Thermodynamics2

History

The history of thermodynamics as a scientific discipline generally begins with Otto von Guericke who, in 1650, built and designed the world's first vacuum pump and demonstrated a vacuum using hisMagdeburg hemispheres. Guericke was driven to make a vacuum in order to disprove Aristotle's long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the English physicist and chemist Robert Boyle had learned of Guericke's designs and, in 1656, in coordination with English scientist Robert Hooke, built an air pump.^[24] Using this pump, Boyle and Hooke noticed a correlation between pressure, temperature, and volume. In time,Boyle's Law was formulated, which states that pressure and volume are inversely proportional. Then, in 1679, based on these concepts, an associate of Boyle's named Denis Papin built asteam digester, which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated.

Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a piston and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer Thomas Savery built the first engine, followed by Thomas Newcomen in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.

The fundamental concepts of heat capacity and latent heat, which were necessary for the development of thermodynamics, were developed by Professor Joseph Black at the University of Glasgow, whereJames Watt was employed as an instrument maker. Black and Watt performed experiments together, but it was Watt who conceived the idea of the external condenser which resulted in a large increase in steam engine efficiency.^[25] Drawing on all the previous work led Sadi Carnot, the "father of thermodynamics", to publish Reflections on the Motive Power of Fire (1824), a discourse on heat, power, energy and engine efficiency. The paper outlined the basic energetic relations between the Carnot engine, the Carnot cycle, and motive power. It marked the start of thermodynamics as a modern science.^[11]

The first thermodynamic textbook was written in 1859 by William Rankine, originally trained as a physicist and a civil and mechanical engineering professor at the University of Glasgow.^[26] The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of William Rankine, Rudolf Clausius, and William Thomson (Lord Kelvin).

The foundations of statistical thermodynamics were set out by physicists such as James Clerk Maxwell, Ludwig Boltzmann, Max Planck,Rudolf Clausius and J. Willard Gibbs.

During the years 1873-76 the American mathematical physicist Josiah Willard Gibbs published a series of three papers, the most famous being On the Equilibrium of Heterogeneous Substances,^[4] in which he showed how thermodynamic processes, including chemical reactions, could be graphically analyzed, by studying the energy, entropy, volume, temperature and pressure of the thermodynamic systemin such a manner, one can determine if a process would occur spontaneously.^[27] Also Pierre Duhem in the 19th century wrote about chemical thermodynamics.^[5] During the early 20th century, chemists such as Gilbert N. Lewis, Merle Randall,^[6] and E. A. Guggenheim^[7][8]applied the mathematical methods of Gibbs to the analysis of chemical processes.

In 1909, Constantin Carathéodory presented a purely mathematical axiomatic formulation of equilibrium thermodynamics, a description often referred to as geometrical thermodynamics.

[edit]Etymology

The etymology of thermodynamics has an intricate history.^[28] It was first spelled in a hyphenated form as an adjective (thermo-dynamic) and from 1854 to 1868 as the noun thermo-dynamics to represent the science of generalized heat engines.^[28]

The components of the word thermodynamics are derived from the Greek words θέρμη therme, meaning heat, and δύναμις dynamis, meaning power.^[29][30][31]

Pierre Perrot claims that the term thermodynamics was coined by James Joule in 1858 to designate the science of relations between heat and power.^[11] Joule, however, never used that term, but used instead the term perfect thermo-dynamic engine in reference to Thomson’s 1849^[32] phraseology.^[28]

By 1858, thermo-dynamics, as a functional term, was used in William Thomson's paper An Account of Carnot's Theory of the Motive Power of Heat.^[32]

[edit]Branches of description

The study of thermodynamical systems has developed into several related branches, each using a different fundamental model as a theoretical or experimental basis, or applying the principles to varying types of systems.

[edit]Classical thermodynamics

Classical thermodynamics is the description of the states (especially equilibrium states) and processes of thermodynamical systems, using macroscopic, empirical properties directly measurable in the laboratory. It is used to model exchanges of energy, work, heat, and matter, based on the laws of thermodynamics. The qualifier classical reflects the fact that it represents the descriptive level in terms of macroscopic empirical parameters that can be measured in the laboratory, that was the first level of understanding in the 19th century. A microscopic interpretation of these concepts was provided by the development of statistical thermodynamics.

[edit]Statistical thermodynamics

Statistical thermodynamics, also called statistical mechanics, emerged with the development of atomic and molecular theories in the second half of the 19th century and early 20th century, supplementing thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states. This field relates the microscopic properties of individual atoms and molecules to the macroscopic, bulk properties of materials that can be observed on the human scale, thereby explaining thermodynamics as a natural result of statistics, classical mechanics, and quantum theory at the microscopic level.

[edit]Chemical thermodynamics

Chemical thermodynamics is the study of the interrelation of energy with chemical reactions and chemical transport and with physical changes of state within the confines of the laws of thermodynamics.

[edit]Treatment of equilibrium

Equilibrium thermodynamics studies transformations of matter and energy in systems as they approach equilibrium. The equilibrium means balance. In a thermodynamic equilibrium state there is no macroscopic flow and no macroscopic change is occurring or can be triggered; within the system, every microscopic process is balanced by its opposite; this is called the principle of detailed balance. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial state, subject to accurately specified constraints, to calculate what the state of the system will be once it has reached equilibrium. A thermodynamic system is said to be homogeneous when all its locally defined intensive variables are spatially invariant. A system in thermodynamic equilibrium is homogeneous unless it is affected by a time-invariant externally imposed field of force, such as gravity, electricity, or magnetism.

Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium; for they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. For their thermodynamic study, more general concepts are required for non-equilibrium systems than for equilibrium systems. Non-equilibrium systems can be in stationary states that are not homogeneous even when there is no externally imposed field of force; in this case, the description of the internal state of the system requires a field theory.^[33][34][35] Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.

[edit]Laws of thermodynamics

Main article: Laws of thermodynamics

Thermodynamics states a set of four laws which are valid for all systems that fall within the constraints implied by each. In the various theoretical descriptions of thermodynamics these laws may be expressed in seemingly differing forms, but the most prominent formulations are the following:

• Zeroth law of thermodynamics: If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.

This statement implies that thermal equilibrium is an equivalence relation on the set of thermodynamic systems under consideration. Systems are said to be in equilibrium if the small, random exchanges between them (e.g. Brownian motion) do not lead to a net change in energy. This law is tacitly assumed in every measurement of temperature. Thus, if one seeks to decide if two bodies are at the sametemperature, it is not necessary to bring them into contact and measure any changes of their observable properties in time.^[36] The law provides an empirical definition of temperature and justification for the construction of practical thermometers.

The zeroth law was not initially recognized as a law, as its basis in thermodynamical equilibrium was implied in the other laws. The first, second, and third laws had been explicitly stated prior and found common acceptance in the physics community. Once the importance of the zeroth law for the definition of temperature was realized, it was impracticable to renumber the other laws, hence it was numbered the zeroth law.

• First law of thermodynamics: A change in the internal energy of a closed thermodynamic system is equal to the difference between theheat supplied to the system and the amount of work done by the system on its surroundings.^{[37][38][39][40][41][42][43][44][45][46]}

The first law of thermodynamics asserts the existence of a state variable for a system, the internal energy, and tells how it changes in thermodynamic processes. The law allows a given internal energy of a system to be reached by any combination of heat and work. It is important that internal energy is a variable of state of the system (see Thermodynamic state) whereas heat and work change the state of the system.

The first law observes that the internal energy obeys the principle of conservation of energy, which states that energy can be transformed (changed from one form to another), but cannot be created or destroyed.^[47]

• Second law of thermodynamics: Heat cannot spontaneously flow from a colder location to a hotter location.

The second law of thermodynamics is an expression of the universal principle of decay observable in nature. The second law is an observation of the fact that over time, differences in temperature, pressure, and chemical potential tend to even out in a physical system that is isolated from the outside world. Entropy is a measure of how much this process has progressed. The entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos. There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of irreversibility in nature.

• Third law of thermodynamics: As a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.

The third law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching absolute zero of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions are, "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".

Absolute zero, at which all activity (with the exception of that caused by zero point energy) would stop is −273.15 °C (degrees Celsius), or −459.67 °F (degrees Fahrenheit) or 0 K (kelvin).

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Thermodynamics1

Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation. It interrelates macroscopic variables, such as temperature, volume and pressure, which describe physical properties of material bodies and radiation, which in this science are called thermodynamic systems.

Historically, thermodynamics developed out of a desire to increase the efficiency of earlysteam engines, particularly through the work of French physicist Nicolas Léonard Sadi Carnot (1824) who believed that the efficiency of heat engines was the key that could help France win the Napoleonic Wars.^[1] Scottish physicist Lord Kelvin was the first to formulate a concise definition of thermodynamics in 1854:^[2]

Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency.

Initially, the thermodynamics of heat engines concerned mainly the thermal properties of their 'working materials', such as steam. This concern was then linked to the study of energy transfers in chemical processes, for example to the investigation, published in 1840, of the heats of chemical reactions^[3] by Germain Hess, which was not originally explicitly concerned with the relation between energy exchanges by heat and work. Chemical thermodynamics studies the the role of entropy in chemical reactions.^{[4][5][6][7][8][9] [10][11][12]}Also, statistical thermodynamics, or statistical mechanics, gave explanations of macroscopic thermodynamics by statistical predictions of the collective motion of particles based on the mechanics of their microscopic behavior.

Thermodynamics describes how systems change when they interact with one another or with their surroundings. This can be applied to a wide variety of topics in science and engineering, such asengines, phase transitions, chemical reactions, transport phenomena, and even black holes. The results of thermodynamics are essential for other fields of physics and for chemistry, chemical engineering, aerospace engineering, mechanical engineering, cell biology, biomedical engineering,materials science, and are useful for other fields such as economics.^[13][14]

Many of the empirical facts of thermodynamics are comprehended in its four laws. The first law specifies that energy can be exchanged between physical systems as heat and thermodynamic work.^[15] The second law concerns a quantity called entropy, that expresses limitations, arising from what is known as irreversibility, on the amount of thermodynamic work that can be delivered to an external system by a thermodynamic process.^[16] Many writers offer various axiomatic formulations of thermodynamics, as if it were a completed subject, but non-equilibrium processes continue to make difficulties for it.

Introduction

Thermodynamics concerns material and radiative phenomena that are experimentally reproducible. For example, a state of thermodynamic equilibrium is a steady state reached after a system has aged so that it no longer changes with the passage of time. But more than that, for thermodynamics, a system, defined by its being prepared in a certain way must, consequent on every particular occasion of preparation, upon aging, reach one and the same eventual state of thermodynamic equilibrium, entirely determined by the way of preparation. The meanings of the terms used in this statement are clarified in the following, but experimental reproducibility is a primary and fundamental requirement for thermodynamics. This is the source of the strengths and the weaknesses of thermodynamics. Thermodynamics does not deal with phenomena that are not experimentally reproducible.

Thermodynamics is built on the study of energy transfers that can be strictly resolved into two distinct components, heat and work, specified by macroscopic variables.^[17] Though thermodynamics originated in the study of cyclic non-equilibrium processes such as the working of heat engines, study of the subject gradually revealed that the notion of heat is inextricably tied to the notion of thermodynamic equilibrium.^[18]Thermodynamics is well understood and validated for systems in thermodynamic equilibrium, but as the systems of interest become further and further from thermodynamic equilibrium, their thermodynamical study becomes more and more difficult. Systems in thermodynamic equilibrium have very well experimentally reproducible behaviour, and as interest moves further towards non-equilibrium systems, experimental reproducibility becomes more difficult. The present article takes a gradual approach to the subject, starting with a focus on cyclic processes and thermodynamic equilibrium, and then gradually beginning to further consider non-equilibrium systems.

Basic for thermodynamics are the concepts of system and surroundings.^[8][19]

There are two fundamental kinds of entity in thermodynamics, states of a system, and processes of a system. This allows two fundamental approaches to thermodynamic reasoning, that in terms of states of a system, and that in terms of cyclic processes of a system.

A thermodynamic system can be defined in terms of its states. In this way, a thermodynamic system is a macroscopic physical object, explicitly specified in terms of macroscopic physical and chemical variables which describe its macroscopic properties. The macroscopic state variables of thermodynamics have been recognized in the course of empirical work in physics and chemistry.^[9]

A thermodynamic system can also be defined in terms of the processes which it can undergo. Of particular interest are cyclic processes. This was the way of the founders of thermodynamics in the first three quarters of the nineteenth century.

The surroundings of a thermodynamic system are other thermodynamic systems that can interact with it. An example of a thermodynamic surrounding is a heat bath, which is considered to be held at a prescribed temperature, regardless of the interactions it might have with the system.

The macroscopic variables of a thermodynamic system can under some conditions be related to one another through equations of state. They express the constitutive peculiarities of the material of the system. Classical thermodynamics is characterized by its study of materials that have equations of state that express relations between mechanical variables and temperature that are reached much more rapidly than any changes in the surroundings. A classical material can usually be described by a function that makes pressure dependent on volume and temperature, the resulting pressure being established much more rapidly than any imposed change of volume or temperature.^[20]

Thermodynamic facts can often be explained by viewing macroscopic objects as assemblies of very many microscopic or atomic objects that obey Hamiltonian dynamics.^[8][21][22] The microscopic or atomic objects exist in species, the objects of each species being all alike. Because of this likeness, statistical methods can be used to account for the macroscopic properties of the thermodynamic system in terms of the properties of the microscopic species. Such explanation is called statistical thermodynamics; also often it is also referred to by the term 'statistical mechanics', though this term can have a wider meaning, referring to 'microscopic objects', such as economic quantities, that do not obey Hamiltonian dynamics.^[21]

The thermodynamicists representative of the original eight founding schools of thermodynamics. The schools with the most-lasting effect in founding the modern versions of thermodynamics are the Berlin school, particularly as established inRudolf Clausius’s 1865 textbook The Mechanical Theory of Heat, the Vienna school, with the statistical mechanics of Ludwig Boltzmann, and the Gibbsian school at Yale University, American engineer Willard Gibbs' 1876 On the Equilibrium of Heterogeneous Substances launching chemical thermodynamics.^[23]

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