Fundamental temperature scales
Temperature is one of the most important variables used to describe the state of a physical system. Throughout chemistry and thermodynamics, three temperature scales are commonly encountered: Fahrenheit (\(^\circ\)F), Celsius (\(^\circ\)C), and Kelvin (K). Although each scale measures the same physical property, they differ in how their zero points and degree sizes are defined.
The Fahrenheit scale was developed by Gabriel Fahrenheit for laboratory use. On this scale, water freezes at \(32^\circ\text{F}\) and boils at \(212^\circ\text{F}\) under standard atmospheric pressure. Because there are 180 Fahrenheit degrees between these two temperatures, a Fahrenheit degree is smaller than a Celsius degree. The Fahrenheit scale is still commonly used in weather reports and everyday applications in the United States.
The Celsius scale is based on the phase changes of water. Water freezes at \(0^\circ\text{C}\) and boils at \(100^\circ\text{C}\) under standard atmospheric pressure, creating a convenient 100-degree interval between these two reference points. Most scientific measurements are reported in Celsius because it is directly related to the Kelvin scale.
The Kelvin scale is an absolute temperature scale used throughout chemistry and physics. Its zero point corresponds to absolute zero, the lowest temperature theoretically possible. On This scale, water freezes at 273.15 K, and boils at 373.15 K, a difference of 100 K. Because the size of one Kelvin is identical in magnitude to one Celsius degree, temperatures can be converted between these scales by simply adding or subtracting 273.15, although technically one must also convert between units as well.
Further, since mnay thermodynamic calculations depend on a change in temperature, it is usefule to note that a change of 1 \(^\circ\text{C}\) is the same temperature difference as 1 \(\text{K}\). As such, the two are often used (almost) interchangeably when discussing \(\Delta\)T. (But as always, be careful with units!)
Temperature conversion equations
The most useful conversion relationships are
\[ x\ ^\circ\mathrm{C} \left( \frac{9\ ^\circ\mathrm{F}} {5\ ^\circ\mathrm{C}} \right) + 32\ ^\circ\mathrm{F} = y\ ^\circ\mathrm{F} \]
\[ \left( y\ ^\circ\mathrm{F} - 32\ ^\circ\mathrm{F} \right) \left( \frac{5\ ^\circ\mathrm{C}} {9\ ^\circ\mathrm{F}} \right) = x\ ^\circ\mathrm{C} \]
\[ x\ ^\circ\mathrm{C} \left( \frac{1\ \mathrm{K}} {1\ ^\circ\mathrm{C}} \right) + 273.15\ \mathrm{K} = z\ \mathrm{K} \]
Notice that Celsius and Kelvin differ only by an additive constant, whereas converting between Fahrenheit and Celsius requires both multiplication and addition because the two scales use different degree sizes and different zero points.
Worked examples
First convert to Fahrenheit:
\[y ^\circ F = \frac{9 ^\circ F}{5 ^\circ C}(25 ^\circ C)+32 ^\circ F\] \[25 ^\circ C \rightarrow 77 ^\circ F\]Now convert to Kelvin:
\[z\ K = 25 ^\circ C \left( \frac{1 K}{1 ^\circ C} \right) + 273.15 K\] \[25 ^\circ C \rightarrow 298.15 K\]Therefore, \(25^\circ\text{C} = 77^\circ\text{F} = 298.15\text{ K}\).
First convert to Celsius:
\[x\ ^\circ C = 450 K \left( \frac{1 ^\circ C}{1 K} \right) - 273.15 ^\circ C = 176.85^\circ\text{C}\]Next convert to Fahrenheit:
\[y\ ^\circ F = 176.85 ^\circ C \left( \frac{9 ^\circ F}{5 ^\circ C} \right) + 32 ^\circ F\ = 350.33^\circ\text{F}\]Therefore, \(450\text{ K} = 176.85^\circ\text{C} = 350.33^\circ\text{F}\).
First convert to Celsius:
\[x ^\circ C = 98.6 ^\circ F \left( \frac{5 ^\circ C}{9 ^\circ F} \right) -32 ^\circ C = 37.0^\circ\text{C} \]Now convert to Kelvin:
\[z\ K = 37.0 ^\circ C \left( \frac{1 K}{1 ^\circ C} \right) + 273.15 K = 310.15\text{ K} \]Therefore, \(98.6^\circ\text{F} = 37.0^\circ\text{C} = 310.15\text{ K}\).
Practice
Temperature Conversion Practice
Convert the temperature shown below to the requested unit.
Convert:
Key points (one glance)
- Temperature is commonly measured using the Fahrenheit (\(^\circ\)F), Celsius (\(^\circ\)C), and Kelvin (K) scales.
- Water freezes at \(32^\circ\text{F}\), \(0^\circ\text{C}\), and \(273.15\text{ K}\), and boils at \(212^\circ\text{F}\), \(100^\circ\text{C}\), and \(373.15\text{ K}\).
- The Kelvin scale is an absolute temperature scale whose zero point corresponds to absolute zero.
- The size of one Kelvin is identical to the size of one Celsius degree, so temperature differences satisfy \[ \Delta T(\mathrm{K}) = \Delta T(^\circ\mathrm{C}). \]
- To convert between Celsius and Fahrenheit, both the degree size and the zero point must be adjusted.
- To convert between Celsius and Kelvin, only an additive constant of 273.15 is required.
- Always include units throughout a conversion to help verify that the calculation is performed correctly.
Big picture: Temperature scales provide different numerical ways to describe the same physical property. Successful temperature conversions require understanding both the size of the temperature unit and the location of the scale's zero point.