A piece of dry ice (solid carbon dioxide) sitting in a classroom has a temperature of approximately \(-79^{\circ} \mathrm{C}\) a) What is this temperature in kelvins? b) What is this temperature in degrees Fahrenheit?

Understanding how to convert temperatures from degrees Celsius to kelvins is a fundamental skill in many scientific fields. The key thing to remember is that these two units measure the same thing—temperature—but on different scales. The Kelvin scale is an absolute thermodynamic temperature scale where 0 K is absolute zero - the point where molecular motion stops.

To convert a temperature from Celsius to Kelvin, you simply add 273.15 to the Celsius temperature. This number represents the difference in the starting points of the two scales. Absolute zero, for instance, is \(0 \mathrm{K}\), but it is \-273.15 degrees Celsius. Let's use the example from the exercise where a piece of dry ice has a temperature of \-79 degrees Celsius. Using the formula:

\[\text{Temperature in Kelvins} = \(\text{-79}\) + 273.15\]

We find that the temperature of dry ice in kelvins is 194.15 K. It's vital for students to grasp this simple addition because Kelvin is widely used in scientific experiments where precise temperature measurements are crucial, like those in physics and chemistry.

The conversion from degrees Celsius to degrees Fahrenheit requires a two-step process and is necessary for understanding temperature in contexts where the Fahrenheit scale is used, such as weather reports in the United States. To convert Celsius to Fahrenheit, we first multiply the Celsius temperature by \(\frac{9}{5}\), and then add 32 to the result. This formula accounts for the differences in how each scale increments per degree.

For example, when converting the dry ice temperature of \-79 degrees Celsius to Fahrenheit, we use the formula:

\[\text{Temperature in degrees Fahrenheit} = (\text{-79} × \frac{9}{5}) + 32\]

The result is \-110.2 degrees Fahrenheit. Students often struggle with this concept because it involves both multiplication and addition. However, it's a crucial part of understanding temperature reporting in various regions, as well as for working with historical data that might only be available in Fahrenheit.

Thermodynamic temperature scales are based on principles of thermodynamics, which is the field of physics dealing with heat and its relation to other forms of energy and work. The two most commonly used thermodynamic temperature scales are Celsius and Kelvin. While the Kelvin scale is an absolute scale starting at absolute zero, where all thermal motion ceases, the Celsius scale is relative and set with the freezing point of water at 0 degrees and boiling point at 100 degrees under standard atmospheric conditions.

Each scale serves different purposes. Scientists mainly use the Kelvin scale for scientific measurements because it allows them to calculate the thermal energy in a system without the need to include arbitrary constants in their calculations. Conversely, the Celsius scale is often used in daily life and many scientific applications due to its easier relatability to common experiences with water and weather.

Incorporating thermodynamics into temperature conversion helps students relate these scales to real-world phenomena, bridging abstract theory and practical application. Grasping different temperature scales and their inter-conversion forms a foundational understanding for students pursuing science, technology, engineering, and mathematics (STEM) fields.