Chaos and Disorder

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Chaos and Disorder (The Second Law of Thermodynamics)

Countless processes have a preferred or “natural” direction. Heat flows spontaneously from hot objects to cold ones. Water will flow from high mountains toward rivers. Air rushes out of a punctured rubber balloon. Smells tend to diffuse outward to span greater distances. Humans grow older by the minute. When a house is left unattended, it quickly becomes disorganized. All these processes have one thing in common; they all tend to become more dispersed (chaotic). This is one statement of the second law of thermodynamics, which can be generally stated as:

The Second Law of Thermodynamics:

All natural processes tend to go from order (concentrated) to disorder (dispersed).

More simply put — events happen in a certain direction. Although many people think the second law of thermodynamics must only be of interest to physicists, engineers, and those who deal directly with heat and energy, the second law has far-reaching consequences not only in predicting the fate of the universe, but also in all aspects of our daily lives. The second law gives us guidelines for what we can and cannot do. It tells us how to design better machines and provides us with a blueprint for using our resources more efficiently. In short, it gives us a sense of direction.

Question: It is often said that it is impossible to obtain negative absolute temperatures. Why?

Answer: Because absolute zero is the state where all molecular motion ceases and the complete order is achieved. Negative temperatures imply better than perfect order!

Question: What does the second law tell us about the ultimate fate of the universe? What should we expect after a severe earthquake? After dropping a glass cup from the edge of a table?

Answer: According to the second law, the universe will continue toward complete disorder (thermodynamic equilibrium), where all non-uniformities in temperature, electric potential, pressure, etcetera, vanish and eventually reach a heat death. Accordingly, it predicts that earthquakes flatten buildings – decreasing order. Similarly, dropping a glass cup off a table edge will likely break it into many pieces, increasing the disorder. Remember that an unbroken glass cup, by the virtue of the careful positioning of the atoms in a lattice structure, is highly ordered.

Contents

Entropy

Measuring the temperature of a room or the pressure of the tires of a car are probably easy and routine tasks. All that is needed is a thermometer or a pressure gauge. But how can we measure chaos? Is there a way to quantify how much dirtier my room is than yours? Ludwig Boltzmann (1844-1906), an Austrian scientist, attempted to do exactly that. The result of his studies is summarized in a single equation that defines entropy (from the Greek root meaning transformation) as a measure of randomness, or the total number of configurations that a system can assume. The concept of entropy is closely intertwined with the second law of thermodynamics in the sense that processes happen such that the total entropy of the universe is constantly increasing. When dealing with energy, the second law implies that it must flow from the one with the least amount of disorder (lower entropy) to the one with a higher amount of disorder (higher entropy).

Figure 1: With the aid of a few hundred pounds of dynamite, demolition experts caused this hotel- casino in Las Vegas to go from an ordered state (lower entropy) to a disordered state (higher entropy).

Question: It is an easy task to mix two tablespoons of salt and pepper. It takes quite a bit of work, however, to separate a mixture of salt and pepper into its constituents. Why?

Answer: Salt and pepper by themselves are relatively orderly, but when mixed, disorder will increase considerably. Separating salt and pepper requires work because we need to create order by reducing the mixture’s entropy.

Question: Visualize a deck of cards where all the cards are arranged according to suit and rank. How does the entropy change if the deck is shuffled a few times?

Answer: When suits are to be arranged in some orderly manner, rearrangement is limited. There are a great number of ways that a deck can be rearranged if a particular order is not demanded; the entropy is thus increases.

Question: An electric heater dissipates electrical energy into heat (and some light). What are the implications of the first and second laws of thermodynamics?

Answer: The first law assures that electrical energy is completely converted to heat (and light). The second law implies that the energy flow is from order (flow of electrons in the electric coil) to disorder (random motion of heated air molecules in the room).

Question: When a gas balloon is heated, it expands. What happens to the entropy?

Answer: As the balloon expands, it opens more room for gas molecules to occupy. In other words, the possibility that gas molecules take different configurations increases. Thus the balloon’s entropy increases.

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