Second law of thermodynamics

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Laws of thermodynamics
Zeroth law of thermodynamics
First law of thermodynamics
Second law of thermodynamics
Third law of thermodynamics
= dS + dS_R \ge 0 ] According to the First Law of Thermodynamics, the change dU in the internal energy of the sub-system is the sum of the heat δq added to the sub-system, less any work δw done by the sub-system, plus any net chemical energy entering the sub-system d ∑μiRNi, so that: [ dU = \delta q - \delta w + d(\sum \mu_N_i) \,] where μiR are the chemical potentials of chemical species in the external surroundings. Now the heat leaving the reservoir and entering the sub-system is [ \delta q = T_R (-dS_R) \le T_R dS ] where we have first used the definition of entropy in classical thermodynamics (alternatively, the definition of temperature in statistical thermodynamics); and then the Second Law inequality from above. It therefore follows that any net work δw done by the sub-system must obey [ \delta w \le - dU + T_R dS + \sum \mu_ dN_i \,] It is useful to separate the work done δw done by the subsystem into the useful work δwu that can be done by the sub-system, over and beyond the work PR dV done merely by the sub-system expanding against the surrounding external pressure, giving the following relation for the useful work that can be done: [ \delta w_u \le -d (U - T_R S + P_R V - \sum \mu_ N_i )\,] It is convenient to define the right-hand-side as the exact derivative of a thermodynamic potential, called the availability or exergy X of the subsystem, [ X = U - T_R S + P_R V - \sum \mu_ N_i ] The Second Law therefore implies that for any process which can be considered as divided simply into a subsystem, and an unlimited temperature and pressure reservoir with which it is in contact, [ d X + \delta w_u \le 0 \, ] i.e. the change in the subsystem's exergy plus the useful work done by the subsystem (or, the change in the subsystem's exergy less any work, additional to that done by the pressure reservoir, done on the system) must be less than or equal to zero. Special cases: Gibbs and Helmholtz free energies When no useful work is being extracted from the sub-system, it follows that [ d X \le 0 \, ] with the exergy X reaching a minimum at equilibrium, when dX=0. If no chemical species can enter or leave the sub-system, then the term ∑ μiR Ni can be ignored. If furthermore the temperature of the sub-system is such that T is always equal to TR, then this gives: [X = U - TS + P_R V + \mathrm \,] If the volume V is constrained to be constant, then [X = U - TS + \mathrm = A + \mathrm\,] where A is the thermodynamic potential called Helmholtz free energy, A=U-TS. Under constant volume conditions therefore, dA ≤ 0 if a process is to go forward; and dA=0 is the condition for equilibrium. Alternatively, if the sub-system pressure P is constrained to be equal to the external reservoir pressure PR, then [X = U - TS + PV + \mathrm = G + \mathrm\,] where G is the Gibbs free energy, G=U-TS+PV. Therefore under constant pressure conditions dG ≤ 0 if a process is to go forwards; and dG=0 is the condition for equilibrium. Application In sum, if a proper infinite-reservoir-like reference state is chosen as the system surroundings in the real world, then the Second Law predicts a decrease in X for an irreversible process and no change for a reversible process. [dS_ \ge 0 ] is equivalent to [ dX + \delta w_u \le 0 ] This expression together with the associated reference state permits a design engineer working at the macroscopic scale (above the thermodynamic limit) to utilize the Second Law without directly measuring or considering entropy change in a total isolated system. (Also, see process engineer). Those changes have already been considered by the assumption that the system under consideration can reach equilibrium with the reference state without altering the reference state. An efficiency for a process or collection of processes that compares it to the reversible ideal may also be found (See second law efficiency.) This approach to the Second Law is widely utilized in engineering practice, environmental accounting, systems ecology, and other disciplines. Complex systems and the Second Law It is occasionally claimed that the Second Law is incompatible with autonomous self-organisation, or even the coming into existence of complex systems. The entry self-organisation explains how this claim is a misconception. In fact, as hot systems cool down in accordance with the Second Law, it is not unusual for them to undergo spontaneous symmetry breaking, i.e. for structure to spontaneously appear as the temperature drops below a critical threshold. Complex structures also spontaneously appear where there is a steady flow of energy from a high temperature input source to a low temperature external sink. It is conjectured that such systems tend to evolve into complex, structured, critically unstable "edge of chaos" arrangements, which very nearly maximise the rate of energy degradation (the rate of entropy production). Some opponents of evolution claim that life exhibits complexity whose nature differs from the autonomous complexity and self-organisation which the Second Law allows. The consensus of scientific opinion is that this claim is not well-founded, and that no such distinction can be sustained. For further discussion see Creation-evolution controversy. 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 Second Law is a law about macroscopic irreversibility. Boltzmann first investigated the link with microscopic reversibility. In his H-theorem he gave an explanation, by means of statistical mechanics, for dilute gases in the zero density limit where the ideal gas equation of state holds. He derived the second law of thermodynamics not from mechanics alone, but also from the probability arguments. His idea was to write an equation of motion for the probability that a single particle has a particular position and momentum at a particular time. One of the terms in this equation accounts for how the single particle distribution changes through collisions of pairs of particles. This rate depends of the probability of pairs of particles. Boltzmann introduced the assumption of molecular chaos to reduce this pair probability to a product of single particle probabilities. From the resulting Boltzmann equation he derived his famous H-theorem, which implies that on average the entropy of an ideal gas can only increase. The assumption of molecular chaos in fact violates time reversal symmetry. It assumes that particle momenta are uncorrelated before collisions. If you replace this assumption with "anti-molecular chaos," namely that particle momenta are uncorrelated after collision, then you can derive an anti-Boltzmann equation and an anti-H-Theorem which implies entropy decreases on average. Thus we see that in reality Boltzmann did not succeed in solving Loschmidt's paradox. The molecular chaos assumption 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, now called Maxwell's demon, that challenged the Second Law. This experiment reveals the importance of observability in discussing the Second Law. 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, the Second Law is intimately related to quantum measurement theory and quantum collapse - and none of them is completely understood. Miscellany Flanders and Swann produced a setting of a statement of the Second Law of Thermodynamics to music, called "First and Second Law". The Second Law is exhibited (coarsely) by a box of electrical cables. Cables added from time to time tangle, inside the "closed system" (cables in a box) by adding and then removing cables. The best way to untangle them is to start by taking the cables out of the box and placing them stretched out. The cables in a closed system (the box) will never untangle, but giving them some extra space starts the process of untangling (by going outside the closed system). The economist Nicholas Georgescu-Roegen showed the significance of the Entropy Law in the field of economics (see his work The Entropy Law and the Economic Process (1971), Harvard University Press). See also Entropy Entropy (arrow of time) Final Anthropic Principle First law of thermodynamics History of thermodynamics Jarzynski equality Laws of thermodynamics MaxEnt thermodynamics - Bayesian view of entropy and the Second Law Statistical mechanics Perpetual motion Further reading Goldstein, Martin, and Inge F., 1993. The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction, a bit less technical than this entry. External links [110+ Variations of the 2nd Law.] Stanford Encyclopedia of Philosophy: "[Philosophy of Statistical Mechanics.]" by Lawrence Sklar. [The evolution of Carnot's principle], by E.T. Jaynes, in G. J. Erickson and C. R. Smith (eds.) Maximum-Entropy and Bayesian Methods in Science and Engineering vol. 1, p. 267 (1988). [The Second Law of Thermodynamics.] [2nd Law - In Short]   From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating. All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details. Search Titles 0 1 2 3 4 5 6 7 8 9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ? E-mail this article to: Personal Message: