unit system. Start by converting 534 mm Hg to bar. Use the conversion factor:\[ 1 ext{ mm Hg} = 0.00133322 ext{ bar} \]Thus,\[ 534 ext{ mm Hg} = 534 imes 0.00133322 = 0.712847 ext{ bar} \].

Compare Pressures in Bar for Part (a)

Now compare the pressures of 534 mm Hg and 0.754 bar using the converted value: 534 mm Hg (0.712847 bar) vs. 0.754 bar. 0.754 bar is higher than 0.712847 bar.

Convert 534 mm Hg to kPa

Next, convert 534 mm Hg to kilopascal (kPa). Use the conversion factor:\[ 1 ext{ mm Hg} = 0.133322 ext{ kPa} \]Thus,\[ 534 ext{ mm Hg} = 534 imes 0.133322 = 71.192748 ext{ kPa} \].

Compare Pressures in kPa for Part (b)

Compare the pressures of 534 mm Hg and 650 kPa using the converted value: 534 mm Hg (71.192748 kPa) vs. 650 kPa. 650 kPa is higher than 71.192748 kPa.

Convert 1.34 bar to kPa

Finally, convert 1.34 bar to kPa. Use the conversion factor:\[ 1 ext{ bar} = 100 ext{ kPa} \]Thus,\[ 1.34 ext{ bar} = 1.34 imes 100 = 134 ext{ kPa} \].

Compare Pressures in kPa for Part (c)

Compare the pressures of 1.34 bar and 934 kPa using the converted value: 1.34 bar (134 kPa) vs. 934 kPa. 934 kPa is higher than 134 kPa.

Key concepts

Understanding Pressure Units

Pressure is a measure of force applied over a unit area. It's an important concept in various scientific fields and everyday life. The basic unit of pressure in the International System of Units (SI) is the pascal (Pa). However, other units like millimeters of mercury (mm Hg), bar, and kilopascal (kPa) are also commonly used.

Understanding these different units helps in converting measurements from one unit to another, especially when comparisons are necessary.

• The pascal (Pa) is a very small unit, so often kilopascal (kPa) is used where 1 kPa = 1000 Pa.
• The bar is another pressure unit, which is equal to 100,000 Pa.
• Millimeters of mercury (mm Hg) is a unit based on the measurement of atmospheric pressure using a mercury column.

By grasping these units, you can make accurate and relevant comparisons between pressures.

Millimeters of Mercury (mm Hg) Conversion

The use of mm Hg is widespread in clinical and laboratory settings, such as measuring blood pressure. This unit is linked to a standard atmospheric pressure represented by the height of a mercury column in a barometer.

To convert mm Hg into other units, use specific conversion factors. A common conversion is to bars, using the factor 1 mm Hg = 0.00133322 bar. For kilopascals, the conversion factor is 1 mm Hg = 0.133322 kPa.

For example, in the exercise given, you convert 534 mm Hg to:

• Bar: Multiply by 0.00133322 to get 0.712847 bar.
• kPa: Multiply by 0.133322 to get 71.192748 kPa.

Knowing these conversions allows you to switch between units effortlessly and ensures accurate readings and comparisons.

Converting Bar to Kilopascals (kPa)

Converting bar to kilopascal is straightforward since both are metric units. The conversion is simple and easy to memorize: 1 bar is equal to 100 kPa.

This simplicity makes bar to kPa conversion a common practice, especially in scientific and engineering contexts. In the example given, you can see how 1.34 bar is effortlessly converted into kPa:

• Multiply 1.34 by 100 to obtain 134 kPa.

This conversion allows easy comparison with measurements given in kilopascals, making it an essential skill in working with pressure units.

Comparing Different Pressure Values

When you’re comparing pressure values, it’s crucial to ensure that all values are expressed in the same unit. This allows you to accurately judge which value is higher or lower.

In our example exercise, initially, different units like mm Hg, bar, and kPa were used. The solution was to convert all values to a single unit, such as bar or kPa, to facilitate comparison.

This equalization enables:

• Easy recognition of measurement superiority or inferiority.
• Clear understanding of pressure differences and their implications.

Being adept at pressure conversion simplifies many tasks in physics, chemistry, and engineering, aiding accurate and quick decision-making. This is key in fields where pressure impacts material behavior or operating conditions.