The energy dispersal approach to teaching entropy was developed to facilitate teaching entropy to students beginning university chemistry and biology. This new approach also avoids ambiguous terms such as disorder and chaos, which have multiple everyday meanings, and tend to confuse students.
Problem: entropy as disorder is hard to teach
The term "entropy" has been in use from early in the history of classical thermodynamics, and with the development of statistical thermodynamics and quantum theory, entropy changes have been described in terms of the mixing or "spreading" of the total energy of each constituent of a system over its particular quantized energy levels.Such descriptions have tended to be used together with commonly used terms such as disorder and chaos which are ambiguous, and whose everyday meaning is the opposite of what they are intended to mean in thermodynamics. Not only does this situation cause confusion, but it also hampers the teaching of thermodynamics. Students were being asked to grasp meanings directly contradicting their normal usage, with equilibrium being equated to "perfect internal disorder" and the mixing of milk in coffee from apparent chaos to uniformity being described as a transition from an ordered state into a disordered state.Studies found that few understood what these terms were intended to convey.
The description of entropy as the amount of "mixedupness" or "disorder," as well as the abstract nature of the statistical mechanics grounding this notion, can lead to confusion and considerable difficulty for those beginning the subject.Even though courses emphasised microstates and energy levels, most students could not get beyond simplistic notions of randomness or disorder. Many of those who learned by practising calculations did not understand well the intrinsic meanings of equations, and there was a need for qualitative explanations of thermodynamic relationships.[
Solution: entropy as energy dispersal
To overcome the difficulties described in the previous section, entropy can be exposited in terms of "energy dispersal" and the "spreading of energy," while carefully avoiding all mention of "disorder" and "chaos" except when explaining misconceptions. All explanations of where and how energy is dispersing or spreading have been recast in terms of energy disperal, so as to emphasise the underlying qualitative meaning.In this approach, the second law of thermodynamics is introduced as "Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so." in the context of common experiences such as a rock falling, a hot frying pan cooling down, iron rusting, air leaving a punctured tire and ice melting in a warm room. Entropy is then depicted as a sophisticated kind of "before and after" yardstick — measuring how much energy is spread out over time as a result of a process such as heating a system, or how widely spread out the energy is after something happens in comparison with its previous state, in a process such as gas expansion or fluids mixing (at a constant temperature). The equations are explored with reference to the common experiences, with emphasis that in chemistry the energy that entropy measures as dispersing is internal energy, which beginners can most clearly understand as “motional energy”, the translational, vibrational, and rotational energy of molecules.
By giving concrete examples, this approach is effective in explaining entropy to assist those who have great difficulty in grasping mathematical abstractions. The statistical interpretation is related to quantum mechanics in describing the way that energy is distributed (quantized) amongst molecules on specific energy levels, with all the energy of the macrostate always in only one Microstate at one instant. Entropy is described as measuring the energy dispersal for a system by the number of accessible microstates, the number of different arrangements of all its energy at the next instant. Thus, an increase in entropy means a greater number of microstates for the Final state than for the Initial state, and hence more possible arrangements of a system's total energy at any one instant. Here, the greater 'dispersal of the total energy of a system' means the existence of so many possibilities.
Continuous movement and molecular collisions visualised as being like bouncing balls blown by air as used in a lottery can then lead on to showing the possibilities of many Boltzmann distributions and continually changing "distribution of the instant", and so on to the idea that when the system changes, dynamic molecules will have a greater number of accessible microstates. In this approach, all everyday spontaneous physical happenings and chemical reactions are depicted as involving some type of energy flows from being localized or concentrated to becoming spread out to a larger space, always to a state with a greater number of microstates.
This approach provides a good basis for understanding the conventional approach, except in very complex cases where the qualitative relation of energy dispersal to entropy change can be so inextricably obscured that it is moot.Thus in situations such as in the entropy of mixing when the two or more different substances being mixed are at the same temperature and pressure so there will be no net exchange of heat or work, the entropy increase will be due to the literal spreading out of the motional energy of each substance in the larger combined final volume. Each component’s energetic molecules become more separated from one another than they would be in the pure state, when in the pure state they were colliding only with identical adjacent molecules, leading to an increase in its number of accessible microstates.
Variants of the energy dispersal approach have been adopted in number of undergraduate chemistry texts, mainly in the United States. F. A distinguished advanced text, Physical Chemistry by Peter Atkins of Oxford University and Julio De Paula, has followed suit. Starting with the 8th edition, Atkins and De Paula describe entropy in terms of dispersal of energy, without mentioning "disorder."
