The second law of thermodynamics is an expression of the universal law of increasing entropy, stating that the entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.
The second law traces its origin to French physicist Sadi Carnot's 1824 paper Reflections on the Motive Power of Fire, which presented the view that motive power (work) is due to the fall of caloric (heat) from a hot to cold body (working substance). In simple terms, the second law is an expression of the fact that over time, differences in temperature, pressure, and density tend to even out in a physical system that is isolated from the outside world. Entropy is a measure of how far along this evening-out process has progressed.
There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of irreversibility in nature.
Introduction
Versions of The Law
There are many statements of the second law which use different terms, but are all equivalent. [#wp-endnote_Fermi_ (Fermi, 1936)] Another statement by Clausius is:
Heat cannot of itself pass from a colder to a hotter body.
An equivalent statement by Lord Kelvin is:
A transformation whose only final result is to convert heat, extracted from a source at constant temperature, into work, is impossible.
The second law is only applicable to macroscopic systems. The second law is actually a statement about the probable behavior of an isolated system. As larger and larger systems are considered, the probability of the second law being practically true becomes more and more certain. For any system with a mass of more than a few picograms, the second law is true to within a few parts in a million.
The formulation of the second law that refers to entropy directly is due to Rudolf Clausius:
In an isolated system, a process can occur only if it increases the total entropy of the system.
Thus, the system can either stay the same, or undergo some physical process that increases entropy. (An exception to this rule is a reversible or "isentropic" process, such as frictionless adiabatic compression.) Processes that decrease total entropy of an isolated system do not occur. If a system is at equilibrium, by definition no spontaneous processes occur, and therefore the system is at maximum entropy.
Also due to Clausius is the simplest formulation of the second law, the heat formulation:
Heat cannot spontaneously flow from a material at lower temperature to a material at higher temperature.
Informally, "Heat doesn't flow from cold to hot (without work input)", which is obviously true from everyday experience. For example in a refrigerator, heat flows from cold to hot, but only when electrical energy is added. Note that from the mathematical definition of entropy, a process in which heat flows from cold to hot has decreasing entropy. This is allowable in a non-isolated system, however only if entropy is created elsewhere, such that the total entropy is constant or increasing, as required by the second law. For example, the electrical energy going into a refrigerator is converted to heat and goes out the back, representing a net increase in entropy.
A third formulation of the second law, the heat engine formulation, by Lord Kelvin, is:
It is impossible to convert heat completely into work.
That is, it is impossible to extract energy by heat from a high-temperature energy source and then convert all of the energy into work. At least some of the energy must be passed on to heat a low-temperature energy sink. Thus, a heat engine with 100% efficiency is thermodynamically impossible.
Microscopic systems
Thermodynamics is a theory of macroscopic systems at equilibrium and therefore the second law applies only to macroscopic systems with well-defined temperatures. No violation of the second law of thermodynamics has ever been observed in a macroscopic system. But on scales of a few atoms, the second law does not apply; for example, in a system of two molecules, it is possible for the slower-moving ("cold") molecule to transfer energy to the faster-moving ("hot") molecule. Such tiny systems are outside the domain of thermodynamics, but they can be investigated using statistical mechanics. For any isolated system with a mass of more than a few picograms, the second law is true to within a few parts in a million.
Energy dispersal
The second law of thermodynamics is an axiom of thermodynamics concerning heat, entropy, and the direction in which thermodynamic processes can occur. For example, the second law implies that heat does not spontaneously flow from a cold material to a hot material, but it allows heat to flow from a hot material to a cold material. Roughly speaking, the second law says that in an isolated system, concentrated energy disperses over time, and consequently less concentrated energy is available to do useful work. Energy dispersal also means that differences in temperature, pressure, and density even out. Again roughly speaking, thermodynamic entropy is a measure of energy dispersal, and so the second law is closely connected with the concept of entropy.
Overview
In a general sense, the second law says that temperature differences between systems in contact with each other tend to even out and that work can be obtained from these non-equilibrium differences, but that loss of heat occurs, in the form of entropy, when work is done.Pressure differences, density differences, and particularly temperature differences, all tend to equalize if given the opportunity. This means that an isolated system will eventually come to have a uniform temperature. A heat engine is a mechanical device that provides useful work from the difference in temperature of two bodies:
Heat engine diagram
During the 19th century, the second law was synthesized, essentially, by studying the dynamics of the Carnot heat engine in coordination with James Joule's Mechanical equivalent of heat experiments. Since any thermodynamic engine requires such a temperature difference, it follows that no useful work can be derived from an isolated system in equilibrium; there must always be an external energy source and a cold sink. By definition, perpetual motion machines of the second kind would have to violate the second law to function.
History
The first theory on the conversion of heat into mechanical work is due to Nicolas Léonard Sadi Carnot in 1824. He was the first to realize correctly that the efficiency of this conversion depends on the difference of temperature between an engine and its environment.
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 does not spontaneously flow from cold to hot bodies. While common knowledge now, this was contrary to the caloric theory of heat popular 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 the 19th century, the Kelvin-Planck statement of the Second Law 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 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.
Using quantum mechanics it has been shown that the local von Neumann entropy is at its maximum value with an extremely high probability, thus proving the second law. The result is valid for a large class of isolated quantum systems (e.g. a gas in a container). While the full system is pure and has therefore no entropy, the entanglement between gas and container gives rise to an increase of the local entropy of the gas. This result is one of the most important achievements of quantum thermodynamics.
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