Question

Liquid helium boils at \(4.2 \mathrm{~K}\). Convert this temperature to degrees Fahrenheit and Celsius.

Short answer

The temperature of liquid helium in Celsius is approximately -268.95 \( ^\circ C \) and in Fahrenheit is approximately -452.11 \( ^\circ F \).

Step-by-step solution

Convert Kelvin to Celsius

To convert Kelvin to Celsius, use the formula: \( C = K - 273.15 \). Where \( C \) is the temperature in Celsius, and \( K \) is the temperature in Kelvin.

Calculate Celsius Temperature

Substitute \( 4.2 \) for \( K \) in the formula to find the Celsius temperature: \( C = 4.2 - 273.15 \).

Convert Celsius to Fahrenheit

To convert Celsius to Fahrenheit, use the formula: \( F = \frac{9}{5}C + 32 \). Where \( F \) is the temperature in Fahrenheit, and \( C \) is the temperature in Celsius.

Calculate Fahrenheit Temperature

Substitute the Celsius temperature obtained from Step 2 into the Fahrenheit conversion formula to find the Fahrenheit temperature.

Key concepts

Kelvin to Celsius Conversion

Understanding the conversion of temperatures from Kelvin to Celsius is crucial when dealing with scientific measurements. Kelvin is the base unit of temperature in the International System of Units (SI), and it is widely used in scientific research because it begins at absolute zero, the theoretically coldest possible temperature.

To convert Kelvin to Celsius, simply subtract 273.15 from the Kelvin value. This number represents the difference in the starting points of the two scales: absolute zero is 0K but -273.15°C. The formula looks like this:
\[ C = K - 273.15 \]
For example, if we take the boiling point of liquid helium at 4.2K, we substitute the Kelvin value into the formula as follows:
\[ C = 4.2 - 273.15 \]
After calculating, we find the Celsius equivalent of the boiling point of liquid helium, which is a necessary step before converting to Fahrenheit.

Celsius to Fahrenheit Conversion

Once we have the temperature in Celsius, we often need to convert it to Fahrenheit, especially in regions where the Fahrenheit scale is still used for everyday temperatures. Knowing how to change Celsius to Fahrenheit is a common practical skill.

The formula to convert Celsius to Fahrenheit is:
\[ F = \frac{9}{5}C + 32 \]
This formula implies that Fahrenheit temperature is proportional to 1.8 (or \(\frac{9}{5}\)) times the Celsius temperature and then 32 is added to adjust for the differences in the zero points of the two scales. For example, after converting the Kelvin temperature of liquid helium to Celsius, we use the resulting value to find its Fahrenheit equivalent:
\[ F = \frac{9}{5} \times (-268.95) + 32 \]
By substituting the Celsius value into the formula, we find the temperature in Fahrenheit.

Understanding this conversion allows students to navigate between the two units seamlessly, which is particularly helpful in scientific experiments and real-world contexts where both units might be in use.

Scientific Problem Solving

Scientific problem solving is a critical skill that involves using a systematic approach to understand complex issues. In the context of temperature conversion, problem solving is about applying mathematical formulas correctly and understanding the physical science concepts behind these formulas.

The following steps illustrate scientific problem solving through our temperature conversion exercise:

• Identify the problem: We need to convert the boiling point of liquid helium from Kelvin to both Celsius and Fahrenheit.
• Understand the concepts: Grasp the conversion formulas between temperature scales.
• Execute conversions: Perform calculations accurately by substituting the known values into the formulas.
• Review the solutions: Once you get the results, check if they make sense logically and scientifically. For instance, since liquid helium is extremely cold, we expect very low temperatures in both Celsius and Fahrenheit.

Scientific problem solving is not just about arriving at an answer; it's about developing an understanding of the method and its underlying principles. This approach empowers learners to tackle a wide range of problems beyond just temperature conversions.