Problem 42 - General Chemistry: Principles and Modern Applications

Question

The highest and lowest temperatures on record for San Bernardino, California, are \(118^{\circ} \mathrm{F}\) and \(17^{\circ} \mathrm{F}\), respectively. What are these temperatures on the Celsius scale?

Step-by-Step Solution

Answer

The highest temperature in San Bernardino, California on the Celsius scale is approximately \(47.8^{\circ} \mathrm{C}\), and the lowest temperature is approximately \(-8.3^{\circ} \mathrm{C}\).

Step 1: Convert Highest Temperature

First, convert the highest temperature from Fahrenheit to Celsius using the conversion formula. Plug \(118^{\circ} \mathrm{F}\) into the formula to get \(C = (118 - 32) \times \frac{5}{9}\). Calculate the expression on the right to find the Celsius temperature.

Step 2: Convert Lowest Temperature

Next, convert the lowest temperature from Fahrenheit to Celsius using the same conversion formula. Plug \(17^{\circ} \mathrm{F}\) into the formula to get \(C = (17 - 32) \times \frac{5}{9}\). Calculate the expression on the right to find the Celsius temperature.

Key Concepts

Fahrenheit to Celsius

The process of converting a temperature from Fahrenheit to Celsius is crucial for understanding temperature differences across regions using different measurement systems. Fahrenheit and Celsius are both scales used to measure temperature, but they have different starting points and units of measure. The Fahrenheit scale is commonly used in the United States, while the Celsius scale is used by most other countries and in scientific communities.
To convert Fahrenheit to Celsius, you need to understand that the scales are offset by the freezing point of water, which is 32 degrees in Fahrenheit and 0 degrees in Celsius. The formula considers this difference, allowing you to make accurate conversions between these scales.

Temperature Scales

Temperature scales are the ways we measure how hot or cold something is. The two primary scales used are Fahrenheit and Celsius. Each scale has its own interval system and uses different fixed points to set these intervals.

• Fahrenheit: Established in 1724 by Daniel Gabriel Fahrenheit, this scale sets 32 degrees as the water's freezing point and 212 degrees as the boiling point.
• Celsius: Developed in 1742 by Anders Celsius, this scale aligns with the metric system and sets 0 degrees for the freezing point of water and 100 degrees for boiling.

These scales are used in various regions for different purposes, such as weather forecasts, cooking, or academic research. Understanding both can help you navigate global and scientific contexts.

Conversion Formula

The conversion formula is a mathematical equation used to change a temperature from Fahrenheit to Celsius. This formula is vital because it allows people in Fahrenheit-using countries to understand Celsius temperatures, and vice versa.
The formula is:
\[ C = (F - 32) \times \frac{5}{9} \]
Where:
- \(C\) represents the temperature in Celsius.
- \(F\) is the temperature in Fahrenheit.
To use the formula, first subtract 32 from the Fahrenheit temperature. Then, multiply the result by \(\frac{5}{9}\). This step adjusts for the different sizes of the degrees on each scale.Remember, this formula is essential whenever converting from Fahrenheit to Celsius, whether for academic exercises or everyday temperature-related activities.