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13.23 The Laws of Thermodynamics

Energy behaves in regular and predictable ways in the universe. Thermodynamics is the study of the way that heat flows. We can generalize that discussion to include heat and all other forms of energy. The rules that scientists have discovered, applying to every region of the universe looked at so far, are called the laws of thermodynamics.

The first law of thermodynamics states that the total amount of energy in a closed system is always conserved. This is a statement of the law of conservation of energy. For example, an elliptical orbit has a constant interplay between kinetic energy and gravitational potential energy. When it is close to its star, a planet moves faster in its orbit — the kinetic energy is high and the gravitational energy is low. When it is far from its star, a planet moves slower in its orbit — the kinetic energy is low and the gravitational energy is high. The total energy of the planet remains constant. When energy appears not to be conserved, the answer is usually that some energy has leaked away in the form of heat. When a swing slows down or a rolling ball comes to a stop, kinetic energy has steadily been converted into heat.

When we look at the Sun blazing in the sky and consider that it will keep doing so for billions of years, it seems as if we get this energy for free. In what way do stars conserve energy? Stars create heavier elements in a fusion chain that moves from hydrogen to helium and, if the star is massive enough, to carbon and on to iron. Atomic nuclei are bound together with an attractive force that acts like "glue." It takes energy to undo this glue. Since Einstein showed that the energy that binds an atomic nucleus must have an equivalent energy (E = mc2), it follows that things stuck together have less mass than the same things pulled apart. Therefore, whenever a nucleus becomes more tightly bound, energy that has been frozen in the form of mass gets released as radiant energy. Going from hydrogen to iron, atomic nuclei are held together more and more tightly. So each step up the fusion chain releases mass-energy. Think of mass as a form of potential energy that stars convert into light.

The second law of thermodynamics is also familiar. The principle of thermal equilibrium describes how heat always flows from a hot object to a cold object. Equilibrium is established when both objects have the same temperature. The second law makes the strong proposition: heat cannot flow spontaneously from a cold to a hot object. A cup of coffee cools down as it loses heat to the cooler atmosphere. An ice cube melts as heat flows into it from the warmer atmosphere. Notice that the first law, conservation of energy, does not require this behavior. Energy would be conserved if coffee actually got hotter at the expense of cooling the air, or if an ice cube got colder at the expense of warming the air. But we never see this happen. In nature, heat always flows in one direction from hot to cold.

When the second law of thermodynamics appears to be violated, it is because we are not considering the whole system. Heat always flows so as to warm things up, but that doesn't mean we can't make ice cubes. A refrigerator can extract enough heat from water to make ice cubes, but it comes at the expense of releasing a larger amount of heat into the air. Feel along the top and bottom of your refrigerator if you don't believe this. It is easy to see that stars follow the second law. Energy is created in the core of a star by nuclear fusion and then it flows out from hotter to cooler regions.

It is possible to express the second law of thermodynamics uses a microscopic description of heat energy. Heat is a measure of the kinetic energy (or amount of motion) of atoms and molecules. Fast-moving particles tend to share their motion with slower-moving particles, and the result is that they all approach the same motion or temperature. This is the idea of thermal equilibrium. Notice two important features of this description. First, it is possible for a slow-moving particle to give up speed to a fast-moving particle, but it is unlikely to happen. When considering a large number of particles, the energy will always flow from the quick to the slow. The second law of thermodynamics describes nature with probability rather than with certainty. A few water molecules might happen to lose enough energy to stick together as an ice crystal, but the chances of an ice cube spontaneously forming in your glass of water are incredibly small!

The second consequence of the microscopic description of heat flow is even more interesting. Heat is a measure of the random motions of particles, so it is really a measure of disorder. The second law of thermodynamics also states that the disorder of a physical system will always increase when it undergoes changes. Scientists use the term entropy as a measure of disorder. Entropy is a profound scientific concept, useful in many areas of astronomy.

The increase of entropy seems to be a fact of life as well as a law of nature. The papers on your desk tend to get disordered, odd socks turn up in your sock drawer, and the kitchen always seems to get messy. Why is it so much easier to break an egg than to put it back together? Why can you easily stir a sugar cube into your coffee, while no amount of stirring will make the sugar cube come back together? Let's use the example of a deck of cards. Start with a deck where all the cards are ranked by number and suit. The deck is perfectly ordered and it has low entropy. Anything you do to the deck will make it less ordered. After a few shuffles, there will be little groups of cards in sequence, but overall the deck will have more disorder and more entropy. Shuffle many times and the deck will begin to look truly random; the disorder and entropy are now very high. Experience tells you that no matter how often you shuffle the deck, you will never return the cards to their initial, ordered state. Entropy always increases.

There is a clear connection between disorder or entropy and the probability of a system being in a certain state. Situations of disorder are more probable than situations of order. When an ice cube (or a sugar cube) melts, the order in the crystal lattice turns into the disorder of randomly moving water molecules. Heat is a random or high entropy form of energy. Change is all around us, and energy is always changing from one form to another. The first law says that energy is conserved. The second law says that energy tends to transform into disordered energy or heat.

Ordered energy changes systematically into disordered energy, as we can see with many everyday examples. The motion of a swing or a pendulum decays, and the lost kinetic energy turns into heat energy in the slight heating of air molecules. Our world runs on fossil fuel, which taps the energy stored in the structure of the chemical bond. No matter how efficiently we use that energy, much of it is turned into heat. The electricity in your house heats the wires that it travels through, and later that heat leaks into the atmosphere. A magnet loses its strength with time and use. In this case, the aligned iron grains gradually become less aligned due to heat and due to the magnet striking other objects. (This also creates heat.) Magnetic energy is converted into heat energy. What does this have to do with stars? A star converts mass into energy. This is a very direct translation of order, in the form of a localized particle, into disorder, in the form of radiation or heat energy that extends through space.

In any case where the second law appears to be violated, we are not looking at the whole picture. A refrigerator can make ice cubes, creating the order of a crystal lattice, but only at the expense of releasing a far larger amount of disordered (heat) energy. A star can build heavy elements, creating the structure of a massive nucleus, but only at the expense of disordered (radiation) energy sent into space. How does life comply with the second law of thermodynamics? Surely the creation of structure of a brain, or a cell, or DNA itself, violates the trend toward disorder? It is true that living organisms have lower entropy than their surroundings. However, in the microscopic view, many scientists think that aging is caused by the gradual accumulation of damage to the DNA molecule. This increasing disorder in the genetic code compromises the operation of cells and limits the ability of the organism to repair itself. And in the larger view, the Earth intercepts only a tiny fraction of the Sun's heat energy. Life eventually dies and returns that energy to the atmosphere and then into deep space as a waste product. The second law is obeyed.

Physicists have identified another principle that is often called the third law of thermodynamics. It states that no physical system can be cooled to a temperature of absolute zero. Think of it — at absolute zero there would be no atomic motion so there would be no heat and no friction. Machines could be perfectly efficient. Perpetual motion would be possible. But it is impossible to remove all the heat from a system. Take the coldest gas you can imagine. If you expand its container the gas will cool. But you would have to expand it by an infinite amount to completely remove its heat content. Absolute zero cannot be reached.

The three laws of thermodynamics can be summarized as follows:

• Energy can change forms, but the total amount of energy in a system, including heat energy, is always conserved.

• The entropy, or disorder, of a system always increases, so as energy changes forms the amount of heat energy tends to increase.

• It is impossible to remove all the heat from a physical system.

Here is a colloquial aid to memorizing these important laws. Think of the exchange of heat and other forms of energy as a game. In physics, it turns out you cannot get something for nothing. The first law says you can't win. The second law says you can't break even. Worst of all, the third law says you can't get out of the game!