Entropy and Disorder

Entropy is a measure of order and organization (or disorder and disorganization, depending on one’s viewpoint). The reason physicists started thinking about order is Carnot’s theory. As discussed in chapter 3, Carnot correctly realized that no heat engine could ever be 100 percent efficient. Efficiency determines the amount of work a machine does for a given amount of heat input, and what Carnot said was that some of the heat’s energy will always be wasted. The wasted heat does no work, it simply escapes in the heat engine’s exhaust. This theory applies to all heat engines, from the steam engines of Carnot’s day to the jet engines of today.

Carnot’s theory puzzled physicists, and out of their curiosity came the concept of entropy. The beauty of this idea is that it explains a lot more than just the odd behavior of heat engines.

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To understand entropy, one must understand the notion of order and disorder. Consider a pack of cards. Suppose the cards are in order, running from low to high, and the suits (spades, hearts, diamonds, and clubs) are also neatly arranged. But then someone throws the cards up in the air, and they scatter every- where. If the cards are picked up at random, their sequence will almost certainly be out of order. Now suppose someone throws the out-of-order cards into the air and the cards are picked up at random, as before. Will the new arrangement of cards return to the proper order? Once again, this is highly unlikely; the sequence of cards will be different than before, but they will not be in order, they will have a different out-of-order arrangement.

Everyone is familiar with processes similar to the card experi- ment described above. All things tend to get more disorganized and disordered over time—machines break down; carefully stacked piles topple over; fresh and clean objects get dirty and erode, rust, or simply wear down. The opposite does not tend to happen, at least not without help—disordered or dirty objects do not tend to become ordered and clean without someone doing a lot of work.

The old gravestone on the left has suffered the ravages of time, losing its shape and engraving. The gravestone on the right is newer. (Kyle Kirkland)

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Another example is the way that an odor spreads throughout a room. If a person wearing perfume walks into a room, initially the odor can only be detected by people who are nearby, but soon the odor molecules travel and fill up the room, and everyone smells it. Once the odor molecules fill the whole room, they stay there—they do not suddenly return to a small space surrounding the perfumed person. (Some of the people in the room might wish this would happen, but it never does.) The odor molecules were at first confined to a small space and so they were initially more organized, but gradually they spread evenly throughout all available space and so the odor molecules became disorganized—just like an orderly pile of sand becomes disorganized when it is shaken and spread across the floor.

Heat is yet another example. When a hot object enters a cold room, gradually the object’s temperature falls and the rest of the room warms up a little—the heat spreads throughout the room, whereas the energy was initially confined to the hot object. Because this is true, heat is the basis of one way to measure entropy, which is not surprising since thermodynamics was the primary reason why physicists starting thinking about the concept. The change in entropy, ∆S (the symbol ∆ means “change in”), of an object or a

system is given by the heat, Q, flowing into (or out of) it, divided by the temperature, T (given in the Kelvin scale):

∆S = Q/T.

Measurements show that entropy always increases for a spon- taneous process—a process that occurs naturally, without any out- side help. Heat naturally flows from hot objects to cold, and in the process, entropy increases. An ordered pack of cards becomes random when scattered over the floor. Molecules initially confined in a small corner eventually spread throughout the entire room. Ordered systems have low entropy and disordered systems have high entropy. As time passes, orderly systems became increasingly disordered. No matter what the process, entropy tends to increase. This important statement, discussed in the following sidebar, is one way of stating the second law of thermodynamics.

Entropy explains the mystery of Carnot’s theory concerning the

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Entropy and Disorder