Question

Convert the following pressures into units of kilopascals. a. \(2.07 \times 10^{6} \mathrm{Pa}\) c. 10.9 atm b. \(795 \mathrm{mm} \mathrm{Hg}\) d. 659 torr

Short answer

The converted pressures are as follows: a. \(2.07 \times 10^{3}\, \mathrm{kPa}\) b. 80.553375 kPa c. 1104.3425 kPa d. 87.872418 kPa

Step-by-step solution

1. Convert 2.07 x 10^6 Pa to kPa

To convert pascals (Pa) to kilopascals (kPa), simply multiply the given value by 0.001. \(2.07 \times 10^{6} \mathrm{Pa} \times \frac{0.001 \mathrm{kPa}}{1 \mathrm{Pa}} = 2.07 \times 10^3 \mathrm{kPa}\) The pressure in kPa is 2.07 x 10^3 kPa.

2. Convert 10.9 atm to kPa

To convert atmospheres (atm) to kilopascals (kPa), multiply the given value by 101.325. \(10.9 \mathrm{atm} \times \frac{101.325 \mathrm{kPa}}{1 \mathrm{atm}} = 1104.3425 \mathrm{kPa}\) The pressure in kPa is 1104.3425 kPa.

3. Convert 795 mmHg to kPa

To convert millimeters of mercury (mmHg) to kilopascals (kPa), multiply the given value by 0.101325. \(795 \mathrm{mmHg} \times \frac{0.101325 \mathrm{kPa}}{1 \mathrm{mmHg}} = 80.553375 \mathrm{kPa}\) The pressure in kPa is 80.553375 kPa.

4. Convert 659 torr to kPa

To convert torr to kilopascals (kPa), multiply the given value by 0.133322. \(659 \mathrm{torr} \times \frac{0.133322 \mathrm{kPa}}{1\, \mathrm{torr}} = 87.872418 \mathrm{kPa}\) The pressure in kPa is 87.872418 kPa.

Key concepts

Units of Pressure

Pressure is the force exerted per unit area on a surface. It is an important concept in various fields of science and engineering. Understanding different units of pressure and how they relate to each other is key when working with pressure-related calculations.

Common units of pressure include:

• Pascals (Pa) - The SI unit of pressure, defined as one newton per square meter. It's often used in scientific contexts.
• Atmospheres (atm) - A unit of pressure based on the average atmospheric pressure at sea level, widely used in chemistry and physics.
• Millimeters of Mercury (mmHg) - Also known as torr, this unit is commonly used in medicine and meteorology. 1 atm is equivalent to 760 mmHg.
• Kilopascals (kPa) - Another SI unit, which is simply 1000 pascals. It's preferred in many engineering applications due to its larger size and easier readability.

Converting between these units is vital for accurate measurements and computations. This ensures that pressure values can be compared and analyzed consistently across different applications.

Kilopascal Conversion

Kilopascal conversion is an essential skill when working with various pressure measurements. Since kilopascals (kPa) are commonly used in both scientific and engineering contexts due to their convenience and readability, it's important to know how to convert other pressure units into kPa.

Let's go through some common conversions:

• From Pascals (Pa) to Kilopascals: Multiply by 0.001, as 1 kPa equals 1000 Pa. For instance, \( 2.07 \times 10^{6} \mathrm{Pa} \times 0.001 = 2.07 \times 10^3 \mathrm{kPa} \).
• From Atmospheres (atm) to Kilopascals: Multiply by 101.325, as this factor represents the number of kPa in 1 atm. This means \( 10.9 \mathrm{atm} \times 101.325 = 1104.3425 \mathrm{kPa} \).
• From Millimeters of Mercury (mmHg) to Kilopascals: Use the factor 0.133322 to convert mmHg to kPa, understanding that this relates to the density of mercury's pressure equivalency.
• From Torr to Kilopascals: Likewise, multiply by 0.133322 because the torr is equivalent numerically to mmHg.

Being adept at these conversions allows for standardized calculations and ensures compatibility in diverse scientific analyses.

Pressure Measurement

Pressure measurement is crucial in various applications, from meteorology to engineering and medicine. In essence, it involves determining the force exerted on surfaces and understanding its impact.

Several devices and tools are used to measure pressure, including:

• Barometers: These measure atmospheric pressure, often used to forecast weather changes.
• Manometers: These devices measure the pressure within closed systems, crucial for mechanical and scientific applications.
• Sphygmomanometers: Employed in healthcare settings to measure blood pressure, offering vital health indicators.

Understanding the concept of pressure measurement means more than just using tools: it involves interpreting readings across different conditions and environments.

It's important to remember that factors like temperature and altitude can also affect pressure readings. These influences should be considered for accurate assessments.

Moreover, ensuring that pressure measurements are expressed in compatible units (like converting to kPa) allows for consistency across various domains, ensuring that the data is both useful and applicable to real-world scenarios.