Problem 86 - Chemistry: An Atoms-Focused Approach

Question

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

Step-by-Step Solution

Answer

Answer: The highest recorded temperature in the United States (134°F) is equivalent to 56.67°C on the Celsius scale and 329.82 K on the Kelvin scale.

Step 1: Convert Fahrenheit to Celsius

To convert Fahrenheit to Celsius, we can use the following formula: \[C = \frac{5}{9}(F -32)\] Where \(C\) is the temperature in Celsius and \(F\) is the temperature in Fahrenheit. In our case, \(F = 134^{\circ}\mathrm{F}\). So we can plug this value into the formula to find the Celsius temperature: \[C = \frac{5}{9}(134 - 32)\]

Step 2: Calculate Celsius temperature

Now we simplify the formula to find the Celsius temperature: \begin{align*} C &= \frac{5}{9}(102)\\ &= 56.67^{\circ}\mathrm{C} \end{align*} So the temperature in Celsius is \(56.67^{\circ}\mathrm{C}\).

Step 3: Convert Celsius to Kelvin

To convert Celsius to Kelvin, we can use the following formula: \[K = C + 273.15\] Where \(K\) is the temperature in Kelvin and \(C\) is the temperature in Celsius. In our case, \(C = 56.67^{\circ}\mathrm{C}\). So we can plug this value into the formula to find the Kelvin temperature: \[K = 56.67 + 273.15\]

Step 4: Calculate Kelvin temperature

Now we simplify the formula to find the Kelvin temperature: \begin{align*} K &= 56.67 + 273.15\\ &= 329.82\,\mathrm{K} \end{align*} So the temperature in Kelvin is \(329.82\,\mathrm{K}\). To summarize, the temperature of \(134^{\circ}\mathrm{F}\) is equivalent to \(56.67^{\circ}\mathrm{C}\) on the Celsius scale and \(329.82\,\mathrm{K}\) on the Kelvin scale.