book_cover_big.gif In previous blogs  I have explained how entropy could be calculated from the amount of heat exchanged divided by the temperature at which that heat exchange occurred ( S = Q/T, see blog of 5/6/07). Rudolf Clausius introduced this definition around 1865. His motivation was that something was missing as the First Law of thermodynamics (conservation of energy) could not explain why heat flows always from hot to cold regions and that the opposite was never observed. While he studied the properties of this new concept he came to the conclusion that in an isolated system (a system that cannot exchange energy or material with its environment) the entropy always increases for processes that change the energy distribution within that system. [i] This proved to an important conclusion, as we are about to find out. Let me elaborate a bit on this. 

As I have mentioned before, in all the processes where we say that we are consuming energy, the only thing we are really doing is that we are transforming or re-distributing energy. An example of energy transformation is when we are burning fossil fuels. Here we transform chemical energy stored in the chemical bonds between the atoms of the fuel into heat. That heat can then be used to power a car and in doing that we transform (part of ) the heat into work. The net result of this process is that the fuel is completely gone (except for some ashes or soot) and is transformed into gaseous products (such as CO2  and water), and that we have travelled over a certain distance (that is where we used the work obtained from the heat for) and that the remaining heat that we could not convert into work is diffused into the air. Now, the question arises whether we could come up with a clever idea to get the energy back in its intial condition because then we could use it another time to power our car? If we would have to deal only with the First Law, then in principle this would be achievable since we have not “consumed” the energy, we have only transformed it into other forms (work and heat) and have distributed the energy into a larger volume (it was first contained in a condensed volume of fuel but is at the end all over the place). Unfortunately we know from experience that this idea has not yet materialized. In fact if we would be able to do this we would invent a sort of perpetual engine. So what is going on, why can we not do this?

Well folks here it is that the Second Law or entropy of thermodynamics kicks in. If we would make an entropy calculation of the situation described above we would come to the conclusion that the entropy would have been increased. The entropy law forbids that the entropy can decrease. Every time that we transform (“use”) energy it comes automatically with an increase in entropy [ii]. Of course you could argue that we could catch all the evolved molecules from burning the fuel after we completed our car ride and restore them such that we get back to our original amount of fuel. Indeed that can be done (in principle at least) but in doing so you will need to transform even more energy (and thus produce even more entropy!). So we are trapped in this viscieuze circle where we only can produce entropy and never be able to restore it.

Although we do not change at all the total amount of energy available to us, the entropy law hinders us to recycle energy so to say. Energy is only useful to us when it is in a form that it is capable of doing work. With work I mean here lifting weights, because once you can lift weights you can use that work to drive wheels, engines and so forth. Another, more popular, way to put this is to say that the quality of the energy while transforming it, degrades. Therefore, entropy can be used to determine the quality of energy. This we can summarize as:

High quality energy (capacity to do work)  has a low entropy value

Low quality energy (less or no capacity to do work) has a high entropy value

To recap this: the entropy law learns us that transforming energy from a high quality state to a low quality state can only be done once. There is absolutely no way to recycle the low quality energy back to high quality energy. During the process of energy transformation there is always an inherent production of entropy that can never be reversed. There is a fundamental reason that the entropy only can increase and, in a way, makes our life miserable. I will come back to this matter in one of the next blogs.

[i] As a matter of fact what see is that such an isolated system the energy tends to distribute evenly and in doing so will let all gradients (whether there are material, temperature, electrical or temperature gradients, it doesn’t matter) disappear. Let me give an example. If we place a piece of aluminum of say 1cc and at -10 °C in 100 ml of water at 20 °C in an isolated vessel (for instance a Dewar), if we wait long enough the temperature will be equal everywhere in the system. The final temperature will be slightly below 20°C and the entropy will be increased by  about 0.015 J/K (for those interested how the calculation is done see my book). The entropy for this isolated system can no longer increase and has obtained its maximum value. One can also say that the system in in equilibrium and will no longer change.[ii] There is an exception to this rule and that is for energy transformations that proceed under reversible conditions. In that case the change in entropy is zero. However, in real life situations that is never the case.

© Copyright 2007, John E.J. Schmitz