Problem 83 - Chemistry Principles and Practice

Question

(a) Helium has the lowest boiling point of any substance; it boils at \(4.21 \mathrm{~K}\). Express this temperature in degrees Celsius and degrees Fahrenheit. (b) The oven temperature for a roast is \(400^{\circ} \mathrm{F}\). Convert this temperature to degrees Celsius.

Step-by-Step Solution

Answer

Helium boils at \(-268.94^\circ C\) and \(-452.1^\circ F\); Oven is \(204.44^\circ C\).

Step 1: Convert Kelvin to Celsius

To convert from Kelvin to Celsius, use the formula: \[°C = K - 273.15\]For the given boiling point of helium at \(4.21\,K\):\[°C = 4.21 - 273.15 = -268.94°C\]

Step 2: Convert Celsius to Fahrenheit

To convert Celsius to Fahrenheit, use the formula: \[°F = (°C \times \frac{9}{5}) + 32\]Using the Celsius value from Step 1:\[°F = (-268.94 \times \frac{9}{5}) + 32 \approx -452.1°F\]

Step 3: Convert Fahrenheit to Celsius

To convert Fahrenheit to Celsius, use the formula:\[°C = (°F - 32) \times \frac{5}{9}\]Given the oven temperature of \(400^{\circ}F\):\[°C = (400 - 32) \times \frac{5}{9} = 204.44°C\]

Step 4: Conclusion

The conversions are completed: a) Helium boils at \(-268.94^{\circ}C\) and \(-452.1^{\circ}F\).b) The oven temperature is \(204.44^{\circ}C\).

Key Concepts

Kelvin to Celsius conversion

Converting temperatures from Kelvin to Celsius is a straightforward process involving simple subtraction. This conversion is essential when dealing with scientific measurements since Kelvin is the standard unit of temperature in the scientific community. The Kelvin to Celsius formula is:

• \[°C = K - 273.15\]

Kelvin begins at absolute zero, which is the coldest theoretical temperature, making its scale directly relatable to Celsius. For instance, if you're converting the boiling point of helium, which is 4.21 K, use the formula to find:

• \[°C = 4.21 - 273.15 = -268.94°C\]

This negative value might seem unusual, but it reflects the extremely low temperatures achieved for liquefied gases like helium. Understanding this scale helps in grasping how close temperatures are to absolute zero.

Celsius to Fahrenheit conversion

To convert a temperature from Celsius to Fahrenheit, multiply the Celsius temperature by \(\frac{9}{5}\) and then add 32. This conversion is used frequently in countries like the United States, where Fahrenheit is more common.

• Conversion formula: \[°F = (°C \times \frac{9}{5}) + 32\]

For instance, our earlier conversion of helium's temperature indicated it was \(-268.94°C\). To convert this to Fahrenheit:

• \[°F = (-268.94 \times \frac{9}{5}) + 32 \approx -452.1°F\]

This extremely low Fahrenheit value reinforces just how cold liquid helium is. Converting temperatures correctly ensures proper understanding and communication in scientific and everyday contexts.

Fahrenheit to Celsius conversion

Converting from Fahrenheit to Celsius is crucial, especially when dealing with recipes, weather reports, and other daily uses in Fahrenheit-centric countries. The conversion involves subtracting 32 from the Fahrenheit value and then multiplying by \(\frac{5}{9}\).

• Here's the formula: \[°C = (°F - 32) \times \frac{5}{9}\]

Take, for example, the oven temperature set at 400°F. To convert this to Celsius:

• \[°C = (400 - 32) \times \frac{5}{9} = 204.44°C\]

This conversion is important for international recipe sharing and understanding global temperature standards. It makes clear how Fahrenheit and Celsius scales relate at common temperature points.