Problem 88 - Chemistry The Science in Context

Question

Record High The highest temperature ever recorded in the United States is \(134^{\circ} \mathrm{F}\) at Greenland Ranch, Death Valley, CA, on July \(13,1913 .\) What is this temperature on the Celsius and Kelvin scales?

Step-by-Step Solution

Answer

Question: Convert the given temperature of 134°F to Celsius and Kelvin. Answer: The temperature of 134°F is equivalent to 56.67°C and 329.82 K.

Step 1: Convert Fahrenheit to Celsius

First, use the given temperature in Fahrenheit (\(134^{\circ} \mathrm{F}\)) and the Celsius to Fahrenheit conversion formula: \(C = \frac{5}{9}(F - 32)\) Plug in the value of \(F (134^{\circ} \mathrm{F})\): \(C = \frac{5}{9}(134 - 32)\) Now, calculate the Celsius temperature: \(C = \frac{5}{9}(102) = 56.67^{\circ} \mathrm{C}\)

Step 2: Convert Celsius to Kelvin

Now, we'll use the Celsius temperature calculated in the previous step and the Celsius to Kelvin conversion formula: \(K = C + 273.15\) Plug in the value of \(C (56.67^{\circ} \mathrm{C})\): \(K = 56.67 + 273.15\) Calculate the Kelvin temperature: \(K = 329.82 \mathrm{K}\)

Step 3: Present the final result

The given temperature of \(134^{\circ} \mathrm{F}\) in Celsius and Kelvin scales is: Celsius: \(56.67^{\circ} \mathrm{C}\) Kelvin: \(329.82 \mathrm{K}\)

Key Concepts

Celsius to Fahrenheit

Temperature conversion is a common need in science and everyday life, particularly when traveling or working with weather data. Let's start by discussing how to convert from Celsius to Fahrenheit. The formula to make this conversion is:\[ F = \frac{9}{5}C + 32 \]

• F is the temperature in Fahrenheit.
• C is the temperature in Celsius.

This formula helps to understand the relationship between these two scales. The factor \(\frac{9}{5}\) scales the Celsius value to align with the Fahrenheit scale. The addition of 32 accounts for the difference in the zero points of the scales, as water freezes at 0°C but at 32°F.
To illustrate, consider a temperature of 25°C. Plugging into the formula, we calculate:\[ F = \frac{9}{5}(25) + 32 = 77^{\circ}F \]Therefore, 25°C corresponds to 77°F. This conversion is helpful for interpreting temperatures reported in different parts of the world.

Fahrenheit to Celsius

Converting temperatures from Fahrenheit to Celsius is essential in contexts such as international scientific research or to understand temperature readings from regions using different systems. The formula for this conversion is: \[ C = \frac{5}{9}(F - 32) \]

• C is the temperature in Celsius.
• F is the temperature in Fahrenheit.

In this formula, subtracting 32 from the Fahrenheit temperature adjusts for the difference in freezing points, and multiplying by \(\frac{5}{9}\) rescales the value to match the Celsius scale. Consider the example of converting 134°F (from our exercise):\[ C = \frac{5}{9}(134 - 32) = 56.67^{\circ}C \]This shows that the super high temperature recorded in Death Valley is equivalent to 56.67°C. Understanding this conversion aids in interpreting weather forecasts and scientific data.

Kelvin scale

The Kelvin scale is a vital temperature measurement in science, especially in physics and chemistry. Unlike the Celsius and Fahrenheit scales, Kelvin does not use degrees and starts at absolute zero, the theoretical point of no thermal energy. The conversion from Celsius to Kelvin is straightforward:\[ K = C + 273.15 \]

• K represents the temperature in Kelvin.
• C is the temperature in Celsius.

Since both Celsius and Kelvin scales have the same incremental value, converting between them just involves a simple offset. For the temperature conversion from our exercise, 56.67°C translates into Kelvin as:\[ K = 56.67 + 273.15 = 329.82 \text{ K} \]This conversion places the severe Death Valley temperature in a scientific context. It is critical, for example, in calculations requiring absolute temperatures, such as evaluating thermodynamic processes.