| Second Law Of Thermodynamics |
Article Index for Second |
Website Links For Second |
Information AboutSecond Law Of Thermodynamics |
| CATEGORIES ABOUT SECOND LAW OF THERMODYNAMICS | |
| fundamental physics concepts | |
| laws of thermodynamics | |
| 2 | |
| non-equilibrium thermodynamics | |
| philosophy of thermal and statistical physics | |
|
The second law of Thermodynamics states that ''"the Entropy of an Isolated System not at Thermal Equilibrium will tend to increase over time, approaching a maximum value."'' The Second Law is a statistical law and thus applicable only to macroscopic systems. When one part of an isolated system interacts with another part, energy tends to distribute equally among the accessible energy states of the system. As a result, the system tends to approach Thermal Equilibrium , at which point the entropy is at a maximum and the Free Energy is zero. GENERAL DESCRIPTION In a general sense, the Second Law says that the differences between systems in contact with each other tend to even out. 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 thermodynamic engine is an engine that provides useful work from the difference in temperature of two bodies. 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 energy fed from the outside. The Second Law is often invoked as the reason why perpetual motion machines cannot exist. The Second Law can be stated in various succinct ways, including:
A mathematical statement of the Second Law is: : "is likely to be true." where S t Note that this equation does not ''need'' to be true, but the Second Law asserts that it is ''usually'' true. Entropy can decrease, but this simply tends not to happen as often. A common misconception is that the Second Law means that entropy never decreases. In fact, the Second Law asserts only a statistical tendency, hence it is only ''highly unlikely'' that entropy will decrease in a closed system at any given instant. AVAILABLE USEFUL WORK :See also: '' Available Useful Work (thermodynamics) '' An important and revealing idealised special case is to consider applying the Second Law to the scenario of an isolated system (called the total system or universe), made up of two parts: a sub-system of interest, and the sub-system's surroundings. These surroundings are imagined to be so large that they can be considered as an ''unlimited'' heat reservoir at temperature ''TR'' and pressure ''PR'' — so that no matter how much heat is transferred to (or from) the sub-system, the temperature of the surroundings will remain ''TR''; and no matter how much the volume of the sub-system expands (or contracts), the pressure of the surroundings will remain ''PR''. Whatever changes ''dS'' and ''dSR'' occur in the entropies of the sub-system and the surroundings individually, according to the Second Law the entropy ''Stot'' of the isolated total system must increase: : 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: : where μiR are the Chemical Potential s of chemical species in the external surroundings. Now the heat leaving the reservoir and entering the sub-system is : 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 : 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: : 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, : 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, : 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 : 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: : If the volume ''V'' is constrained to be constant, then : 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 : 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. : is equivalent to 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 threshhold. 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 :See also: '' History Of Entropy '' 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 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). SEE ALSO
FURTHER READING
EXTERNAL LINKS
|
|
|