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The most likely conditions (or macrostates) for a gas are those we see all the time—a random distribution of atoms in space with a Maxwell-Boltzmann distribution of speeds in random directions, as predicted by kinetic theory. This is the most disorderly and least structured condition we can imagine. In contrast, one type of very orderly and structured macrostate has all of the atoms in one corner of a container with identical velocities. There are very few ways to accomplish this (very few microstates corresponding to it), and so it is exceedingly unlikely ever to occur. (See [link] (b).) Indeed, it is so unlikely that we have a law saying that it is impossible, which has never been observed to be violated—the second law of thermodynamics.

Two states of a container of gas are shown. In state a, the gas molecules, depicted as small green spheres, are randomly distributed in the container, with random velocities (an arrow is attached to each sphere, and the arrows vary in length and direction). This state is labeled likely. In state b, the molecules are clustered in the lower left-hand corner of the container and the arrows are much shorter. This state is labeled highly unlikely.
(a) The ordinary state of gas in a container is a disorderly, random distribution of atoms or molecules with a Maxwell-Boltzmann distribution of speeds. It is so unlikely that these atoms or molecules would ever end up in one corner of the container that it might as well be impossible. (b) With energy transfer, the gas can be forced into one corner and its entropy greatly reduced. But left alone, it will spontaneously increase its entropy and return to the normal conditions, because they are immensely more likely.

The disordered condition is one of high entropy, and the ordered one has low entropy. With a transfer of energy from another system, we could force all of the atoms into one corner and have a local decrease in entropy, but at the cost of an overall increase in entropy of the universe. If the atoms start out in one corner, they will quickly disperse and become uniformly distributed and will never return to the orderly original state ( [link] (b)). Entropy will increase. With such a large sample of atoms, it is possible—but unimaginably unlikely—for entropy to decrease. Disorder is vastly more likely than order.

The arguments that disorder and high entropy are the most probable states are quite convincing. The great Austrian physicist Ludwig Boltzmann (1844–1906)—who, along with Maxwell, made so many contributions to kinetic theory—proved that the entropy of a system in a given state (a macrostate) can be written as

S = k ln W , size 12{S=k" ln"W} {}

where k = 1 . 38 × 10 23 J/K size 12{k=1 "." "38" times "10" rSup { size 8{ - "23"} } "J/K"} {} is Boltzmann’s constant, and ln W size 12{"ln" W} {} is the natural logarithm of the number of microstates W size 12{ W} {} corresponding to the given macrostate. W size 12{ W} {} is proportional to the probability that the macrostate will occur. Thus entropy is directly related to the probability of a state—the more likely the state, the greater its entropy. Boltzmann proved that this expression for S size 12{ S} {} is equivalent to the definition Δ S = Q / T size 12{ ΔS=Q/T} {} , which we have used extensively.

Thus the second law of thermodynamics is explained on a very basic level: entropy either remains the same or increases in every process. This phenomenon is due to the extraordinarily small probability of a decrease, based on the extraordinarily larger number of microstates in systems with greater entropy. Entropy can decrease, but for any macroscopic system, this outcome is so unlikely that it will never be observed.

Questions & Answers

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what's acceleration
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The change in position of an object with respect to time
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the air molecules are very light enough to oppose the gravitational pull of the earth on the man..... hence, freefall occurs
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study of matter and energy and an inter-relation between them.
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Practice Key Terms 3

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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