Question

Convert the following Celsius temperatures to Kelvin and to Fahrenheit degrees. a. the temperature of someone with a fever, \(39.2^{\circ} \mathrm{C}\) b. a cold wintery day, \(-25^{\circ} \mathrm{C}\) c. the lowest possible temperature, \(-273^{\circ} \mathrm{C}\) d. the melting-point temperature of sodium chloride, \(801^{\circ} \mathrm{C}\)

Short answer

The converted temperatures are as follows: a. Fever: \(312.35 \ \mathrm{K}\), \(102.56 ^{\circ} \mathrm{F}\) b. Cold wintery day: \(248.15 \ \mathrm{K}\), \(-13 ^{\circ} \mathrm{F}\) c. Lowest possible temperature: \(0.15 \ \mathrm{K}\), \(-459.4 ^{\circ} \mathrm{F}\) d. Melting-point of sodium chloride: \(1074.15 \ \mathrm{K}\), \(1473.8 ^{\circ} \mathrm{F}\)

Step-by-step solution

Convert to Kelvin

Use the formula: \( K = C + 273.15 \) For \(39.2^{\circ} \mathrm{C}\), the Kelvin will be: \(K = 39.2 + 273.15 = 312.35 \) Kelvin

Convert to Fahrenheit

Use the formula: \( F = \frac{9}{5}C + 32 \) For \(39.2^{\circ} \mathrm{C}\), the Fahrenheit will be: \(F = \frac{9}{5}(39.2) + 32 = 102.56^{\circ} \mathrm{F}\) For b. a cold wintery day, \(-25^{\circ} \mathrm{C}\)

Convert to Kelvin

Use the formula: \( K = C + 273.15 \) For \(-25^{\circ} \mathrm{C}\), the Kelvin will be: \(K = -25 + 273.15 = 248.15 \) Kelvin

Convert to Fahrenheit

Use the formula: \( F = \frac{9}{5}C + 32 \) For \(-25^{\circ} \mathrm{C}\), the Fahrenheit will be: \(F = \frac{9}{5}(-25) + 32 = -13^{\circ} \mathrm{F}\) For c. the lowest possible temperature, \( -273^{\circ} \mathrm{C}\)

Convert to Kelvin

Use the formula: \( K = C + 273.15 \) For \(-273^{\circ} \mathrm{C}\), the Kelvin will be: \(K = -273 + 273.15 = 0.15 \) Kelvin

Convert to Fahrenheit

Use the formula: \( F = \frac{9}{5}C + 32 \) For \(-273^{\circ} \mathrm{C}\), the Fahrenheit will be: \(F = \frac{9}{5}(-273) + 32 = -459.4^{\circ} \mathrm{F}\) For d. the melting-point temperature of sodium chloride, \(801^{\circ} \mathrm{C}\)

Convert to Kelvin

Use the formula: \( K = C + 273.15 \) For \(801^{\circ} \mathrm{C}\), the Kelvin will be: \(K = 801 + 273.15 = 1074.15 \) Kelvin

Convert to Fahrenheit

Use the formula: \( F = \frac{9}{5}C + 32 \) For \(801^{\circ} \mathrm{C}\), the Fahrenheit will be: \(F = \frac{9}{5}(801) + 32 = 1473.8^{\circ} \mathrm{F}\)

Key concepts

Celsius to Kelvin Conversion

The Celsius to Kelvin conversion is essential in various scientific fields as both scales are widely used. To convert temperature from Celsius to Kelvin, you use the simple formula:
\[\begin{equation} K = C + 273.15 \end{equation}\]
This equation highlights that the Kelvin scale and the Celsius scale are offset by 273.15. The Kelvin scale is an absolute temperature scale where zero Kelvin (\[\begin{equation} 0 K \end{equation}\]) is absolute zero, the point at which the fundamental particles of nature have minimal thermal motion.
To understand this concept better, consider a real-life scenario such as the temperature of boiling water. At sea level, water boils at \[\begin{equation}100^{\text{\circ} \text{C}}\end{equation}\]. Using the conversion formula, you end up with a temperature of \[\begin{equation}373.15 K\end{equation}\]. It's important to pay attention to the decimal places and use the formula accurately to ensure precision in scientific calculations.

Celsius to Fahrenheit Conversion

Converting temperatures from Celsius to Fahrenheit may seem complex at first, but it is actually quite straightforward with the correct formula. When you want to convert Celsius to Fahrenheit, you use the following equation:
\[\begin{equation} F = \frac{9}{5}C + 32 \end{equation}\]
This equation takes the Celsius temperature, multiplies it by \[\begin{equation}9/5\end{equation}\] or 1.8, and then adds 32 to adjust for the differences in the starting points of the two scales.
For example, the average human body temperature is approximately \[\begin{equation}37^{\text{\circ} \text{C}}\end{equation}\] which is equivalent to \[\begin{equation}98.6^{\text{\circ} \text{F}}\end{equation}\] when converted. This conversion is particularly useful in everyday life, especially when you are dealing with weather temperature reports or cooking recipes that prefer one scale over the other.

Temperature Scales

Temperature scales provide a consistent way to measure thermal energy or heat. The Celsius (\[\begin{equation}^{\text{\circ} \text{C}}\end{equation}\]), Fahrenheit (\[\begin{equation}^{\text{\circ} \text{F}}\end{equation}\]), and Kelvin (K) scales are the most prevalent. Each of these has its own place and purpose.
The Celsius scale is used worldwide for most temperature measurements. It has a freezing point of water at \[\begin{equation}0^{\text{\circ} \text{C}}\end{equation}\] and a boiling point at \[\begin{equation}100^{\text{\circ} \text{C}}\end{equation}\] at standard atmospheric pressure. In contrast, the Fahrenheit scale is mainly used in the United States and has water freezing at \[\begin{equation}32^{\text{\circ} \text{F}}\end{equation}\] and boiling at \[\begin{equation}212^{\text{\circ} \text{F}}\end{equation}\].
The Kelvin scale is the base unit of temperature in the International System of Units (SI). It is widely used in the scientific community because it is an absolute scale with its zero point at absolute zero, the coldest possible temperature where thermal motion ceases. The different scales serve various purposes, from day-to-day weather forecasts in Celsius or Fahrenheit to scientific research which typically resorts to Kelvin.