Problem 14 - Chemistry The Molecular Science

Question

These temperatures are measured at various locations during the same day in the winter in North America: \(-10^{\circ} \mathrm{C}\) at Montreal, \(28^{\circ} \mathrm{F}\) at Chicago, \(20^{\circ} \mathrm{C}\) at Charlotte, and \(40^{\circ} \mathrm{F}\) at Philadelphia. Which city is the warmest? Which city is the coldest?

Step-by-Step Solution

Answer

Charlotte is the warmest city; Montreal is the coldest city.

Step 1: Convert Fahrenheit to Celsius

First, we need to convert the temperatures given in Fahrenheit to Celsius to make them comparable. We use the formula: \( C = \frac{5}{9}(F - 32) \). For Chicago, with \(28^{\circ} F\): \( C = \frac{5}{9}(28 - 32) = \frac{5}{9}(-4) = -2.22^{\circ} C \). For Philadelphia, with \(40^{\circ} F\): \( C = \frac{5}{9}(40 - 32) = \frac{5}{9}(8) = 4.44^{\circ} C \).

Step 2: List All Temperatures in Celsius

Now, we have all temperatures in Celsius: Montreal: \(-10^{\circ} C\), Chicago: \(-2.22^{\circ} C\), Charlotte: \(20^{\circ} C\), and Philadelphia: \(4.44^{\circ} C\).

Step 3: Determine the Warmest City

To find the warmest city, compare all the temperatures in Celsius. Charlotte has the highest temperature at \(20^{\circ} C\), making it the warmest city.

Step 4: Determine the Coldest City

To find the coldest city, compare all the temperatures in Celsius. Montreal has the lowest temperature at \(-10^{\circ} C\), making it the coldest city.

Key Concepts

Fahrenheit to Celsius conversion

Converting temperatures from Fahrenheit to Celsius is important in order to make accurate comparisons between figures presented in different units. This is especially so when analyzing temperatures across regions that may use different scales.
The standard formula used is:

• \( C = \frac{5}{9}(F - 32) \)

Here, \(F\) represents the temperature in Fahrenheit, while \(C\) is the converted temperature in Celsius.
This formula helps you understand the relationship between the two scales and can simplify your calculations in real-world scenarios, such as weather analysis or scientific research.
Make sure to always subtract 32 from the Fahrenheit value before applying the fraction. This helps to account for the difference in where each scale starts, allowing for direct conversions.

Temperature comparison

After converting temperatures to a single scale, comparing them becomes a straightforward task. To determine which temperatures are higher or lower, list all temperatures given in the same unit, such as Celsius.
For example:

• Montreal: \(-10^{\circ} C\)
• Chicago: \(-2.22^{\circ} C\)
• Charlotte: \(20^{\circ} C\)
• Philadelphia: \(4.44^{\circ} C\)

Look for the smallest number to identify the coldest temperature, and the largest number for the warmest.
Here, Charlotte at \(20^{\circ} C\) is the warmest, and Montreal at \(-10^{\circ} C\) is the coldest. These comparisons help make informed conclusions about climate conditions in different regions.

Weather analysis

Weather analysis involves comparing temperatures over different locations, often measured in varying units. Understanding climate differences is crucial for activities ranging from agriculture to planning vacation trips.
The first step in weather analysis is data collection, which involves recording temperatures accurately.
Next, conversion of all figures, if needed, must be done before any significant comparisons. This ensures uniformity in the analysis process.
By comparing temperatures from different cities, we can identify which places are warmer or cooler and can predict weather patterns.
Such insights can lead to better readiness and planning for weather events or just understanding seasonal changes in various geographic areas.