Question

Hurricane Wilma of 2005 is the most intense hurricane on record in the Atlantic basin, with a low-pressure reading of 882 mbar (millibars). Convert this reading into \((\mathbf{a})\) atmospheres, \((\mathbf{b})\) torr, and \((\mathbf{c})\) inches of Hg.

Short answer

The pressure of Hurricane Wilma in different units is approximately: \(\mathbf{a})\) 0.8707 atmospheres, \(\mathbf{b})\) 893.42 Torr, and \(\mathbf{c})\) 26.0571 inches of Hg.

Step-by-step solution

Convert from millibars to atmospheres

To convert the pressure reading of Hurricane Wilma from millibars to atmospheres, we can use the conversion factor: 1 atm = 1013.25 mbar. This means that we need to divide the given pressure (882 mbar) by the conversion factor. \(\mathrm{atm} = \frac{882\,\mathrm{mbar}}{1013.25\,\mathrm{mbar}}\) Now, we can calculate the pressure in atmospheres.

Calculate the pressure in atmospheres

Now we can calculate the pressure using the formula from Step 1: \(\mathrm{atm} = \frac{882}{1013.25}\) \(\mathrm{atm} ≈ 0.8707\) So, the pressure of Hurricane Wilma in atmospheres is approximately 0.8707 atm.

Convert from millibars to torr

Now we will convert the 882 mbar pressure into torr using the conversion factor: 1 Torr = 0.98692 mbar. To accomplish this, we must divide the given pressure value by the conversion factor: \(\mathrm{Torr} = \frac{882\,\mathrm{mbar}}{0.98692\,\mathrm{mbar}}\) Now, we can calculate the pressure in torr.

Calculate the pressure in torr

Now we can calculate the pressure using the formula from Step 3: \(\mathrm{Torr} = \frac{882}{0.98692}\) \(\mathrm{Torr} ≈ 893.42\) So, the pressure of Hurricane Wilma in torr is approximately 893.42 Torr.

Convert from millibars to inches of Hg

Finally, we will convert the 882 mbar pressure into inches of Hg using the conversion factor: 1 in Hg = 33.8638 mbar. To do this, we must divide the given pressure value by the conversion factor: \(\mathrm{in\, Hg} = \frac{882\,\mathrm{mbar}}{33.8638\,\mathrm{mbar}}\) Now, we can calculate the pressure in inches of Hg.

Calculate the pressure in inches of Hg

Now we can calculate the pressure using the formula from Step 5: \(\mathrm{in\, Hg} = \frac{882}{33.8638}\) \(\mathrm{in\, Hg} ≈ 26.0571\) So, the pressure of Hurricane Wilma in inches of Hg is approximately 26.0571 in Hg. After solving all the required conversions, we found that the pressure of Hurricane Wilma was: - \(\mathbf{a})\) 0.8707 atmospheres - \(\mathbf{b})\) 893.42 Torr - \(\mathbf{c})\) 26.0571 inches of Hg.

Key concepts

Atmospheres

Atmospheric pressure is often measured in atmospheres (atm), especially when discussing meteorological events like hurricanes. The atmosphere unit is based on the average pressure at sea level on Earth, which is approximately 1013.25 millibars (mbar). This value serves as a standard reference point for other pressure units.

To convert from millibars to atmospheres, you divide the pressure value in millibars by 1013.25. In this way, you can determine how many times the given pressure fits into the standard atmospheric pressure. For instance, converting 882 mbar to atmospheres, as seen for Hurricane Wilma, results in about 0.8707 atm.

Here's the formula used:

• Atmospheres: \( \text{atm} = \frac{\text{mbar}}{1013.25} \)

The value reveals that Wilma's pressure dropped significantly below the average sea level pressure, indicating its extreme intensity.

Torr

The torr is another common unit for measuring pressure, named after the Italian scientist Evangelista Torricelli. One torr defines the pressure exerted by a one millimeter column of mercury, correlating closely with the concept of a millimeter of mercury (mmHg).

Converting millibars to torr requires using a conversion factor where 1 torr equals approximately 0.98692 millibars. This makes the torr slightly larger than a millibar but smaller than an atmosphere.

For example, transforming 882 mbar into torr involves dividing the millibars by 0.98692, resulting in approximately 893.42 torr. This computation allows us to understand how lowering atmospheric pressure in hurricanes, like Wilma's, can be expressed accurately in different units.

• Torr: \( \text{Torr} = \frac{\text{mbar}}{0.98692} \)

Inches of Hg

Pressure measurements sometimes use inches of mercury (in Hg), originating from mercury columns in barometers. This method involves measuring how high the atmospheric pressure can push mercury up a tube. One inch of mercury is equivalent to 33.8638 millibars.

Converting from millibars to inches of Hg then involves dividing the given pressure by this conversion factor. In our example with Hurricane Wilma, the conversion from 882 mbar to approximately 26.0571 inches of Hg provides insight into the severely low pressure characteristic of powerful hurricanes.

The conversion calculation is straightforward:

• Inches of Hg: \( \text{in Hg} = \frac{\text{mbar}}{33.8638} \)

Understanding how the units convert is key to interpreting pressure data effectively in meteorology and related fields.