Question

A recipe calls for heating the oven to \(425^{\circ} \mathrm{F}\). If you are vacationing in Europe and the oven only has temperature marked in \({ }^{\circ} \mathrm{C}\), to what temperature do you preheat the oven? What is this temperature in \(\mathrm{K}\) ?

Short answer

The temperature is 218.33 \textdegree C or 491.48 K.

Step-by-step solution

Convert F to C

To convert from Fahrenheit (\textdegree F) to Celsius (\textdegree C), use the formula: \[C = \frac{5}{9} (F - 32)\] Here, \(F = 425\textdegree F\). Substitute this into the formula: \[C = \frac{5}{9} (425 - 32) = \frac{5}{9} \times 393 = 218.33\textdegree C\]

Convert C to K

To convert from Celsius (\textdegree C) to Kelvin (K), use the formula: \[K = C + 273.15\] Here, \(C = 218.33\textdegree C\). Substitute this into the formula: \[K = 218.33 + 273.15 = 491.48 K\]

Key concepts

Fahrenheit to Celsius conversion

Understanding how to convert temperatures between Fahrenheit and Celsius is essential. The formula to convert Fahrenheit to Celsius is:

• \[C = \frac{5}{9} (F - 32)\]

Here, \(F\) is the temperature in Fahrenheit, and \(C\) is the temperature in Celsius. The formula adjusts for the fact that the scales use different starting points and increments.

For instance, using the problem, the oven temperature in Fahrenheit is \(425^{\circ}F\). Substituting into the formula, we get:

• \[C = \frac{5}{9} (425 - 32)\]
• \[C = \frac{5}{9} \times 393\]
• \[C = 218.33^{\circ}C\]

This means you need to preheat the oven to \(218.33^{\circ}C\) when in Europe.

Celsius to Kelvin conversion

To convert temperatures from Celsius to Kelvin, use the following simple formula:

• \[K = C + 273.15\]

In this formula, \(C\) is the temperature in Celsius and \(K\) is the temperature in Kelvin. Remember, Kelvin is an absolute temperature scale, starting from absolute zero.

If we continue with the earlier example, after converting \(425^{\circ} F\) to \(218.33^{\circ}C\), we now need to convert this Celsius temperature to Kelvin. Using the formula, we get:

• \[K = 218.33 + 273.15\]
• \[K = 491.48 K\]

Thus, the oven temperature in Kelvin would be \(491.48 K\).

temperature units

Temperature is measured in different units around the world, primarily Fahrenheit (\(^\circ F\)), Celsius (\(^\circ C\)), and Kelvin (K). Each unit has its distinct uses and geographical preferences.

• Fahrenheit is commonly used in the United States for daily weather and domestic appliance settings. It sets the freezing point of water at \(32^{\circ}F\) and the boiling point at \(212^{\circ}F\).
• Celsius is widely used around the world, especially in scientific contexts and daily life in most countries outside the US. Here, water freezes at \(0^{\circ}C\) and boils at \(100^{\circ}C\).
• Kelvin is mainly used in scientific research where absolute temperatures are required. The scale starts from absolute zero (\(0 K\) where there is no thermal motion), water freezes at \(273.15 K\), and boils at \(373.15 K\).

Understanding these units and their conversions is fundamental for anything from cooking and weather forecasting to scientific research.