Question

Absolute zero is \(-273.15^{\circ} \mathrm{C}\). Find absolute zero on the Fahrenheit scale.

Short answer

Absolute zero in Fahrenheit scale is \(-459.67^{\circ} \mathrm{F}\).

Step-by-step solution

Identify the given temperature in Celsius

The temperature given is absolute zero, which is \(-273.15^{\circ} \mathrm{C}\). This is the value we will need to convert into Fahrenheit.

Apply the conversion formula

The formula to convert from Celsius to Fahrenheit is \( F = C \times \frac{9}{5} + 32 \). Substituting in the given Celsius temperature, we get \( F = -273.15 \times \frac{9}{5} + 32 \).

Calculate the temperature in Fahrenheit

Perform the multiplication and addition to find the temperature in Fahrenheit. Plugging it into a calculator, we get \( F = -459.67 ^{\circ} \mathrm{F} \).

Key concepts

Temperature Conversion

Understanding how to convert temperature from one unit to another is essential in various fields like meteorology, science, and even cooking. Temperature conversion between Celsius and Fahrenheit can be perplexing due to the different starting points and scaling factors the two systems use. The basic formula to convert from Celsius to Fahrenheit is
\[\begin{equation} F = C \times \frac{9}{5} + 32 \end{equation}\].
Here, F represents the temperature in Fahrenheit, C is the temperature in Celsius, and \(\frac{9}{5}\) with an addition of 32 accounts for the scaling and offset differences between the two scales. It's important for students to remember this formula and understand that the number 32 is added because the Fahrenheit scale starts at a higher temperature compared to Celsius for the point defined as freezing (32°F is equal to 0°C).

Celsius to Fahrenheit

In the conversion from Celsius to Fahrenheit, every degree Celsius is equivalent to 1.8 degrees Fahrenheit. To successfully convert temperatures, you should first multiply the Celsius temperature by 1.8 (or \(\frac{9}{5}\)) then add 32 to the result. This operation reflects the relative size of Celsius and Fahrenheit degrees and the temperature difference between the two scales' zero points.
For example, when converting absolute zero from Celsius to Fahrenheit, you multiply -273.15 by 1.8 and then add 32, resulting in the Fahrenheit scale equivalent of -459.67°F. This conversion is particularly important when dealing with scientific data, as precision is crucial and even small variations in temperature can lead to significant variations in experimental outcomes.

Thermodynamic Temperature Scale

The thermodynamic temperature scale, often referred to as the absolute temperature scale, is key to understanding the concept of absolute zero. This scale is based on the laws of thermodynamics and is independent of the properties of any specific material. The Kelvin scale is an example of a thermodynamic temperature scale and it starts at absolute zero, the theoretical point where particles have minimum thermal motion.
Absolute zero is 0 K, which is equivalent to -273.15°C. This is the basis for a pivotal temperature reference point in scientific work. It's significant that unlike Celsius or Fahrenheit, Kelvin does not use degrees; a temperature difference of one Kelvin is the same magnitude as one degree Celsius. This universality makes the Kelvin scale particularly useful in the scientific community, providing a clear standard for temperature measurements.