Question

Convert \(0 \mathrm{~K}\) to degrees Fahrenheit. What is the significance of the temperature in degrees Fahrenheit?

Short answer

0 K is -459.67 °F, indicating absolute zero, where molecular motion ceases.

Step-by-step solution

Understanding the Formula for Temperature Conversion

To convert from Kelvin to Fahrenheit, we need to first convert Kelvin to Celsius using the formula: \[ \text{Celsius} = \text{Kelvin} - 273.15 \]Then, convert Celsius to Fahrenheit using the formula: \[ \text{Fahrenheit} = \left( \frac{9}{5} \times \text{Celsius} \right) + 32 \].

Convert Kelvin to Celsius

Using the formula \( \text{Celsius} = \text{Kelvin} - 273.15 \), substitute \(0 \text{ K}\) into the equation:\[ \text{Celsius} = 0 - 273.15 = -273.15 \text{ °C} \].This means that \(0 \text{ K}\) is equivalent to \(-273.15 \text{ °C}\).

Convert Celsius to Fahrenheit

Now, using the formula \( \text{Fahrenheit} = \left( \frac{9}{5} \times \text{Celsius} \right) + 32 \), substitute \(-273.15 \text{ °C}\):\[ \text{Fahrenheit} = \left( \frac{9}{5} \times (-273.15) \right) + 32 \]\[ \text{Fahrenheit} = -459.67 \text{ °F} \].Thus, \(0 \text{ K}\) is equal to \(-459.67 \text{ °F}\).

Understanding the Significance

The temperature \(-459.67 \text{ °F}\) signifies absolute zero. Absolute zero is the lowest physically possible temperature, where molecular motion stops. This temperature represents a point of no thermal energy.

Key concepts

Kelvin to Fahrenheit

Converting temperature from Kelvin to Fahrenheit involves a multi-step process. This is because the Kelvin and Fahrenheit scales measure temperature differently and require intermediate conversion via Celsius. At first, you convert Kelvin to Celsius using this formula:

• \[ \text{Celsius} = \text{Kelvin} - 273.15 \]

Once you have the temperature in Celsius, you then convert it to Fahrenheit. To do this, you use the formula:

• \[ \text{Fahrenheit} = \left( \frac{9}{5} \times \text{Celsius} \right) + 32 \]

These calculations stem from the different zero points on each temperature scale. Zero on the Kelvin scale is known as "absolute zero" and is equivalent to \(-273.15 \text{ °C} \) or \(-459.67 \text{ °F} \). Hence, converting temperatures involves careful mathematical manipulation, starting from one scale to another.

Absolute Zero

Absolute zero is the coldest theoretical temperature a system can reach. It is precisely defined as 0 Kelvin, or equivalently \(-273.15 \text{ °C} \) and \(-459.67 \text{ °F} \). At absolute zero, all molecular motion comes to a standstill.

In the realm of thermodynamics, absolute zero signifies the point at which a system possesses no thermal energy. Molecules are in their lowest energy state and vibrational motion ceases.

This concept is an idealization, as in practice, reaching absolute zero is impossible. However, it plays a crucial role as a reference point in scientific measurements. Understanding absolute zero helps scientists and engineers explore the physical properties of materials at very low temperatures.

Temperature Scales

There are several temperature scales used to measure heat. The most commonly used are Kelvin, Celsius, and Fahrenheit.

• Kelvin Scale: Often used in scientific settings, the Kelvin scale starts at absolute zero. It is an absolute scale with no negative numbers.
• Celsius Scale: Known as a metric scale, Celsius sets water's freezing point at 0°C and boiling point at 100°C under standard atmospheric pressure. It is convenient for everyday use.
• Fahrenheit Scale: Predominantly used in the United States, the Fahrenheit scale sets water freezing at 32°F and boiling at 212°F.

These scales have different zero points and units of increment. Consequently, conversion between them requires specific formulas, such as those mentioned for Kelvin to Celsius and Celsius to Fahrenheit. Each scale is suited to different applications, be it scientific, household, or regional usage.