Question

Make the following conversions: (a) \(72^{\circ} \mathrm{F}\) to \({ }^{\circ} \mathrm{C}\), (b) \(216.7{ }^{\circ} \mathrm{C}\) to \({ }^{\circ} \mathrm{F},(\mathrm{c}) 233^{\circ} \mathrm{C}\) to \(\mathrm{K},\) (d) \(315 \mathrm{~K}\) to \({ }^{\circ} \mathrm{F},(\mathrm{e}) 2500^{\circ} \mathrm{F}\) to \(\mathrm{K},(\mathrm{f}) 0 \mathrm{~K}\) to \({ }^{\circ} \mathrm{F}\)

Short answer

The short answers for the conversions are: (a) \(22.22^{\circ}\mathrm{C}\), (b) \(452.04^{\circ}\mathrm{F}\), (c) \(506.15\mathrm{K}\), (d) \(139.13^{\circ}\mathrm{F}\), (e) \(1644.26\mathrm{K}\), and (f) \(-427.67^{\circ}\mathrm{F}\).

Step-by-step solution

Convert 72°F to °C

Using the formula to convert Fahrenheit to Celsius: \[C = \frac{5}{9} (F - 32)\] \[C = \frac{5}{9} (72 - 32)\] \[C = \frac{5}{9} (40)\] \[C = 22.22^{\circ}\mathrm{C}\]

Convert 216.7°C to °F

Using the formula to convert Celsius to Fahrenheit: \[F = \frac{9}{5} C + 32\] \[F = \frac{9}{5} (216.7) + 32\] \[F = 422.04 + 32\] \[F = 452.04^{\circ}\mathrm{F}\]

Convert 233°C to K

Using the formula to convert Celsius to Kelvin: \[K = C + 273.15\] \[K = 233 + 273.15\] \[K = 506.15\mathrm{K}\]

Convert 315 K to °F

First, convert Kelvin to Celsius using the formula: \[C = K - 273.15\] \[C = 315 - 273.15\] \[C = 41.85^{\circ}\mathrm{C}\] Next, convert Celsius to Fahrenheit using the formula: \[F = \frac{9}{5} C + 32\] \[F = \frac{9}{5} (41.85) + 32\] \[F = 107.13 + 32\] \[F = 139.13^{\circ}\mathrm{F}\]

Convert 2500°F to K

First, convert Fahrenheit to Celsius using the formula: \[C = \frac{5}{9} (F - 32)\] \[C = \frac{5}{9} (2500 - 32)\] \[C = \frac{5}{9} (2468)\] \[C = 1371.11^{\circ}\mathrm{C}\] Next, convert Celsius to Kelvin using the formula: \[K = C + 273.15\] \[K = 1371.11 + 273.15\] \[K = 1644.26\mathrm{K}\]

Convert 0 K to °F

First, convert Kelvin to Celsius using the formula: \[C = K - 273.15\] \[C = 0 - 273.15\] \[C = -273.15^{\circ}\mathrm{C}\] Next, convert Celsius to Fahrenheit using the formula: \[F = \frac{9}{5} C + 32\] \[F = \frac{9}{5} (-273.15) + 32\] \[F = -459.67 + 32\] \[F = -427.67^{\circ}\mathrm{F}\]

Key concepts

Fahrenheit to Celsius conversion

Converting temperatures from Fahrenheit to Celsius is a common task in science and everyday life. The process involves using the conversion formula: \(C = \frac{5}{9} (F - 32)\). This formula arises from the way the two scales are defined, with one degree of Fahrenheit being 5/9 of a Celsius degree around the 0°C mark.

Let's break it down with an example: If you start with 72°F and want to know its equivalent in Celsius, you first subtract 32 from 72, yielding 40. Then, multiply 40 by \(\frac{5}{9}\), which results in approximately 22.22°C.

Understanding this conversion is particularly helpful when you encounter weather reports, scientific data, or cooking instructions from international sources. Remembering this straightforward formula makes it easy to switch between Fahrenheit and Celsius.

Celsius to Fahrenheit conversion

Converting from Celsius to Fahrenheit is almost the reverse process of going from Fahrenheit to Celsius. The formula used is \(F = \frac{9}{5} C + 32\). This conversion considers not only the difference in the size of the Celsius and Fahrenheit degrees but also the offset due to their differing starting points at freezing.

To illustrate, suppose you have a temperature of 216.7°C and wish to convert it to Fahrenheit. Start by multiplying 216.7 by \(\frac{9}{5}\), which gives you 390.06. Next, add 32 to get 422.06°F.

Knowing this conversion can be quite useful, for instance, when you are reading scientific articles or recipes that use Celsius but you are more accustomed to Fahrenheit. It's beneficial to have this formula handy, as it bridges the gap between two of the most commonly used temperature scales.

Celsius to Kelvin conversion

The Celsius to Kelvin conversion is essential in fields such as physics and chemistry. This conversion is straightforward, thanks to the established relationship between these two scales. The Kelvin scale starts at absolute zero, making zero Kelvin the lowest possible temperature. In contrast, Celsius is based around the freezing point of water.

The equation used to convert from Celsius to Kelvin is \(K = C + 273.15\). This formula simply adds 273.15 to the Celsius temperature because that's the fixed difference between the starting points of these scales.

For example, to convert 233°C to Kelvin, you add 273.15 to 233, resulting in 506.15 K. This conversion is critical for scientific calculations where absolute temperature is necessary. It helps scientists ensure the consistency of their measurements across disciplines.

Kelvin to Fahrenheit conversion

Converting Kelvin to Fahrenheit involves a two-step process since there is no direct formula linking these two scales. You must first convert Kelvin to Celsius and then Celsius to Fahrenheit.

First, use the formula \(C = K - 273.15\) to convert Kelvin to Celsius. Once you have the Celsius temperature, use the formula \(F = \frac{9}{5} C + 32\) to find the Fahrenheit temperature.

Take 315 K as an example: Subtract 273.15 to get 41.85°C. Then, convert to Fahrenheit by multiplying by \(\frac{9}{5}\) and adding 32, giving an approximate result of 107.33°F. This method is essential for situations where temperatures in absolute terms need to be shared in more common terms, such as in weather forecasting or engineering applications.