Question

The highest barometric pressure ever recorded was 823.7 torr at Agata in Siberia, Russia on December 31,1968 . Convert this pressure to (a) atm, (b) \(\mathrm{mm} \mathrm{Hg}\), (c) pascals, (d) bars, (e) psi.

Short answer

The highest barometric pressure ever recorded is approximately equivalent to: (a) 1.0841 atm (b) 823.7 mmHg (c) 109905.4 Pa (d) 1.0985 bar (e) 15.936 psi

Step-by-step solution

Convert torr to atm

To convert the given pressure in torr to atm, we can use the following equivalence relation between torr and atm: 1 atm \(\approx\) 760 torr From this equivalence relation, the given pressure in atm is: \( Pressure_{atm} = \frac{Pressure_{torr}}{760torr} \)

Convert atm to other units

Now that we have the pressure in atm, we can convert it to other units using known conversion factors for each of these units. The conversion factors are as follows: a) 1 atm = 760 mmHg b) 1 atm = 101325 Pa c) 1 atm = 1.01325 bar d) 1 atm = 14.696 psi

Use conversion factors to calculate pressure in other units

With the conversion factors established, we can now calculate the pressure in each unit using the pressure in atm: (a) Pressure in atm is already calculated in step 1, so we don't need to convert it. (b) To convert pressure in atm to mmHg: \( Pressure_{mmHg} = Pressure_{atm} \times 760 mmHg \) (c) To convert pressure in atm to Pa: \( Pressure_{Pa} = Pressure_{atm} \times 101325 Pa \) (d) To convert pressure in atm to bar: \( Pressure_{bar} = Pressure_{atm} \times 1.01325 bar \) (e) To convert pressure in atm to psi: \( Pressure_{psi} = Pressure_{atm} \times 14.696 psi \)

Calculate the pressure in each unit

Calculate the pressure in each unit by plugging in the value for pressure in atm (from step 1) into the formulas derived in step 3: (a) Pressure in atm: \( Pressure_{atm} = \frac{823.7 torr}{760 torr} = 1.0841 atm \) (b) Pressure in mmHg: \( Pressure_{mmHg} = 1.0841 atm \times 760 mmHg = 823.7 mmHg \) (c) Pressure in Pa: \( Pressure_{Pa} = 1.0841 atm \times 101325 Pa = 109905.4 Pa \) (d) Pressure in bar: \( Pressure_{bar} = 1.0841 atm \times 1.01325 bar = 1.0985 bar \) (e) Pressure in psi: \( Pressure_{psi} = 1.0841 atm \times 14.696 psi = 15.936 psi \) In summary, the highest barometric pressure ever recorded is approximately equivalent to: (a) 1.0841 atm (b) 823.7 mmHg (c) 109905.4 Pa (d) 1.0985 bar (e) 15.936 psi

Key concepts

torr to atm conversion

Converting from torr to atm involves understanding the relationship between these two units of pressure. The atmospheric pressure at sea level is defined as 1 atmosphere (atm), which is equivalent to about 760 torr. Torr is a unit derived from the millimeter of mercury (mmHg) and is used to measure pressure.
If you have a pressure value in torr and wish to convert it to atm, you simply divide the pressure value in torr by the conversion factor of 760.

• Formula: \( Pressure_{atm} = \frac{Pressure_{torr}}{760} \)
• Example: For 823.7 torr, the conversion to atm is \( \frac{823.7}{760} \approx 1.0841 \text{ atm} \)

This conversion is crucial when comparing pressures in different contexts, such as weather reports or scientific experiments, where atmospheric pressure is a common reference.

pressure units

Pressure is a key concept in both science and engineering, and it's measured using various units. Understanding the different units of pressure is important because pressure can be reported in various ways depending on the context. The most common units include:

• Atmospheres (atm): Often used in scientific contexts, representing average atmospheric pressure at sea level.
• Torr: Directly related to mmHg, often used in weather and medical measurements.
• Millimeters of Mercury (mmHg): Common in medical and meteorological applications.
• Pascals (Pa): The SI unit for pressure, where 1 Pa is a relatively small pressure, often used in physics and engineering.
• Bars: Another metric unit, where 1 bar is roughly equal to atmospheric pressure.
• Pounds per square inch (psi): Frequently used in the United States, especially for tire pressure and other mechanical applications.

In practice, converting between these units is common, and knowing how to navigate these conversions can improve comprehension and communication in diverse fields.

pressure conversion factors

To convert one pressure unit to another, you need to use conversion factors. These factors are established based on known equivalences between the units. Knowing the correct conversion factors is essential for exact calculations and comparisons in different pressure contexts.
Here are some common conversion factors:

• 1 atm = 760 mmHg
• 1 atm = 760 torr
• 1 atm = 101325 Pa (Pascals)
• 1 atm = 1.01325 bar
• 1 atm = 14.696 psi

These conversion factors enable seamless transitions between pressure units, allowing for consistent measurements across various scientific and engineering disciplines. Use these factors to convert pressure values from one unit to another by multiplying or dividing, depending on the direction of conversion.

atmospheric pressure

Atmospheric pressure is the pressure exerted by the Earth's atmosphere on objects within it. At sea level, this value is standardized at 1 atmosphere (atm), although it can fluctuate due to changes in weather or altitude.

• Importance: Understanding atmospheric pressure is crucial for meteorology, as it affects weather patterns and climate.
• Measurement: Atmospheric pressure is measured using barometers, and it's reported in various units such as atm, torr, or mmHg.
• Variability: Atmospheric pressure decreases with altitude. Hence, high-altitude locations have lower atmospheric pressure than sea-level areas.

Awareness of atmospheric pressure is also vital in fields like aviation, where pressure impacts flight dynamics, and in medicine, where it influences respiratory and circulatory health. Recognizing atmospheric pressure's role and its measurement units can provide insights into both natural phenomena and technological processes.