A column of liquid is found to expand linearly on heating \(5.25\) \(\mathrm{cm}\) for a \(10.0^{\circ} \mathrm{F}\) rise in temperature. If the initial temperature of the liquid is \(98.6^{\circ} \mathrm{F}\), what will the final temperature be in \({ }^{\circ} \mathrm{C}\) if the liquid has expanded by \(18.5 \mathrm{~cm}\) ?

When substances are heated, they tend to expand; this phenomenon is known as linear expansion. The basics of linear expansion can be understood as the proportional increase in a material's dimensions owing to an increase in temperature. In the context of our problem, a liquid column expands as its temperature increases. This expansion is directly proportional to the temperature change—meaning that for a known temperature increase, the expansion can be predicted, and vice versa.

Understanding linear expansion is crucial in various applications, from designing thermometers to constructing bridges, where allowances must be made for changes in length with temperature. The formula representing this relationship, typically written as ΔL = αL₀ΔT, is simplified in the exercise, correlating expansion directly with temperature change without explicitly mentioning the coefficient of linear expansion (α) or the original length (L₀).

Temperature scales provide a way to quantify the warmth or coldness of an object. The most commonly used temperature scales are Celsius (°C), Fahrenheit (°F), and Kelvin (K). Understanding these scales is fundamental in chemistry, as reactions are often dependent on specific temperatures.

Celsius is based on the freezing and boiling points of water, set at 0°C and 100°C respectively. The Fahrenheit scale, primarily used in the United States, sets the freezing point of water at 32°F and the boiling point at 212°F. The Kelvin scale is the standard unit of temperature in the scientific community and starts at absolute zero, the point at which particles theoretically stop moving. There is no degree symbol used with the Kelvin scale; temperatures are simply stated in kelvins.

Converting between these scales requires understanding their relationships and the mathematical formulas that link them. For instance, the conversions between Celsius and Fahrenheit are important when dealing with different scientific and cultural norms.

Converting from Fahrenheit to Celsius is a key skill in chemistry, especially for students who are accustomed to one temperature scale and need to work with the other. The conversion between these two scales can be achieved through a simple formula: \( T(°C) = \left(T(°F) - 32\right) \times \frac{5}{9} \).

This formula was used in the step-by-step solution to convert the final temperature of the liquid from Fahrenheit to Celsius after determining its expansion. When engaging in temperature conversion, it is essential to pay close attention to detail and ensure any addition or subtraction is done prior to the application of the multiplication or division step, preventing potential errors in the final result.