1.6 Temperature
There are two temperature scales that are used in chemistry, Celsius and kelvin. In America the Fahrenheit scale is used, though it is only used in a handful of countries, it is important to know the conversion between these three temperature scales.
For the Fahrenheit scale, the freezing point of water is defined as 32 °F and the boiling temperature of pure water is defined as 212 °F. There is a conversion that can be used to convert from Fahrenheit to Celsius. This equation is below:
\[T_{\mathrm{^{\circ}C}} = \dfrac{5}{9} \left ( T_{\mathrm{^{\circ}F}} - 32~\mathrm{^{\circ}F}\right ) \] or
\[T_{\mathrm{^{\circ}C}} = \dfrac{\left ( T_{\mathrm{^{\circ}F}} - 32 \right )}{1.8}\] The Celsius scale has the freezing point of pure water defined as 0 °C and the boiling point of pure water defined as 100 °C. Both values are important to remember.
The kelvin scale, is an absolute temperature scale, with the lowest theoretical temperature that can be reached set at 0 K. You can’t go below zero with the kelvin scale. Conversion from Celsius to kelvin is done by adding 273.15 to the Celsius temperature, which will give the temperature in kelvin.
\[T_{\mathrm{K}} = T_{\mathrm{^{\circ}C}} + 273.15\]
Since the temperature in kelvin is obtained by adding 273.15 to the Celsius temperature, the freezing temperature of pure water is 273.15 K and the boiling temperature of pure water is 373.15 K.
Practice – Celsius to kelvin
Normal human body temperatures can range over the course of a day from about 36 °C in the early morning to about 37 °C in the afternoon. Express these two temperatures and the range that they span using the kelvin scale.
Solution
Convert °C to K.
\[\begin{align*} T_{\mathrm{K}} &= T_{\mathrm{^{\circ}C}} + 273.15 \\[1.5ex] &= 36~^{\circ}\mathrm{C} + 273.15 \\[1.5ex] &= 309.15~\mathrm{K}\\[3ex] T_{\mathrm{K}} &= T_{\mathrm{^{\circ}C}} + 273.15 \\[1.5ex] &= 37~^{\circ}\mathrm{C} + 273.15 \\[1.5ex] &= 310.15~\mathrm{K} \end{align*}\]
Therefore, the range of temperatures in kelvin is 1 K.
To move from Celsius to kelvin the addition of 273.15 is made to the Celsius temperatures, giving a 309.15 K and 310.15 K temperatures. This addition is made to both 36 °C and 37 °C. Therefore, for both scales, there is only a one-degree or 1 K difference. This is due to the linear relationship between both Celsius and kelvin. because we’re adding the same amount to both values.
Practice – Celsius to Fahrenheit
A body temperature above 39 °C constitutes a high fever. Convert this temperature to the Fahrenheit scale.
Solution
Convert °C to °F.
\[\begin{align*} T_{\mathrm{^{\circ}C}} &= \dfrac{5}{9} \left ( T_{\mathrm{^{\circ}F}} - 32~\mathrm{^{\circ}F}\right ) \rightarrow \\[2ex] T_{\mathrm{^{\circ}F}} &= \dfrac{9}{5}T_{\mathrm{^{\circ}C}} + 32 \\[2ex] &= \dfrac{9}{5}\left (39~^{\circ}\mathrm{C} \right ) + 32 \\ &= 102~^{\circ}\mathrm{F} \end{align*}\]
Practice
A body temperature above 39 °C constitutes a high fever. Convert this temperature to the Fahrenheit scale.
Solution
\[\begin{align*} T_{^{\circ}\mathrm{F}} &= \left ( \dfrac{9}{5} \times 39.0 \right ) + 32 \\[2ex] &= 102~^{\circ}\mathrm{F} \end{align*}\]
Practice
Gold boils at 5173 °F. What is the boiling point of gold (in °C)?
Solution
\[\begin{align*} T_{^{\circ}\mathrm{C}} &= \dfrac{5}{9} \left ( 5173 - 32 \right ) \\[2ex] &= 2856~^{\circ}\mathrm{C} \end{align*}\]
Practice
Chlorine melts at –100.95 °C. What is that in °F?
Solution
\[\begin{align*} T_{^{\circ}\mathrm{F}} &= \left ( \dfrac{9}{5} \times -100.95 \right ) + 32 \\[2ex] &= -149.71~^{\circ}\mathrm{F} \end{align*}\]
Practice
Perform the following conversions:
- 41 °F to °C
- 68 °C to K
- 246 K to °C
- 681 K to °F
Solution
\[\begin{align*} T_{^{\circ}\mathrm{C}} &= \dfrac{5}{9} \left ( 41 - 32 \right ) \\[2ex] &= 5.0~^{\circ}\mathrm{C} \\[4ex] T_{\mathrm{K}} &= 68 + 273.15 \\ &= 341.15~\mathrm{K} \\[4ex] T_{^{\circ}\mathrm{C}} &= 426 - 273.15 \\ &= 152.85~^{\circ}\mathrm{C} \\[4ex] T_{^{\circ}\mathrm{F}} &= \left ( \dfrac{9}{5} \times (681 + 273.15) \right ) + 32 \\[2ex] &= 766.13~^{\circ}\mathrm{F} \end{align*}\]