a 



of water by one degree Celsius as it does to warm the 

 same mass of dry air by that amount. The heat capacity 

 of water acts as a buffer, or perhaps a heavy flywheel, on 

 climate, smoothing out what would otherwise be sharp 

 changes in temperature. 



Heat capacity is a good example of a macroscopic 

 property of water that can be explained by what takes 

 place at a molecular level. The chemical formula EbO, 

 instantly recognized round the world, indicates that the 

 water molecule is a bound system of three atoms, two of 

 hydrogen and one of oxygen. When you add heat (a form 

 of energy) to a macroscopic sample of water molecules, 

 the molecules increase their average speed and collide 

 more otten. The temperature of the sample is simply a 

 measure of their average speed. Any energy added to or 

 subtracted from the energy stored as such "translational" 

 motion — movement from one place to another — changes 

 the temperature. 



But molecules can absorb and store energy in other ways, 

 too. A water molecule can spin or rotate like a top, or it can 

 wiggle and vibrate. Both rotational and vibrational motion 

 can store energy. Yet they can't completely explain liquid 

 water's observed heat capacity. In general, the more ways 

 molecules can absorb heat energy without increasing the 

 average speed of their translational motion — that is, the 

 greater the molecules' capacity to act as heat sinks without 

 raising the temperature of a substance — the greater the 

 heat capacity of that substance. 



You might think that no matter how little energy a 

 molecule may have stored, the energy would still 

 spread more or less evenly among all the possible 

 kinds of motions. In other words, the energy would be 

 partitioned among all possible "degrees of freedom." 

 Because virtually all molecules made up of three atoms 



have the same number of degrees of freedom, their heat 

 capacity, too, should not differ substantially. And sure 

 enough, the heat capacity of the water molecule is about 

 the same as that of other triatomic molecules. 



Although the conclusion to the preceding argument 

 agrees with the observed result, the argument itself is 

 faulty. In the world of atoms and molecules, energy cannot 

 be absorbed by the various kinds of molecular motions in 

 arbitrarily small amounts. Rather, atoms and molecules 

 are subject to the laws of quantum mechanics. In the 

 quantum world, all changes in the energy stored by an 

 atom or molecule are quantized. Each kind of molecular 

 motion — translational, rotational, and vibrational — can 

 absorb energy only in discrete chunks, whose sizes 

 depend on the details of a particular molecule and the 

 kind of motion involved. Expose a water molecule to the 

 right-size chunk of incident energy (from the Sun, for 

 instance), and the molecule will suddenly rotate or vibrate 

 faster. Expose it to the wrong-size chunk, and nothing 

 will happen; the molecule will simply "disregard" the 

 passing energy. As it happens, the amount of energy 

 available at the normal range of temperatures on Earth 

 is only enough to generate translations and rotations 

 of a single water molecule, but not enough to generate 

 vibrations. Thus, on its own, the single water molecule 

 isn't enough to explain the heat capacity of liquid water. 

 In fact, the heat capacity of water vapor is smaller than 

 that of liquid water by more than a factor of two! So the 

 puzzle reemerges: how can the heat capacity of water be 

 explained from a molecular point of view? 



The solution is to look beyond the properties of a single 

 water molecule and consider the interactions among 

 the vast number of molecules in a bulk sample. Begin 

 by considering the interaction of two water molecules. Each 

 molecule is shaped like a tetrahedron, with the oxygen atom 

 at its center. Each of the two hydrogen atoms lies at one 

 of the four corners of the tetrahedron, and each one acts 

 as a center of positive electric charge. When it bonds with 

 hydrogen, the oxygen atom acquires two complementary 



34 



NATURAL HISTORY November 2007 



