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Second law of thermodynamics
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The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and explains the phenomenon of irreversibility in nature. The second law declares the impossibility of machines that generate usable energy from the abundant internal energy of nature by processes called perpetual motion of the second kind.
The second law may be expressed in many specific ways, but the first formulation is credited to the German scientist Rudolf Clausius. The law is usually stated in physical terms of impossible processes. In classical thermodynamics, the second law is a basic postulate applicable to any system involving measurable heat transfer, while in statistical thermodynamics, the second law is a consequence of unitarity in quantum theory. In classical thermodynamics, the second law defines the concept of thermodynamic entropy, while in statistical mechanics entropy is defined from information theory, known as the Shannon entropy.
The first law of thermodynamics provides the basic definition of thermodynamic energy, also called internal energy, associated with all thermodynamic systems, but unknown in mechanics, and states the rule of conservation of energy in nature.
However, the concept of energy in the first law does not account for the observation that natural processes have a preferred direction of progress. For example, spontaneously, heat always flows to regions of lower temperature, never to regions of higher temperature without external work being performed on the system. The first law is completely symmetrical with respect to the initial and final states of an evolving system. The key concept for the explanation of this phenomenon through the second law of thermodynamics is the definition of a new physical property, the entropy.
A change in the entropy (S) of a system is the infinitesimal transfer of heat (Q) to a closed system driving a reversible process, divided by the equilibrium temperature (T) of the system.[1]](http://en.wikipedia.org/wiki/Second_law_of_thermodynamics#cite_note-ref16-0)
The entropy of an isolated system that is in equilibrium is constant and has reached its maximum value.
Empirical temperature and its scale is usually defined on the principles of thermodynamics equilibrium by the zeroth law of thermodynamics.[2]](http://en.wikipedia.org/wiki/Second_law_of_thermodynamics#cite_note-dugdale-1) However, based on the entropy, the second law permits a definition of the absolute, thermodynamic temperature, which has its null point at absolute zero.[3]](http://en.wikipedia.org/wiki/Second_law_of_thermodynamics#cite_note-lieb-2)
The second law of thermodynamics may be expressed in many specific ways,[4]](http://en.wikipedia.org/wiki/Second_law_of_thermodynamics#cite_note-MIT-3) the most prominent classical statements[3]](http://en.wikipedia.org/wiki/Second_law_of_thermodynamics#cite_note-lieb-2) being the original statement by Rudolph Clausius (1850), the formulation by Lord Kelvin (1851), and the definition in axiomatic thermodynamics by Constantin Carathéodory (1909). These statements cast the law in general physical terms citing the impossibility of certain processes. They have been shown to be equivalent.
edit] Clausius statement
German scientist Rudolf Clausius is credited with the first formulation of the second law, now known as the Clausius statement:[4]](http://en.wikipedia.org/wiki/Second_law_of_thermodynamics#cite_note-MIT-3)
No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.[note 1]](http://en.wikipedia.org/wiki/Second_law_of_thermodynamics#cite_note-4) Spontaneously, heat cannot flow from cold regions to hot regions without external work being performed on the system, which is evident from ordinary experience of refrigeration, for example. In a refrigerator, heat flows from cold to hot, but only when forced by an external agent, a compressor.
edit] Kelvin statement
Lord Kelvin expressed the second law in another form. The Kelvin statement expresses it as follows:[4]](http://en.wikipedia.org/wiki/Second_law_of_thermodynamics#cite_note-MIT-3)
No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work. This means 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. This also means that it is impossible to build solar panels that generate electricity solely from the infrared band of the electromagnetic spectrum without consideration of the temperature on the other side of the panel (as is the case with conventional solar panels that operate in the visible spectrum).
Note that it is possible to convert heat completely into work, such as the isothermal expansion of ideal gas. However, such a process has an additional result. In the case of the isothermal expansion, the volume of the gas increases and never goes back without outside interference.
edit] Principle of Carathéodory
Constantin Carathéodory formulated thermodynamics on a purely mathematical axiomatic foundation. His statement of the second law is known as the Principle of Carathéodory, which may be formulated as follows:[5]](http://en.wikipedia.org/wiki/Second_law_of_thermodynamics#cite_note-5)
In every neighborhood of any state S of an adiabatically isolated system there are states inaccessible from S.[6]](http://en.wikipedia.org/wiki/Second_law_of_thermodynamics#cite_note-6) With this formulation he described the concept of adiabatic accessibility for the first time and provided the foundation for a new subfield of classical thermodynamics, often called geometrical thermodynamics.
edit] Equivalence of the statements
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Derive Kelvin Statement from Clausius Statement
that
Inserting the formula for P**j for the canonical ensemble in here gives:
