Question

Which air temperature feels coldest? a) \(-40^{\circ} \mathrm{C}\) c) \(233 \mathrm{~K}\) b) \(-40^{\circ} \mathrm{F}\) d) All three are equal.

Short answer

Answer: d) All three are equal.

Step-by-step solution

Convert Fahrenheit to Celsius

To convert from Fahrenheit to Celsius, use the formula: \(\mathrm{C} = \frac{5}{9} (\mathrm{F} - 32)\). We need to convert \(-40^{\circ}\mathrm{F}\) to Celsius: \(\mathrm{C} = \frac{5}{9}((-40) - 32) = -40^{\circ}\mathrm{C}\).

Compare the temperatures in Celsius

Now, we have the three temperatures in Celsius: a) \(-40^{\circ}\mathrm{C}\) b) \(-40^{\circ}\mathrm{C}\) (converted from Fahrenheit)

Convert Kelvin to Celsius

To convert from Kelvin to Celsius, use the formula: \(\mathrm{C} = \mathrm{K} - 273.15\). We need to convert \(233\mathrm{K}\) to Celsius: \(\mathrm{C} = 233 - 273.15 = -40^{\circ}\mathrm{C}\).

Compare all temperatures

Now, we have all three temperatures in Celsius: a) \(-40^{\circ}\mathrm{C}\) b) \(-40^{\circ}\mathrm{C}\) (converted from Fahrenheit) c) \(-40^{\circ}\mathrm{C}\) (converted from Kelvin) All three temperatures are equal, so the correct answer is d) All three are equal.

Key concepts

Fahrenheit to Celsius Conversion

Understanding how to convert Fahrenheit to Celsius is essential in several scientific fields and when traveling to countries using different temperature scales. To convert a temperature from Fahrenheit to Celsius, you need to know the formula: \(C = \frac{5}{9} (F - 32)\).

This formula takes the Fahrenheit degree, subtracts 32, and then multiplies by 5/9 to find the equivalent Celsius temperature. Let's break this down further with an example. If we have a temperature of \(32^\circ F\), we would subtract 32 from it, resulting in 0. Then, since 0 multiplied by any number is 0, this indicates that \(32^\circ F\) is equivalent to \(0^\circ C\), which is the freezing point of water.

It's interesting to note that \(\frac{5}{9}\) is the exact conversion factor because the Fahrenheit scale and the Celsius scale cross at \( -40^\circ \); at this point, the temperatures are the same in both scales. As a visual aid, it's often helpful to imagine a thermometer showing both scales with the Fahrenheit on the outside and the Celsius on the inside to understand how they correlate.

Kelvin to Celsius Conversion

In scientific contexts, temperatures are often given in Kelvin, which is the base unit of temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale, meaning it starts at absolute zero, the coldest possible temperature where particles have minimum thermal motion.

To convert Kelvin to Celsius, the formula is quite straightforward: \(\mathrm{C} = K - 273.15\). This is because the Kelvin scale is offset from the Celsius scale by 273.15 degrees. In essence, 0 degrees Kelvin is equal to \( -273.15^\circ C\). For instance, if you have a temperature of 300K, you subtract 273.15 to get \(26.85^\circ C\).

This conversion is critical in fields such as astronomy and physics, where Kelvin is often used. Remembering that Kelvin to Celsius is a simple subtraction can help students quickly perform conversions without a calculator.

Comparing Temperatures

Being able to compare temperatures across different scales is a useful skill. It can help us understand weather forecasts, cook using international recipes, or study scientific data. When comparing temperatures, it is vital to convert them to a common scale.

In the exercise, we had temperatures given in both Celsius and Fahrenheit and one in Kelvin. After conversion, it became evident that all values equated to \( -40^\circ C\). This unique point where both Celsius and Fahrenheit scales read the same serves as an intriguing example to help students remember temperature scales and their conversions.

When it comes to day-to-day weather comparison, converting temperatures allows for an accurate understanding of the conditions. A temperature that might seem high in one scale can be moderate or even low in another, like \(80^\circ F\) being a pleasant \(26.67^\circ C\), which may require different types of clothing or activity planning.

For students learning about temperature comparison, visual aids such as side-by-side thermometers or conversion charts can be highly effective in reinforcing these concepts.