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## Isolated systems become disordered

The final form of the 2nd law - systems become more disorganized over time - is at the same time perhaps the most abstract and profound statement of the three. A trivial example of Nature's tendency towards disorder can be achieved by the following experiment. Take a jar full of pennies that have carefully been arranged so that all the heads are facing up. Then tip the jar so that all the pennies fall to the ground - theoretically, it is possible that all the pennies will land with heads facing up. Our experience though is that most of the time, the some pennies will have heads up and some will have tails up. This example illustrates clearly, and quite accurately what is meant by order, and why nature prefers disorder. Having 50 pennies in a jar all with heads up is clearly an ordered state. Having 50 pennies on the ground with some, unspecified number heads, and the rest tails is clearly disordered. The reason the pennies never land all heads up is simply that it is too unlikely. There are far more disordered states possible than the one, and only one ordered state. This example also shows that ordered states are by no means impossible to achieve in Nature, they just require work: someone must put a lot of effort into arranging the pennies so that they are all facing the same way. However, in the absence of such external intervention, a disordered state is overwhelmingly more probably, which is in effect the 3rd version of the 2nd Law.

Heat transfer by conduction works is also an illustration of this statement of the 2nd Law. When a hot and a cold body are initially in contact, the system is somewhat ordered, in that we know most of the molecules in the hot side are moving faster than those in the cool side. However, this degree of order is lost after the system has attained a uniform temperature.

The concept of entropy is introduced to characterize the order of a system. Qualitatively speaking,

Here, state is a very general term, and could include position, speed, etc. What the 2nd law states is then that

This is equivalent to saying that the number of states available to a system increases in general, by which the system thus becomes more disordered. In the coin example, the initial state (all heads up) was unique, whereas the likely finally state (roughly half heads, half tails) could be achieved in a very large number of different ways. The entropy increased.

A key point in this form of the 2nd law is that one is considering isolated systems. One could look at water freezing in a freezer and say the water molecules are becoming more ordered as the ice forms. This though would not violate the 2nd law, as the ice cube by itself is not an isolated system - one must include the freezer and the environment the freezer is in as also part of the system. One finds the entropy of the total system to be increasing over time, although the entropy of an individual subsystem may be decreasing. This is also relevant in the discussion of human evolution; by itself, the progression from simple organisms to complex human beings seems to violate the 2nd law of thermodynamics. However, one must in this remember that the human evolution chain is not an isolated system, and that one must include at least the earth and its environment in the total system. The entropy of this total system is then seen to increase over time, allowing for the fact that the human component of this system may be becoming more ordered.

The property of entropy in a sense defines for us a direction of time. If one took a film of someone dropping a jar of pennies which subsequently scatter all over the floor, then viewed later such a film would not appear unusual. However, if one ran the film backwards, so that we see a group of scattered pennies on the floor spontaneously come together inside of a jar all facing with their heads up, then we would know that something is wrong, even though such an event may be possible by energy conservation, for example. The fact that systems tend to become disordered in time gives us then a sense of direction of time. Note that this does not strictly contradict what we said in the first Chapter about time reversal symmetry of nature. The microscopic laws of physics say that any allowed process is also allowed in the time reversed direction. The 2nd Law of Thermodynamics is simply a consequence of the fact that some outcomes are far more likely to occur than others.

Next: Questions Up: 2nd Law of Thermodynamics Previous: Heat cannot be completely
modtech@theory.uwinnipeg.ca
1999-09-29