5.3.1: Heat Capacity and Molecular Structure

Last updated
Save as PDF

Page ID: 52337

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

It takes 4.12 J to raise 1 gram of water 1 ºC (or 1 K.) If you add energy to a pan of water by heating it on a stove top energy is transferred to the molecules of water by collisions with the pan, which in turn has heated up from contact with the heating element94. The addition of energy to the system results in the faster movement of molecules, which includes moving from place to place, rotating, bending, and vibrating. Each type of movement adds to the overall thermal energy of the material. Although the molecules in a gas very rarely interact with one another, those in a solid and liquid interact constantly. The increase in temperature as a function of added energy is relatively simple to calculate for a gas; it is much more complicated for liquids and solids, where it depends upon molecular structure and intramolecular (within a molecule) as well as intermolecular (between molecules) interactions.

Consider the molar heat capacities and specific heats of water and the hydrocarbon alcohols (which contain an -OH group) methanol, ethanol, and propanol. As you can see in the table below, water has an unusually high specific heat, even though it is smaller than the other molecules. Their specific heats are pretty much constant, but their molar heat capacities increase with molar mass.

Name	Formula	Molar Mass, g	Molar Heat Capacity J/mol ºC	Specific Heat J/g ºC
Water	H₂O	18	75.4	4.18
Methanol	CH₃OH	32	81.0	2.53
Ethanol	CH₃CH₂OH	48	112	2.44
Propanol	CH₃CH₂CH₂OH	60	144	2.39

So an obvious question is, why is the specific heat of water so much higher than that of these alcohols? The reasons for this (apparent) anomaly are:

Water molecules are smaller so there are more molecules per gram than there are in the larger, more complex substances.
Each water molecule can form up to four hydrogen bonds, but the alcohols can only form a maximum of two hydrogen bonds each (why is this?). As thermal energy is added to the system some of that energy must be used to overcome the attractive forces between molecules (that is, hydrogen bonds) before it can be used to increase the average speed of the molecules. Because there are more hydrogen bonds forming attractions between water molecules, it takes more energy to overcome those interactions and raise the kinetic energy of the water molecules. The end result is a smaller increase in temperature for the same amount of energy added to water compared to methanol, ethanol, and propanol.

The relatively high specific heat of water has important ramifications for us. About 70% of the Earth’s surface is covered with water. Because of water’s high specific heat, changes in the amounts of solar energy falling on an area between day and night are “evened out” by the large amount of water in the oceans. During the day, the water absorbs much of the energy radiated from the sun, but without a drastic temperature increase. At night, as the temperature falls, the oceans release some of this stored energy, thus keeping the temperature fluctuations relatively small. This effect moderates what would otherwise be dramatic daily changes in surface temperature. In contrast, surface temperatures of waterless areas (like deserts), planets (like Mars), and the Moon fluctuate much more dramatically, because there is no water to absorb and release thermal energy.⁹⁵ This moderation of day–night temperature change is likely to be one of the factors that made it possible for life to originate, survive, and evolve on the early Earth. As we go on, we will see other aspects of water’s behavior that are critical to life.

References

⁹⁴ Alternatively in microwave ovens, the water molecules gain energy by absorbing microwave radiation which makes them rotate. When they collide with other molecules this energy can also be transformed into vibrations and translations, and the temperature of the water heats up.

⁹⁵ The situation on planets like Venus and Jupiter is rather more complex.