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Second law of thermodynamics - Wikipedia, the fr... file:///media/TOSHIBA/Second_law_of_thermodyn... Second law of thermodynamics From Wikipedia, the free encyclopedia 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 French scientist Sadi Carnot in 1824 (see Timeline of thermodynamics). 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. Thermodynamics Contents 1 Description 1.1 Clausius statement 1.2 Kelvin Branches statement Classical· Statistical· Chemical 1.3 Principle of Equilibrium / Non-equilibrium Carathéodory Thermofluids 1.4 Equivalence of the Laws statements Zeroth· First · Second · Third 2 Corollaries Systems 2.1 Perpetual motion of the State: second kind Equation of state 2.2 Carnot Ideal gas· Real gas theorem Phase of matter· Equilibrium 2.3 Clausius Control volume· Instruments theorem Processes: 2.4 1 of 22 01/15/2017 02:43 PM Second law of thermodynamics - Wikipedia, the fr... file:///media/TOSHIBA/Second_law_of_thermodyn... Thermodynamic Isobaric· Isochoric· Isothermal temperature Adiabatic· Isentropic· Isenthalpic 2.5 Entropy Quasistatic· Polytropic 2.6 Available Free expansion useful work Reversibility· Irreversibility 3 History Endoreversibility 3.1 Informal Cycles: descriptions Heat engines· Heat pumps 3.2 Thermal efficiency Mathematical descriptions System properties 4 Derivation from Property diagrams statistical mechanics Intensive and extensive properties 4.1 Derivation of the entropy State functions: change for Temperature / Entropy (intro.) † reversible Pressure / Volume † processes Chemical potential / Particle no. † 4.2 Derivation († Conjugate variables) for systems Vapor quality described by Reduced properties the canonical ensemble Process functions: 4.3 General Work· Heat derivation from Material properties unitarity of T quantum Specific heat capacity c = mechanics N 5 Non-equilibrium 1 states Compressibility β = − 6 Controversies V 6.1 Maxwell's 1 Thermal expansion α = demon V 6.2 Loschmidt's paradox Property database 6.3 Gibbs Equations paradox Carnot's theorem 6.4 Poincaré Clausius theorem recurrence Fundamental relation theorem Ideal gas law 6.5 Heat death Maxwell relations of the universe 7 Quotes 2 of 22 01/15/2017 02:43 PM Second law of thermodynamics - Wikipedia, the fr... file:///media/TOSHIBA/Second_law_of_thermodyn... 8 Notes Table of thermodynamic equations 9 See also Potentials 10 References Free energy· Free entropy 11 Further reading 12 External links Internal energy U(S,V) Enthalpy H(S,p) = U + pV Helmholtz free energy A(T,V) = U − TS Description Gibbs free energy G(T,p) = H − TS The first law of thermodynamics History and culture provides the basic definition of Philosophy: thermodynamic energy, also Entropy and time· Entropy and life called internal energy, Brownian ratchet associated with all Maxwell's demon thermodynamic systems, but Heat death paradox unknown in mechanics, and Loschmidt's paradox states the rule of conservation of Synergetics energy in nature. History: However, the concept of energy General· Heat· Entropy· Gas laws in the first law does not account Perpetual motion for the observation that natural Theories: processes have a preferred Caloric theory· Vis viva direction of progress. For Theory of heat example, spontaneously, heat Mechanical equivalent of heat always flows to regions of lower Motive power temperature, never to regions of Publications: higher temperature without "An Experimental Enquiry Concerning ... Heat" external work being performed "On the Equilibrium of Heterogeneous Substances" on the system. The first law is "Reflections on the completely symmetrical with respect to the initial and final Motive Power of Fire" states of an evolving system. The Timelines of: key concept for the explanation Thermodynamics· Heat engines of this phenomenon through the second law of thermodynamics is Art: the definition of a new physical Maxwell's thermodynamic surface property, the entropy. Education: A change in the entropy (S) of a Entropy as energy dispersal system is the infinitesimal transfer of heat (Q) to a closed Scientists system driving a reversible Daniel Bernoulli process, divided by the 3 of 22 01/15/2017 02:43 PM Second law of thermodynamics - Wikipedia, the fr... file:///media/TOSHIBA/Second_law_of_thermodyn... equilibrium temperature (T) of Sadi Carnot [1] the system. Benoît Paul Émile Clapeyron Rudolf Clausius Hermann von Helmholtz Constantin Carathéodory Pierre Duhem The entropy of an isolated Josiah Willard Gibbs system that is in equilibrium is James Prescott Joule constant and has reached its James Clerk Maxwell maximum value. Julius Robert von Mayer Empirical temperature and its William Rankine scale is usually defined on the John Smeaton principles of thermodynamics Georg Ernst Stahl equilibrium by the zeroth law of Benjamin Thompson thermodynamics.[2] However, William Thomson, 1st Baron Kelvin based on the entropy, the second John James Waterston law permits a definition of the absolute, thermodynamic temperature, which has its null point at absolute zero.[3] The second law of thermodynamics may be expressed in many specific ways,[4] the most prominent classical statements[3] being the 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. Clausius statement German scientist Rudolf Clausius is credited with the first formulation of the second law, now known as the Clausius statement:[4] 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] 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. Kelvin statement Lord Kelvin expressed the second law in another form. The Kelvin statement expresses it as follows:[4] 4 of 22 01/15/2017 02:43 PM Second law of thermodynamics - Wikipedia, the fr... file:///media/TOSHIBA/Second_law_of_thermodyn... 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. 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] In every neighborhood of any state S of an adiabatically isolated system there are states inaccessible from S.[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. Equivalence of the statements Suppose there is an engine violating the Kelvin statement: i.e.,one that drains heat and converts it completely into work in a cyclic fashion without any other result. Now pair it with a reversed Carnot engine as shown by the graph. The net and sole effect of this newly created engine consisting of the two engines mentioned is transferring heat from the cooler reservoir to the hotter one, which violates the Clausius statement. Thus the Kelvin statement implies the Clausius statement. We can prove in a similar manner that the Clausius statement implies the Kelvin statement, and hence the two are equivalent. Corollaries 5 of 22 01/15/2017 02:43 PM Second law of thermodynamics - Wikipedia, the
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