Question

Make the indicated pressure conversions. a. \(1.54 \times 10^{5}\) Pa to atmospheres b. 1.21 atm to pascals c. 97,345 Pa to \(\mathrm{mm}\) Hg d. 1.32 kPa to pascals

Short answer

a. \(1.54 \times 10^{5} \,\mathrm{Pa} = 1.52\, \mathrm{atm}\) b. \(1.21\, \mathrm{atm} = 122600.25\, \mathrm{Pa}\) c. \(97,345\, \mathrm{Pa} = 729.84\, \mathrm{mm\,Hg}\) d. \(1.32\, \mathrm{kPa} = 1320\, \mathrm{Pa}\)

Step-by-step solution

a. Convert \(1.54 \times 10^{5}\) Pa to atmospheres

To convert pascals (Pa) to atmospheres (atm), we use the following conversion factor: \(1\,\mathrm{atm} = 101325\,\mathrm{Pa}\). We can then set up a proportion: \(x\,\mathrm{atm}=\frac{1.54\times10^{5}\,\mathrm{Pa}}{101325\,\mathrm{Pa}}\) Now, to find \(x\), we can simply divide the numbers: \(x\)=\(\frac{1.54\times10^{5}}{101325} = 1.52\, \mathrm{atm}\) So, \(1.54 \times 10^{5} \,\mathrm{Pa} = 1.52\, \mathrm{atm}\).

b. Convert 1.21 atm to pascals

This time, we need to go from atmospheres to pascals, so we use the conversion factor in the opposite direction: \(x\,\mathrm{Pa} = 1.21\,\mathrm{atm} \times 101325\,\mathrm{Pa}\) Multiply the numbers: \(x = 1.21 \times 101325 = 122600.25\, \mathrm{Pa}\) So, \(1.21\, \mathrm{atm} = 122600.25\, \mathrm{Pa}\).

c. Convert 97,345 Pa to mm Hg

To convert pascals to millimeters of mercury (mm Hg), we use this conversion factor: \(1\,\mathrm{mm\,Hg} = 133.322\,\mathrm{Pa}\). We can set up a proportion as before: \(x\,\mathrm{mm\,Hg} =\frac{97345\,\mathrm{Pa}}{133.322\,\mathrm{Pa}}\) Now, divide the numbers: \(x =\frac{97345}{133.322} = 729.84\, \mathrm{mm\,Hg}\) So, \(97,345\, \mathrm{Pa} = 729.84\, \mathrm{mm\,Hg}\).

d. Convert 1.32 kPa to pascals

In this case, we need to convert from kilopascals (kPa) to pascals (Pa). We know that \(1\,\mathrm{kPa} = 10^3\,\mathrm{Pa}\), so: \(x\,\mathrm{Pa} = 1.32\,\mathrm{kPa} \times 10^3\,\mathrm{Pa}\) Multiply the numbers: \(x = 1.32 \times 10^3 = 1320\, \mathrm{Pa}\) So, \(1.32\, \mathrm{kPa} = 1320\, \mathrm{Pa}\).

Key concepts

Converting from Pascal to Atmosphere

Understanding pressure units is essential in science and engineering. Pascal (Pa) is a standard unit for pressure in the International System of Units, whereas atmosphere (atm) is commonly used in fields like meteorology and aviation. To convert pascals to atmospheres, you can use the conversion factor:

• 1 atm = 101325 Pa

By setting up a ratio or a simple division, you can change a pressure reading from pascal to atmosphere:
\[ x\,\mathrm{atm} = \frac{\text{Pressure in}\,\mathrm{Pa}}{101325} \]
This formula allows you to find atmospheric pressure when you have a value in pascals. For example, if you have a pressure of \(1.54 \times 10^{5}\) Pa, the conversion will give you approximately 1.52 atm.

The outcome means the pressure is slightly higher than the standard atmospheric pressure at sea level.

Converting from Atmosphere to Pascal

When dealing with laboratory conditions or certain scientific calculations, you might need to express atmospheric pressure in pascals. The process is pretty straightforward as you use the same conversion factor in reverse.

• 1 atm = 101325 Pa

By multiplying the atmospheric pressure by 101325, you can convert it to pascals:
\[ x\,\mathrm{Pa} = \text{Pressure in}\,\mathrm{atm} \times 101325 \]
If 1.21 atm is the pressure given, multiplying it by 101325 results in 122600.25 Pa. This means the pressure is significantly higher than the conventional standard pressure.

Such conversions are crucial when precise and detailed scientific measurements are necessary.

Fundamentals of Pressure Unit Conversions

Converting between different pressure units is integral when working in various scientific and engineering disciplines. It allows for a better understanding of scenarios across different fields and ensures proper communication of data. Common pressure units include pascal, atmosphere, and millimeters of mercury (mm Hg). Here are some key conversion factors:

• 1 atm = 101325 Pa
• 1 mm Hg = 133.322 Pa

For example, transforming 97,345 Pa to mm Hg involves dividing by 133.322, giving a result of about 729.84 mm Hg. Each unit serves a specific purpose, and conversions help align these measurements depending on the required application.

This knowledge enhances experimental accuracy and data reporting.

Converting Kilopascal to Pascal

While the pascal is useful for delicate measurements, kilopascal (kPa) provides a more practical unit for larger pressures. Converting between these is straightforward because they belong to the same system.

• 1 kPa = 1000 Pa

This means that any given value in kilopascal can be easily converted to pascal by multiplying by 1000:
\[ x\,\mathrm{Pa} = \text{Pressure in}\,\mathrm{kPa} \times 10^3 \]
Taking 1.32 kPa and converting it to pascals results in 1320 Pa. This conversion helps standardize pressure readings in scientific documents and industrial settings, ensuring consistency across different instruments and scenarios.

Understanding how to interchange these units simplifies many technical procedures.