Question

Perform each temperature conversion. (a) \(212{ }^{\circ} \mathrm{F}\) to Celsius (temperature of boiling water) (b) \(77 \mathrm{~K}\) to Fahrenheit (temperature of liquid nitrogen) (c) \(25^{\circ} \mathrm{C}\) to kelvins (room temperature) (d) \(98.6^{\circ} \mathrm{F}\) to kelvins (body temperature)

Short answer

a) 100°C, b) -321.07°F, c) 298.15 K, d) 310.15 K

Step-by-step solution

Convert Fahrenheit to Celsius

To convert Fahrenheit to Celsius, use the formula: \(C = \frac{5}{9}(F - 32)\). Plug in the Fahrenheit temperature and solve for Celsius.

Convert Celsius to Fahrenheit

The conversion from Celsius to Fahrenheit is given by \(F = \frac{9}{5}C + 32\). However, we need to convert Kelvin to Fahrenheit. To do this, convert Kelvin to Celsius first using the formula \(C = K - 273.15\), then convert the resulting Celsius to Fahrenheit.

Convert Celsius to Kelvin

To convert Celsius to Kelvin, simply add 273.15 to the Celsius temperature using the formula: \(K = C + 273.15\).

Convert Fahrenheit to Kelvin

First convert Fahrenheit to Celsius using the formula from Step 1, and then convert the Celsius temperature to Kelvin using the formula from Step 3.

Key concepts

Fahrenheit to Celsius Formula

Understanding temperature conversions is a foundational skill in both everyday life and science. The formula to convert temperatures from Fahrenheit to Celsius is surprisingly simple. It's given by:
\( C = \frac{5}{9}(F - 32) \)
. To make this conversion, you subtract 32 from the Fahrenheit value, which adjusts the scale from the Fahrenheit freezing point to that of Celsius. Then, you multiply by \frac{5}{9} to account for the difference in degree size between the two scales. For example, the boiling point of water, \(212{ }^{\backslash circ} F\), converts to Celsius as follows:
\( C = \frac{5}{9}(212 - 32) = 100{ }^{\backslash circ} C \)
. This straightforward calculation is essential for various applications, ranging from cooking to scientific research.

Celsius to Fahrenheit Formula

When you're faced with the opposite scenario and need to convert Celsius to Fahrenheit, there is a similarly straightforward formula at your disposal:
\( F = \frac{9}{5}C + 32 \)
. This process begins by multiplying the Celsius temperature by \frac{9}{5}, increasing the relative value to match the smaller degrees in the Fahrenheit scale. You then add 32 to adjust the starting point of the scale to Fahrenheit's freezing point. For instance, room temperature, commonly considered to be \(25^{\backslash circ} C\), is converted as follows:
\( F = \frac{9}{5}(25) + 32 = 77{ }^{\backslash circ} F \)
. This conversion is often used in climates and weather reporting, as well as in culinary recipes when specific temperatures are crucial.

Celsius to Kelvin Formula

Scientists frequently use the Kelvin scale for a variety of research and experimental purposes due to its absolute nature. The Celsius to Kelvin formula is incredibly straightforward:
\( K = C + 273.15 \)
. You simply take the Celsius temperature and add 273.15 to get the corresponding temperature in Kelvins, which shifts the scale from the Celsius freezing point of water to absolute zero. For instance:
\( K = 25 + 273.15 = 298.15 K \)
, highlights the conversion from a common room temperature in Celsius to Kelvin. This concept is essential in physics and engineering, where precise and absolute measurements are vital.

Kelvin to Fahrenheit Conversion

The Kelvin to Fahrenheit conversion may seem daunting at first, given the somewhat indirect nature of this transformation. However, by breaking it down into two steps—first converting Kelvin to Celsius, then Celsius to Fahrenheit—it becomes manageable. Begin by using the inverse of the Celsius to Kelvin formula:
\( C = K - 273.15\)
. After finding the Celsius value, apply the Celsius to Fahrenheit formula:
\( F = \frac{9}{5}C + 32 \)
. So, for a temperature like the cold surroundings of liquid nitrogen at \(77 \backslash \text{K}\), the conversion would be:
\( C = 77 - 273.15 = -196.15{ }^{\backslash circ} C \)
\( F = \frac{9}{5}(-196.15) + 32 = -320.07{ }^{\backslash circ} F \)
. These formulas are fundamental in fields that use temperatures in their absolute form, such as astrophysics, cryogenics, and low-temperature physics.