Problem 22 - Chemistry The Central Science In Si Units

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 (a) atmospheres, \((\mathbf{b})\) torr, and \((\mathbf{c})\) inches of \(\mathrm{Hg}\).

Step-by-Step Solution

Answer

Conversion results: (a) 0.870 atm, (b) 661.705 torr, (c) 26.036 inches of Hg.

Step 1: Convert millibars to atmospheres

First, remember that 1 atmosphere (atm) is equivalent to 1013.25 millibars (mbar). To convert 882 mbar to atmospheres, use the conversion formula:\[\text{atmospheres} = \frac{\text{millibars}}{1013.25}\]Substitute 882 mbar for millibars in the formula:\[\text{atmospheres} = \frac{882}{1013.25} \approx 0.870 \, \text{atm}\]

Step 2: Convert millibars to torr

The torr and millibar can be converted directly using the knowledge that 1 mbar = 0.750062 torr. Use this conversion to find torr:\[\text{torr} = 882 \, \text{mbar} \times 0.750062 \, \text{torr/mbar}\]Calculate the conversion:\[\text{torr} \approx 661.705 \, \text{torr}\]

Step 3: Convert millibars to inches of Hg

To convert the pressure from millibars to inches of Hg, use the conversion factor where 1 mbar is approximately equal to 0.02953 inches of Hg. Use this to calculate:\[\text{inches of Hg} = 882 \, \text{mbar} \times 0.02953 \, \text{inches of Hg/mbar}\]Calculate the conversion:\[\text{inches of Hg} \approx 26.036 \, \text{inches of Hg}\]

Key Concepts

Converting Millibars to Atmospheres

To convert millibars to atmospheres, it’s essential to know the relationship between these two units of pressure. One atmosphere (atm) is defined as 1013.25 millibars (mbar). The atmospheric pressure at sea level is typically around 1 atm, which provides a baseline for comparison. When converting from millibars to atmospheres, you need to divide the number of millibars by 1013.25. This calculation indicates how many atmospheres the given pressure amount corresponds to. This is particularly useful in meteorology, where atmospheric conditions are often expressed in millibars owing to their precision and convenience. In practice, using the formula:\[\text{atmospheres} = \frac{\text{millibars}}{1013.25}\]you substitute 882 millibars to get approximately 0.870 atmospheres. This means that the pressure during Hurricane Wilma was slightly less than the average atmospheric pressure at sea level.

Converting Millibars to Torr

The torr is a unit of pressure based on an absolute scale and is frequently used in measuring partial vacuums or low-pressure systems. The connection between millibars and torr can be quickly made by remembering that 1 millibar equals approximately 0.750062 torr. To perform the conversion, multiply the number of millibars by this conversion factor:- 1 millibar = 0.750062 torrUsing the hurricane data: \[\text{torr} = 882 \, \text{mbar} \times 0.750062 \, \text{torr/mbar}\]results in approximately 661.705 torr. This calculation highlights a different perspective of the hurricane's pressure, useful in various scientific and engineering applications due to the precision torr provides.

Converting Millibars to Inches of Mercury

Inches of mercury (inHg) is a measure of pressure commonly used in meteorology for weather forecasts and in aviation settings. It denotes the height of a column of mercury that pressure can support. Each inch of mercury equates to approximately 33.86389 millibars, or conversely, 1 millibar is about 0.02953 inches of mercury. To convert millibars to inches of mercury, the procedure involves multiplying the number of millibars by 0.02953:- 1 millibar = 0.02953 inches of HgFor Hurricane Wilma's pressure, this calculation is:\[\text{inches of Hg} = 882 \, \text{mbar} \times 0.02953 \, \text{inches of Hg/mbar}\]which comes out to approximately 26.036 inches of Hg. This gives a clear picture of the storm's intensity, as lower values of inHg reflect a lower pressure associated with more severe weather conditions.