Last Word on Entropy
Some considerations...
So far, you have seen the amazing chain of rational thought that produced the idea of entropy (not to mention the ideas of cyclic processes, state properties, and the 2nd Law) and have came to the conclusion entropy is yet another property of a substance, that defines its state. For homogeneous gases, only two of these properties are needed in order to identify its state—in other words, if you have any two of these properties, you can find the others. So far, they are temperature, pressure, volume, and entropy.
There are two others of importance. The first is internal energy, defined only by temperature, so is automatically a state property. Another is enthalpy, which is internal energy, plus any work that was done on the gas, usually as an effect of pressure and change in volume. Pressure and volume are state properties, as well as internal energy, so enthalpy is another state property. It’s clear you could probably go on forever defining new properties based on old ones, but enthalpy is particularly useful, because it can be used to quantify the amount of energy (or power, the time rate of energy) needed to handle a particular gas.
In the earlier posts, a conclusion was that the change in entropy was defined as the total heat divided by the absolute temperature of the environment, for a reversible process. That definition could be rearranged to show temperature times the change in entropy is equal to the total heat for a reversible process. It can be shown through calculus that this product is equal to the change in enthalpy, minus the volume times the change in pressure, beyond what I want to discuss here, but just an example of how these various properties interact. It is also an avenue for calculating properties like entropy that can’t be directly measured. And as a state property, the result is independent of the path, so real world irreversible processes are treated the same. James Clerk Maxwell (yet another genius Scot!) was a master at generating these thermodynamic kind of relations with a weird version of calculus using Hamiltonians, and went on to use similar techniques to establish the electromagnetic relations, the famous Maxwell equations. Without these, we’d have no radio, telephones, TVs, or internet, it’s worth pointing out.
An isolated system has a particular nature, when it comes to entropy. This becomes apparent when the Second Law of thermodynamics is included. Since energy or mass can’t cross the boundary of an isolated system, an isolated system can be considered to be a combinaton of any system and everything external to the system. In other words, any system combined its surroundings is itself an isolated system. The net entropy change of the isolated system therefore includes the entropy change of the system plus the entropy change of the surroundings. This is called the total entropy change associated with the processes the system experiences.
In the prior post, it was established that the entropy change for any process was greater than or equal to zero, with the “equals” part corresponding to reversible processes. Therefore the Second Law of thermodynamics places a curious and notable restriction on the total entropy change. Since heat transfer cannot occur at the boundary of an isolated system, the total entropy change of an isolated system is greater than or equal to zero. For real world irreversible systems, the total entropy change of such a system is always greater than zero.
This sometimes called the increase-in-entropy principle. It doesn’t imply that the entropy change for all processes is greater than or equal to zero. The entropy can and does decrease during a process, but according to this principle, the sum of the entropy change of the system and the entropy change of its surroundings is never negative.
In real world terms, entropy increases in a combustion reaction, as in an internal combustion engine. The CO2 and water produced from such a reaction is at a higher entropy state, so is favored. The CO2 has the interesting quality of absorbing a wide spectrum of electromagnetic radiation and re-emitting that energy as heat. This is the principle behind the so-called greenhouse effect. It goes to show an increase in entropy often has unfavorable effects, at least as far as humans are concerned. But it’s not just restricted to combustion processes—any energy transformation tends to generate more entropy, which explains the earlier reference to the “cost” of energy. Applying complicated pollution controls on such engines is a laudable effort, but its decrease in entropy of the system must be accompanied by an increase at least as much somewhere else. This explains the earlier reference to increasing efficiency having its own costs, which increase the closer you get to the thermodynamic limit.
The increase-in-entropy principle led to talk of “heat death” of the universe, especially after it was realized entropy was a much more global process, and not only had to do with heat transfer and fluids, but increasing disorder in general. Evolution itself seems to contradict the idea of increasing disorder, but has been reconciled by some as just a local event; evolution in the long run may accelerate disorder. That certainly seems true insofar as humans are considered. Perhaps we evolved as a natural imperative to increase disorder, pollution, or heat death, per this increase-in-entropy principle. It’s pure speculation, but a point to raise when so many voices speak with such authority on what is the right thing to do, such as “Green” energy, or “Clean” energy, when most of those authoritative voices have no idea of what these three posts are about.
Finally, another reason for writing this is to try to share what some great minds a couple of hundred years ago or so thought up. It’s common nowadays to dismiss anything not current as primitive, under bourgeois influence, a product of settler colonialism, or what-not, and that only the great minds of today have anything meaningful to say. I think this is pretty good evidence the past has had some great thinkers, and to just toss it away without even trying to understand it is a big mistake.
Prior posts on this topic: