Question

The coldest ground-level temperature ever measured on Earth is \(-128.6^{\circ} \mathrm{F},\) recorded on July \(21,1983,\) in Antarctica. Convert that temperature to \({ }^{\circ} \mathrm{C}\) and \(\mathrm{K}\). MISSED THIS? Read Section 1.6; Watch \(\mathrm{KCV} 1.6\).

Short answer

The temperature of -128.6^{\circ}F is equivalent to -89.2^{\circ}C and 183.95 K.

Step-by-step solution

Convert Fahrenheit to Celsius

To convert Fahrenheit to Celsius, use the formula: \[ T(\mathrm{C}) = (T(\mathrm{F}) - 32) \times \frac{5}{9} \] Substitute \(-128.6^\circ\mathrm{F}\) into the formula to get: \[ T(\mathrm{C}) = (-128.6 - 32) \times \frac{5}{9} \]

Calculate the Celsius Temperature

Perform the calculations: \[ T(\mathrm{C}) = (-160.6) \times \frac{5}{9} \] \[ T(\mathrm{C}) = (-160.6) \times 0.5556 \] \[ T(\mathrm{C}) = -89.2^\circ\mathrm{C} \] (rounded to one decimal place)

Convert Celsius to Kelvin

Use the conversion formula: \[ T(K) = T(\mathrm{C}) + 273.15 \] Substitute the Celsius temperature to get: \[ T(K) = -89.2 + 273.15 \]

Calculate the Kelvin Temperature

Perform the calculation: \[ T(K) = 183.95 \] Since the Kelvin scale does not have degrees, we state it simply as 183.95 K (rounded to two decimal places).

Key concepts

Fahrenheit to Celsius Conversion

Understanding how to convert temperatures from Fahrenheit to Celsius is a fundamental skill in science and daily life. The formula used for conversion is quite straightforward: \( T(\mathrm{C}) = (T(\mathrm{F}) - 32) \times \frac{5}{9} \). To apply this formula, start by subtracting 32 from the Fahrenheit temperature. This adjustment accounts for the difference in the freezing points of water on both scales; 32 degrees Fahrenheit is the freezing point of water, which corresponds to 0 degrees Celsius. After this adjustment, multiply the result by \( \frac{5}{9} \), because each Celsius degree is bigger than a Fahrenheit degree by this ratio.

For example, to convert \(-128.6^\circ \mathrm{F}\), we first subtract 32, resulting in \(-160.6^\circ \mathrm{F}\). Multiplying this by \(0.5556\), which is \( \frac{5}{9} \) expressed as a decimal, gives us \(-89.2^\circ \mathrm{C}\) (rounded to one decimal place). This is useful not only for scientific calculations but also for everyday activities, like adjusting cooking temperatures or interpreting weather forecasts in different countries.

Celsius to Kelvin Conversion

When converting Celsius to Kelvin, a direct addition is all that's needed—no multiplication or division. The Kelvin scale is an absolute temperature scale, starting at absolute zero, the theoretical point where particles have minimum thermal motion. The conversion formula is \( T(K) = T(\mathrm{C}) + 273.15 \). This equation reflects that 0 degrees Celsius is equivalent to 273.15 Kelvin.

In our example with the Antarctic temperature, \(-89.2^\circ \mathrm{C}\) is converted by adding 273.15, resulting in 183.95 K. In Kelvin scale, temperatures are expressed without a degree symbol, reflecting the absolute nature of the measurement. Remembering that there's a fixed numeric difference between Celsius and Kelvin helps in avoiding common mistakes and ensures accuracy in scientific communications.

Temperature Scales

Temperature scales are essential tools for measurement in science. The most commonly used scales are Celsius, Fahrenheit, and Kelvin. Each scale has a different starting point, known as the freezing point of water, and the boiling point, with varying intervals between those points.

The Celsius scale, used around the world for most purposes, sets the freezing point of water at 0 degrees and the boiling point at 100 degrees. On the Fahrenheit scale, often used in the United States for everyday temperatures, water freezes at 32 degrees and boils at 212 degrees. The Kelvin scale is preferred in the scientific community for its consistency and because it starts at absolute zero—thought to be the lowest theoretically possible temperature, where all thermal motion ceases.

Understanding these scales and how to convert between them is crucial, not only for scientific endeavors but also for practical tasks like cooking and understanding weather reports from across the globe.