Question

Calculate each of the following temperatures in degrees Celsius: a. The highest recorded temperature in the continental United States was \(134{ }^{\circ} \mathrm{F}\) in Death Valley, California, on July \(10 .\) \(1913 .\) b. The lowest recorded temperature in the continental United States was \(-69.7{ }^{\circ} \mathrm{F}\) in Rodgers Pass, Montana, January 20 , \(1954 .\)

Short answer

The highest temperature is about 56.67°C and the lowest is about -56.5°C.

Step-by-step solution

- Understanding the Formula

To convert a temperature from Fahrenheit to Celsius, use the formula: \[ C = \frac{5}{9}(F - 32) \] where \( C \) is the temperature in Celsius and \( F \) is the temperature in Fahrenheit.

- Convert the Highest Recorded Temperature

Given the highest recorded temperature: 134°F1. Substitute \( F = 134 \) into the conversion formula: \[ C = \frac{5}{9}(134 - 32) \] 2. Calculate inside the parentheses: \[ 134 - 32 = 102 \] 3. Multiply by \( \frac{5}{9} \): \[ C = \frac{5}{9} \times 102 = 56.67 \] So, the highest recorded temperature in Celsius is approximately 56.67°C.

- Convert the Lowest Recorded Temperature

Given the lowest recorded temperature: -69.7°F1. Substitute \( F = -69.7 \) into the conversion formula: \[ C = \frac{5}{9}(-69.7 - 32) \] 2. Calculate inside the parentheses: \[ -69.7 - 32 = -101.7 \] 3. Multiply by \( \frac{5}{9} \): \[ C = \frac{5}{9} \times -101.7 = -56.5 \] So, the lowest recorded temperature in Celsius is approximately -56.5°C.

Key concepts

Fahrenheit to Celsius

Understanding how to convert temperatures between different scales is crucial in a multitude of academic and practical fields. One of the most common conversions is from Fahrenheit to Celsius. To perform this conversion, we use the formula: \[ C = \frac{5}{9}(F - 32) \] Here, \ C \ represents the temperature in Celsius, and \ F \ stands for the temperature in Fahrenheit. This formula allows us to translate Fahrenheit temperatures into the more widely used Celsius scale, enabling clear and consistent interpretation of temperature data across different contexts.

Temperature Calculation

Let’s dive into the specifics of calculating temperature conversions using the example provided in the exercise. For the highest recorded temperature: Given temperature: 134°F Step-by-step solution: 1. Insert the Fahrenheit value into the formula: \[ C = \frac{5}{9}(134 - 32) \] 2. Simplify the value inside the parentheses: \[ 134 - 32 = 102 \] 3. Multiply by the fraction: \[ C = \frac{5}{9} \times 102 = 56.67 \] Therefore, 134°F is approximately 56.67°C. Now, let’s convert the lowest recorded temperature: Given temperature: -69.7°F Step-by-step solution: 1. Substitute the value into the formula: \[ C = \frac{5}{9}(-69.7 - 32) \] 2. Simplify the value inside the parentheses: \[ -69.7 - 32 = -101.7 \] 3. Multiply by the fraction: \[ C = \frac{5}{9} \times -101.7 = -56.5 \] Hence, -69.7°F is approximately -56.5°C.

Mathematics in Chemistry

Temperature conversions are not just important for everyday applications, but are also essential in the field of chemistry. Accurate temperature measurements and conversions can significantly impact the results of experiments and the interpretation of data. Here are some reasons why temperature conversion is crucial in chemistry:

• Reaction Rate: Many chemical reactions are temperature-dependent, where the rate of reaction changes with temperature.
• Gas Laws: Calculations involving gases often require temperature to be converted into Celsius or Kelvin for accurate results.
• Solubility: The solubility of substances can change drastically with temperature variations, requiring accurate temperature data for predictions and formulations.

Utilizing the correct temperature conversion ensures that chemists and students alike can maintain consistency and precision in their scientific endeavors. By grasping the concept of converting Fahrenheit to Celsius, students can bridge gaps across various scientific disciplines effortlessly.