Question

Convert each temperature. a. \(212^{\circ} \mathrm{F}\) to \({ }^{\circ} \mathrm{C}\) (temperature of boiling water at sea level) b. \(22^{\circ} \mathrm{C}\) to \(\mathrm{K}\) (approximate room temperature) c. \(0.00 \mathrm{~K}\) to \({ }^{\circ} \mathrm{F}\) (coldest temperature possible, also known as absolute zero) d. \(2.735 \mathrm{~K}\) to \({ }^{\circ} \mathrm{C}\) (average temperature of the universe as measured from background black body radiation)

Short answer

a. 100°C, b. 295.15 K, c. -459.67°F, d. -270.415°C.

Step-by-step solution

Convert Fahrenheit to Celsius

To convert the temperature from Fahrenheit to Celsius, use the formula \( \frac{5}{9}(F - 32) = C \) where F is the temperature in degrees Fahrenheit. Plug the value of 212°F into the formula: \( C = \frac{5}{9}(212 - 32) \) and calculate the result.

Convert Celsius to Kelvin

To convert the temperature from Celsius to Kelvin, use the formula \( K = C + 273.15 \) where C is the temperature in degrees Celsius. Plug the value of 22°C into the formula: \( K = 22 + 273.15 \) and calculate the result.

Convert Kelvin to Fahrenheit

To convert the temperature from Kelvin to Fahrenheit, first convert Kelvin to Celsius using the formula \( C = K - 273.15 \) and then use the converted Celsius temperature to find Fahrenheit using the formula \( F = \frac{9}{5}C + 32 \) where C is the temperature in degrees Celsius. Since 0.00 K is the lowest possible temperature, known as absolute zero, you would plug the value of 0 K into the formula: \( F = \frac{9}{5}(0 - 273.15) + 32 \) and calculate the result.

Convert Kelvin to Celsius

To convert the temperature from Kelvin to Celsius, use the formula \( C = K - 273.15 \) where K is the temperature in Kelvin. Plug the value of 2.735 K into the formula: \( C = 2.735 - 273.15 \) and calculate the result.

Key concepts

Fahrenheit to Celsius

Understanding how to convert temperature from Fahrenheit to Celsius is crucial for various scientific calculations and everyday life situations outside the USA, such as cooking or measuring the weather. The core formula used for this conversion is
\( C = \frac{5}{9}(F - 32) \).
For example, the boiling point of water at sea level is traditionally measured as 212°F. Using our formula, we convert it this way:
\( C = \frac{5}{9}(212 - 32) = 100 \).
Therefore, the boiling point of water at sea level is 100°C. It's essential to remember that water boils at 100°C, and this point serves as a significant reference for the Celsius scale.

Celsius to Kelvin

The Kelvin scale is the base unit of temperature in the International System of Units (SI), and it's used primarily in the scientific community. When converting Celsius to Kelvin, you're essentially shifting the starting point from the freezing point of water to absolute zero, the theoretical lowest temperature possible. The equation for this conversion is quite straightforward:
\( K = C + 273.15 \).
If we take a room temperature of 22°C as an example:
\( K = 22 + 273.15 = 295.15 \) K.
Remember, when converting from Celsius to Kelvin, you're not changing the temperature's magnitude, just the scale you're measuring on.

Kelvin to Fahrenheit

The process for converting Kelvin to Fahrenheit is a two-step process since it involves an intermediate conversion to Celsius. The initial step is converting Kelvin to Celsius:
\( C = K - 273.15 \).
After finding the Celsius temperature, you then convert it to Fahrenheit using:
\( F = \frac{9}{5}C + 32 \).
For example, the lowest temperature possible, known as 'absolute zero', is 0.00 K. To convert this to Fahrenheit:
\( C = 0 - 273.15 = -273.15 \text{°C} \), then
\( F = \frac{9}{5}(-273.15) + 32 = -459.67 \text{°F} \).
This two-step process can be used for any Kelvin temperature, effectively bridging the gap between the scientific community, which uses Kelvin, and daily applications in regions that use Fahrenheit.

Absolute Zero

Absolute zero represents the theoretical temperature at which particles have minimal thermal motion and cannot be colder. It is the starting point of the Kelvin scale and is equal to -273.15°C or -459.67°F. Absolute zero is significant in scientific fields, particularly thermodynamics and quantum mechanics, where it establishes a quantifiable limit to the amount of thermal energy in a system. While it's impossible to achieve absolute zero, understanding this concept helps scientists comprehend the behavior of particles at extremely low temperatures and predict the properties of matter under such conditions.