How cold does it have to be for water to freeze in \({ }^{\circ} \mathrm{F}\) ? In \({ }^{\circ} \mathrm{C}\) ? In kelvins?

Understanding temperature conversions is essential in various fields, from cooking to science experiments. The freezing point of water is a benchmark often used for these conversions, as it is consistent and easily reproducible. In Celsius, the freezing point is defined as 0°C. But what if we need to find this temperature in different units like Fahrenheit or Kelvin?

Temperature scales are different methods of measuring thermal energy. The Celsius scale is based on the properties of water, with 0°C as the freezing point and 100°C as the boiling point under standard atmospheric pressure. The Fahrenheit scale, used mainly in the United States, sets the water’s freezing point at 32°F and boiling point at 212°F. Finally, the Kelvin scale is a thermodynamic temperature scale, starting at absolute zero, the point at which all thermal motion ceases. The Kelvin scale uses the same increment as Celsius but has a different starting point.

Performing temperature conversions is a straightforward process once the basic formulas are understood. These conversions allow us to communicate and compare temperatures within different temperature scales without confusion.

To convert the freezing point of water from Celsius to Fahrenheit, we use the following formula:
\( F = \frac{9}{5}C + 32 \).

This formula is derived from the two fixed points on the scales: the freezing and boiling points of water. The steps for conversion are simple: take the Celsius temperature, multiply it by 9/5 or 1.8, and then add 32 to adjust for the offset in the Fahrenheit scale. For example, the freezing point of water in Celsius (\(0^\circ\mathrm{C}\)) converts to Fahrenheit by:\[ F = \frac{9}{5}(0) + 32 = 0 + 32 = 32^\circ\mathrm{F} \].

Remembering this formula is crucial, as it is the foundation for converting temperatures for a variety of practical tasks, such as adjusting cooking temperatures or interpreting weather reports in countries using different temperature scales.

The Celsius to Kelvin conversion does not involve multiples or offsets like the Fahrenheit conversion; instead, it is a simple additive process. The Kelvin scale starts at absolute zero, which is -273.15°C. To convert Celsius temperatures to Kelvin, you add 273.15 to the Celsius temperature. The formula is:
\( K = C + 273.15 \).

Using the freezing point of water (0°C), the conversion would look like:\[ K = 0 + 273.15 = 273.15\mathrm{K} \].

The Kelvin scale is prevalent in scientific fields because it is an absolute scale with no negative numbers, which simplifies calculations involving the laws of thermodynamics. Knowing how to convert temperatures to Kelvin is particularly important in fields like physics, chemistry, and astrophysics.