Some say entropy is a measure for chaos and others that it is a measure for the dispersion of energy. It was originally coined by Rudolph Clausius in the 1850-ies. There are several ways to formulate the Second Law and though very different from each other, they are all considered to be equivalent – if one is wrong, all the others are wrong also. A popular, but wrong formulation says that heat cannot flow spontaneously from a colder to a warmer region.
However, when you are in the tropics, where the air temperature can become above body temperature, your sweating skin cools your body, by which heat flows spontaneously from your cooler body to the warmer environment. In ‘technology’ this effect has been known and practiced since thousands of years, by keeping water cool in jars of porous material. Some of the water exudes (sweats) through the pores of that material and gives off its heat to the warmer surrounding air.
This is not in conflict with the Second Law, because Clausius’ statement did not include the term ‘spontaneously’. His formulation was: A process whose only final result is to transfer thermal energy from a cooler object to a warmer one, is impossible.
Now, the jar loses water and if not replenished, it will become empty and thus the transfer of heat from the jar to the surrounding air is not the only result of the process. Likewise, if you don’t drink water, your sweating body will dry out and die in the end. Thus also here the transfer of heat is not the only result. Nevertheless, as long as the process lasted, heat indeed did flow spontaneously from a colder to a warmer region.
So what is entropy? One thing we can all agree upon is that energy disperses, if it is not hindered to do so – perfect insulation does not exist. This can also be seen as increasing disorder, because, as energy disperses, the molecules involved, move in more chaotic patterns. However, it is true that shuffled cards, or a broken glass on the floor, are rather more chaotic conditions than a dispersion of energy. The confusing point is that one has to do work to restore the original order, not so much work to order the shuffled cards, but basically infinite work to restore the broken glass (without using new materials) to its original condition. This work DQ disperses in the environment and decays to heat at that environment’s temperature T. The according change of entropy: Delta S = Delta Q / We are thus talking about closed loop, cycle processes here and if these processes are irreversible (they must be driven by an external source), the applied energy will disperse in the surroundings. The sweating jar and human body constitute irreversible processes, because the evaporated water will not by itself return as liquid to the jar or body – it’s an open process. To make it a cycle process, work has to be done and then energy disperses again. Hence, if one sees entropy as a measure for disorder, one actually refers to the work done to restore the original order in a cycle process. If such restoration is not done, the shuffled cards and the broken glass on the floor indeed have nothing to do with entropy. But then, you can do things the easy, or the difficult way and thus the effort needed to restore the original condition, is not a given quantity. Therefore entropy cannot be a measure for disorder.
Is it a measure for the dispersion of energy? If so, then the change of entropy should be independent from whether ideal, or real gases are concerned. On the contrary, real gases behave differently from ideal gases. Unlike ideal gases, real gases do not expand freely at constant temperature, which is known as the Joule-Thomson effect. Most real gases expand at decreasing temperatures, but some do at increasing temperatures. Now somebody tells me how to calculate the change of entropy on this? It is not in my physics books and I have found it nowhere on the web.