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- The Second Law of Thermodynamics
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- 2nd Law of Thermodynamics
- Chemistry for the gifted and talented: the second law of thermodynamics
The Second Law of Thermodynamics
The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. Entropy predicts the direction of spontaneous processes, and determines whether they are irreversible or impossible, despite obeying the requirement of conservation of energy , which is established in the first law of thermodynamics. The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always arrive at a state of thermodynamic equilibrium , where the entropy is highest.
If all processes in the system are reversible , the entropy is constant. An increase in entropy accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time. Historically, the second law was an empirical finding that was accepted as an axiom of thermodynamic theory. Statistical mechanics provides a microscopic explanation of the law in terms of probability distributions of the states of large assemblies of atoms or molecules.
The second law has been expressed in many ways. Its first formulation, which preceded the proper definition of entropy and was based on caloric theory , is Carnot's theorem , credited to the French scientist Sadi Carnot , who in showed that the efficiency of conversion of heat to work in a heat engine has an upper limit.
The second law of thermodynamics can also be used to define the concept of thermodynamic temperature , but this is usually delegated to the zeroth law of thermodynamics. The first law of thermodynamics provides the definition of the internal energy of a thermodynamic system , and expresses the law of conservation of energy.
For example, when a path for conduction and radiation is made available, heat always flows spontaneously from a hotter to a colder body. Such phenomena are accounted for in terms of entropy. For an actually possible infinitesimal process without exchange of mass with the surroundings, the second law requires that the increment in system entropy fulfills the inequality  . This is because a general process for this case may include work being done on the system by its surroundings, which can have frictional or viscous effects inside the system, because a chemical reaction may be in progress, or because heat transfer actually occurs only irreversibly, driven by a finite difference between the system temperature T and the temperature of the surroundings T surr.
The second term represents work of internal variables that can be perturbed by external influences, but the system cannot perform any positive work via internal variables. This statement introduces the impossibility of the reversion of evolution of the thermodynamic system in time and can be considered as a formulation of the second principle of thermodynamics — the formulation, which is, of course, equivalent to the formulation of the principle in terms of entropy. The zeroth law of thermodynamics in its usual short statement allows recognition that two bodies in a relation of thermal equilibrium have the same temperature, especially that a test body has the same temperature as a reference thermometric body.
The second law allows [ how? These statements cast the law in general physical terms citing the impossibility of certain processes. The Clausius and the Kelvin statements have been shown to be equivalent. The historical origin  of the second law of thermodynamics was in Carnot's principle.
It refers to a cycle of a Carnot heat engine , fictively operated in the limiting mode of extreme slowness known as quasi-static, so that the heat and work transfers are between subsystems that are always in their own internal states of thermodynamic equilibrium. The Carnot engine is an idealized device of special interest to engineers who are concerned with the efficiency of heat engines. Carnot's principle was recognized by Carnot at a time when the caloric theory of heat was seriously considered, before the recognition of the first law of thermodynamics , and before the mathematical expression of the concept of entropy.
Interpreted in the light of the first law, it is physically equivalent to the second law of thermodynamics, and remains valid today. Carnot's original arguments were made from the viewpoint of the caloric theory, before the discovery of the first law of thermodynamics. Some samples from his book are:. The German scientist Rudolf Clausius laid the foundation for the second law of thermodynamics in by examining the relation between heat transfer and work. Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.
The statement by Clausius uses the concept of 'passage of heat'. As is usual in thermodynamic discussions, this means 'net transfer of energy as heat', and does not refer to contributory transfers one way and the other. Heat cannot spontaneously 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, the refrigeration system.
Lord Kelvin expressed the second law in several wordings. Suppose there is an engine violating the Kelvin statement: i. Now pair it with a reversed Carnot engine as shown by the figure. Thus a violation of the Kelvin statement implies a violation of the Clausius statement, i. We can prove in a similar manner that the Kelvin statement implies the Clausius statement, and hence the two are equivalent.
Planck offered the following proposition as derived directly from experience. This is sometimes regarded as his statement of the second law, but he regarded it as a starting point for the derivation of the second law. It is almost customary in textbooks to speak of the " Kelvin-Planck statement " of the law, as for example in the text by ter Haar and Wergeland. The Kelvin—Planck statement or the heat engine statement of the second law of thermodynamics states that.
In every neighborhood of any state S of an adiabatically enclosed system there are states inaccessible from S. 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.
In , Max Planck wrote an important paper on the basics of thermodynamics. This formulation does not mention heat and does not mention temperature, nor even entropy, and does not necessarily implicitly rely on those concepts, but it implies the content of the second law.
A closely related statement is that "Frictional pressure never does positive work. Not mentioning entropy, this principle of Planck is stated in physical terms. It is very closely related to the Kelvin statement given just above. Nevertheless, this principle of Planck is not actually Planck's preferred statement of the second law, which is quoted above, in a previous sub-section of the present section of this present article, and relies on the concept of entropy. A statement that in a sense is complementary to Planck's principle is made by Borgnakke and Sonntag.
They do not offer it as a full statement of the second law:. Differing from Planck's just foregoing principle, this one is explicitly in terms of entropy change. Removal of matter from a system can also decrease its entropy. The second law has been shown to be equivalent to the internal energy U being a weakly convex function , when written as a function of extensive properties mass, volume, entropy, Before the establishment of the second law, many people who were interested in inventing a perpetual motion machine had tried to circumvent the restrictions of first law of thermodynamics by extracting the massive internal energy of the environment as the power of the machine.
Such a machine is called a "perpetual motion machine of the second kind". The second law declared the impossibility of such machines.
Carnot's theorem is a principle that limits the maximum efficiency for any possible engine. The efficiency solely depends on the temperature difference between the hot and cold thermal reservoirs.
Carnot's theorem states:. In his ideal model, the heat of caloric converted into work could be reinstated by reversing the motion of the cycle, a concept subsequently known as thermodynamic reversibility.
Carnot, however, further postulated that some caloric is lost, not being converted to mechanical work. Hence, no real heat engine could realise the Carnot cycle 's reversibility and was condemned to be less efficient. Though formulated in terms of caloric see the obsolete caloric theory , rather than entropy , this was an early insight into the second law.
The Clausius theorem states that in a cyclic process. The equality holds in the reversible case  and the strict inequality holds in the irreversible case. The reversible case is used to introduce the state function entropy. This is because in cyclic processes the variation of a state function is zero from state functionality. Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient.
In addition, a reversible heat engine operating between temperatures T 1 and T 3 must have the same efficiency as one consisting of two cycles, one between T 1 and another intermediate temperature T 2 , and the second between T 2 and T 3. This can only be the case if. According to the Clausius equality , for a reversible process. So we can define a state function S called entropy, which for a reversible process or for pure heat transfer  satisfies.
With this we can only obtain the difference of entropy by integrating the above formula. For any irreversible process, since entropy is a state function, we can always connect the initial and terminal states with an imaginary reversible process and integrating on that path to calculate the difference in entropy.
Now reverse the reversible process and combine it with the said irreversible process. Applying the Clausius inequality on this loop,.
An important and revealing idealized 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. Whatever changes to dS and dS R occur in the entropies of the sub-system and the surroundings individually, according to the Second Law the entropy S tot of the isolated total system must not decrease:.
It is convenient to define the right-hand-side as the exact derivative of a thermodynamic potential, called the availability or exergy E 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,.
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 E for an irreversible process and no change for a reversible process. 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. Thus, a negative value of the change in free energy G or A is a necessary condition for a process to be spontaneous. This is the most useful form of the second law of thermodynamics in chemistry, where free-energy changes can be calculated from tabulated enthalpies of formation and standard molar entropies of reactants and products.
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 during , in this form: heat does not flow spontaneously 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 fluid.
From there he was able to infer the principle of Sadi Carnot and the definition of entropy Established during 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. 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.
Equivalently, it says that time average and average over the statistical ensemble are the same.
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Engineering Thermodynamics pp Cite as. This chapter presents the second law of thermodynamics. This law will conform to your intuition—once you understand its significance and can apply it properly to both closed and open systems. Unable to display preview. Download preview PDF.
2nd Law of Thermodynamics
Samuel J. Summary 4. An irreversible process is one in which the system and its environment cannot return together to exactly the states that they were in. The irreversibility of any natural process results from the second law of thermodynamics. The Kelvin statement and Clausius statement of the second law of thermodynamics are equivalent.
The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system.
Chemistry for the gifted and talented: the second law of thermodynamics
According to Sommerfeld, the well known Clausius and Kelvin statements of the second law of thermodynamics comprises two parts. The first part includes the Carnot principle that all Carnot engines operating between the same temperatures have the same efficiency. The second part contains the law of increase in entropy.
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The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. Entropy predicts the direction of spontaneous processes, and determines whether they are irreversible or impossible, despite obeying the requirement of conservation of energy , which is established in the first law of thermodynamics. The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always arrive at a state of thermodynamic equilibrium , where the entropy is highest. If all processes in the system are reversible , the entropy is constant. An increase in entropy accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time. Historically, the second law was an empirical finding that was accepted as an axiom of thermodynamic theory. Statistical mechanics provides a microscopic explanation of the law in terms of probability distributions of the states of large assemblies of atoms or molecules.
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS. Carnot cycle. The Carnot process is a reversible cycle process bounded by two isotherms.
Thermodynamics is the study of heat, energy, and motion. Think dynamite-a powerful explosion of energy! The three laws of thermodynamics help us understand how heat, energy, and motion work within the universe. The 1st law of thermodynamics says energy cannot be created or destroyed. This law helps us understand that energy never disappears or goes away, it only gets moved around, or used in different ways.
За конторкой с надписью КОНСЬЕРЖ сидел вежливый подтянутый мужчина, улыбающийся так приветливо, словно всю жизнь ждал минуты, когда сможет оказать любезность посетителю. - En que puedo servile, senor. Чем могу служить, сеньор? - Он говорил нарочито шепеляво, а глаза его внимательно осматривали лицо и фигуру Беккера. Беккер ответил по-испански: - Мне нужно поговорить с Мануэлем. Загорелое лицо консьержа расплылось еще шире. - Si, si, senor. Мануэль - это .
- Ясно, что это будет число-монстр. Сзади послышался возглас: - Двухминутное предупреждение. Джабба в отчаянии бросил взгляд на ВР. Последний щит начал рушиться.
Что вам. Беккер понял, что ему следовало заранее отрепетировать разговор, прежде чем колотить в дверь. Он искал нужные слова. - У вас есть кое-что, что я должен получить.
У меня чутье. У нее чутье. Ну вот, на Мидж снова что-то нашло. - Если Стратмор не забил тревогу, то зачем тревожиться. - Да в шифровалке темно как в аду, черт тебя дери.
Хейл мог понять смысл лишь двух слов. Но этого было достаточно. СЛЕДОПЫТ ИЩЕТ… - Следопыт? - произнес. - Что он ищет? - Мгновение он испытывал неловкость, всматриваясь в экран, а потом принял решение. Хейл достаточно понимал язык программирования Лимбо, чтобы знать, что он очень похож на языки Си и Паскаль, которые были его стихией.
Стратмор замялся, не зная, что ответить.