Second law of thermodynamics
\n\n
In
physics, the
second law of thermodynamics, in its many forms, is a statement about the quality and direction of
energy flow, and it is closely related to the concept of
entropy.
This law and its derivatives, such as the law of
friction, defines the
arrow of time: most other
physical laws are
time-reversal invariant.
General description
\nThe first law of thermodynamics states that one form of energy, e.g. kinetic, potential, electrical energy, thermal,... can be converted into another without loss. The second law states that thermal energy, or heat, is special among the types of energies: all the forms of energy can be converted into heat, but in a way that is not reversible; it is not possible to convert the heat back fully in its original form. In other words, heat is a form of energy of lower quality.
What makes heat so special ? According to the kinetic theory, heat is due to the random movement of atoms and molecules, so it looks much like kinetic energy. The difference is that those movements cannot be observed or predicted, while all the other forms of energy are the result of some orderly movement of particles. The second law says that the amount of random movement, i.e. the entropy, can only increase in a closed system, i.e. that we cannot put this randomness in order without some external influence. (Some systems, for example living cells, spontaneously become structured when they receive energy from the outside - see dissipative structures).
The following example illustrates the law. When a stone falls on earth, its kinetic energy is converted into heat, i.e. it becomes random movements of earth particles. The second law says that this random movement will never become ordered again. For example, the random movement will never become synchronized to throw the stone back in the air: the heat energy will not revert to the original kinetic energy.
Yet, there is one thing predictable about heat: it flows from hot to cold bodies. This can be used to convert some heat into mechanical energy, using a Carnot heat engine. The cycle stops when both bodies reach the same temperature: it can be shown that the amount of random movements has not decreased in the process.
The second law of thermodynamics is important to engineers because it provides a way to determine the quality, as well as the amount of degradation of energy during a process. It is also used to determine the theoretical upper limits for the performance of many commonly used engineering systems like refrigerators, internal combustion engines, and chemical reactors.
Any device that violates the second law of thermodynamics would be called a perpetual motion machine of the second kind. One example of this would be a device that can do work such as pumping water, simply by taking energy from the air.
History and recent developments
\nThe first theory on the conversion of heat into mechanical work is due to Sadi Carnot in 1824. He was the first to realize correctly that the efficiency of the process depends on the difference of temperature between the hot and cold bodies.
Recognizing the significance of James Prescott Joule's work on the conservation of energy, Rudolf Clausius was the first to formulate the second law in 1850, in this form: heat flows only from hot to cold bodies. While common knowledge now, this was contrary to the caloric theory of heat in vogue at the time, which considered heat as a liquid. From there he was able to infer the law of Sadi Carnot and the definition of entropy (1865).
Established in 18??, the Kelvin-Planck statement of the second law of thermodynamics says, "It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work." This was shown to be equivalent to the statement of Clausius.
The second law of thermodynamics is essentially a macroscopic law about non-reversibility. Boltzmann had first investigated the link with microscopic reversibility. He has given explanation by means of Statistical mechanics, first for diluted gases in his H-theorem. He did not derive the second law of thermodynamics from mechanics alone, but also from the probability arguments. His idea was to use the coarse graining, grouping of microstates into macrostates, and then to make a statement about what is most probable to happen for a macrostate - for some microstates the entropy will decrease, but this happens with low probability.
A key assumption in his approach is that particles are not correlated before a collision, and are correlated afterwards. This is the key element that introduces the arrow of time.
The Ergodic hypothesis is also important for the Boltzmann approach. It says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over long period of time. Equivalently, it says that time average and average over the statistical ensemble are the same.
In 1871, James Clerk Maxwell proposed a thought experiment that challenged the second law. It is now called Maxwell's demon and is an example of the importance of observability in discussing the second law (see the article for details).
In Quantum mechanics, the ergodicity approach can also be used. However, there is an alternative explanation, which involves Quantum collapse - it is a straightforward result that quantum measurement increases entropy of the ensemble. Thus, second law of thermodynamics is intimately related to quantum measurement theory and quantum collapse - and none of them is completely understood.
The relation between the second law of thermodynamics and microscopic reversibility has been demonstrated theoretically in 1993 in the form of the Fluctuation theorem, and later observed experimentally. This has important applications in nanotechnology.
In 1988, Stephen Hawking, in his book A Brief History of Time, used the following line of thought to show the effect of the measurement mechanism : if, contrary to the second law, the entropy of all systems decreased with time, our brain would also go from ordered to disordered over time, and we would not be able to remember the observations we made (because in that case our brain would go from disordered to ordered, which would be a contradiction; see arrow of time). In other words, we would not be able to observe a world where the inverse of the second law would hold everywhere.
Other
\nFlanders and Swann produced a particularly insightful explanation of thermodynamics, which was popular in the 1950's and 1960's. Their work, entitled First and Second Law is unique in having been set to music.
See Also
\n* First law of thermodynamics\n* Entropy\n* Statistical mechanics
Category:Thermodynamics
