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# thermodynamics

[thur-moh-dahy-nam-iks]
thermodynamics, branch of science concerned with the nature of heat and its conversion to mechanical, electric, and chemical energy. Historically, it grew out of efforts to construct more efficient heat engines—devices for extracting useful work from expanding hot gases.

## The Thermodynamic System and Its Environment

In thermodynamics, one usually considers both the thermodynamic system and its environment. The environment often contains one or more idealized heat reservoirs—heat sources with infinite heat capacity enabling them to give up or absorb heat without changing their temperature. (An ocean or other large body of water approximates a heat reservoir.) A typical thermodynamic system is a definite quantity of gas enclosed in a cylinder with a sliding piston that allows the volume to vary. In general, a thermodynamic system is defined by its temperature, volume, pressure, and chemical composition. A system is in equilibrium when these variables have the same value at all points.

A mathematical statement that links the variables to show their interdependence is called an equation of state; the gas laws are simple examples of such equations. Equations of state take on their simplest form when the Kelvin temperature scale is used; on this scale 0° corresponds to the lowest temperature theoretically possible.

When the external conditions are altered, a thermodynamic system will respond by changing its state; the temperature, volume, pressure, and chemical composition will adjust to a new equilibrium. The most important kinds of changes are adiabatic and isothermal changes. An adiabatic change is one that occurs without any flow of heat. The system is thermally insulated from the environment, and the first law of thermodynamics requires that the work done by or on the system be equal to the loss or gain of the system's internal energy. An isothermal change occurs when the system is in contact with a heat reservoir, so that the system remains at the temperature of the reservoir. In the isothermal process, heat flows from the reservoir if the system is expanding and into the reservoir if the system is being compressed. For an ideal gas the internal energy depends only on the temperature; hence the internal energy remains constant during an isothermal change, and the heat absorbed from or by the reservoir is equal to the work done on or by the environment.

## The First Law of Thermodynamics

Toward the middle of the 19th cent. heat was recognized as a form of energy associated with the motion of the molecules of a body (see kinetic-molecular theory of gases). Speaking more strictly, heat refers only to energy that is being transferred from one body to another. The total energy a body contains as a result of the positions and motions of its molecules is called its internal energy; in general, a body's temperature is a direct measure of its internal energy. All bodies can increase their internal energies by absorbing heat (see heat capacity). However, mechanical work done on a body can also increase its internal energy; e.g., the internal energy of a gas increases when the gas is compressed. Conversely, internal energy can be converted into mechanical energy; e.g., when a gas expands it does work on the external environment. In general, the change in a body's internal energy is equal to the heat absorbed from the environment minus the work done on the environment. This statement constitutes the first law of thermodynamics, which is a general form of the law of conservation of energy (see conservation laws).

## The Second Law of Thermodynamics

A cyclic process is one that returns the system, but not the environment, to its original state. A closed cycle consisting of two isothermal and two adiabatic transformations is called a Carnot cycle after the French physicist Sadi Carnot, who first discussed the implications of such cycles. During the Carnot cycle occurring in the operation of a heat engine, a definite quantity of heat is absorbed from a reservoir at high temperature; part of this heat is converted into useful work, but the balance is expelled into a low-temperature reservoir and thus "wasted." The greater the temperature difference between the two reservoirs, which in a steam engine are represented by the boiler and the condenser, the greater the fraction of absorbed heat that is converted into useful work. It is, however, theoretically impossible to convert all the heat extracted from the reservoir into useful work.

In general it is impossible to perform a transformation whose only final result is to convert into useful work heat extracted from a source that is at the same temperature throughout. This statement is Lord Kelvin's version of the second law of thermodynamics. Another version of this law, formulated by R. J. E. Clausius, states that a transformation is impossible whose only final result is to transfer heat from a body at a given temperature to a body at higher temperature; in other words, the spontaneous flow of heat from hot to cold bodies is reversible only with the expenditure of mechanical or other nonthermal energy. These two versions of the second law of thermodynamics can be shown to be entirely equivalent.

The second law is expressed mathematically in terms of the concept of entropy. When a body absorbs an amount of heat Q from a reservoir at temperature T, the body gains and the reservoir loses an amount of entropy S=Q/T. Thus, in a reversible adiabatic process (no heat change) there is no change in the total entropy. If an amount of heat Q flows from a hot to a cold body, the total entropy increases; because S=Q/T is larger for smaller values of T, the cold body gains more entropy than the hot body loses. The statement that heat never flows from a cold to a hot body can be generalized by saying that in no spontaneous process does the total entropy decrease.

In all real physical processes entropy increases; in ideal reversible processes entropy remains constant. Thus, in the Carnot cycle, which is reversible, there is no change in the total entropy. The engine itself experiences no net change in entropy because it is returned to its original state at the end of the cycle. The entropy gained by the low temperature reservoir is equal to the entropy lost by the high temperature reservoir. However, according to the formula S=Q/T, less heat need be expelled into the low temperature reservoir than is extracted from the high temperature reservoir for equal and opposite changes in entropy. In the Carnot cycle this difference in heat appears as useful mechanical work.

## The Third Law of Thermodynamics

A postulate related to but independent of the second law is that it is impossible to cool a body to absolute zero by any finite process. Although one can approach absolute zero as closely as one desires, one cannot actually reach this limit. The third law of thermodynamics, formulated by Walter Nernst and also known as the Nernst heat theorem, states that if one could reach absolute zero, all bodies would have the same entropy. In other words, a body at absolute zero could exist in only one possible state, which would possess a definite energy, called the zero-point energy. This state is defined as having zero entropy.

## Bibliography

See E. Fermi, Thermodynamics (1937); F. W. Sears, Thermodynamics, the Kinetic Theory of Gases, and Statistical Mechanics (2d ed. 1953); M. W. Zemansky, Heat and Thermodynamics (5th ed. 1968).

Study of the relationships among heat, work, temperature, and energy. Any physical system will spontaneously approach an equilibrium that can be described by specifying its properties, such as pressure, temperature, or chemical composition. If external constraints are allowed to change, these properties generally change. The three laws of thermodynamics describe these changes and predict the equilibrium state of the system. The first law states that whenever energy is converted from one form to another, the total quantity of energy remains the same. The second law states that, in a closed system, the entropy of the system does not decrease. The third law states that, as a system approaches absolute zero, further extraction of energy becomes more and more difficult, eventually becoming theoretically impossible.

In physics, thermodynamics (from the Greek θερμη, therme, meaning "heat and δυναμις, dynamis, meaning "power") is the study of the transformation of energy into different forms and its relation to macroscopic variables such as temperature, pressure, and volume. Its underpinnings, based upon statistical predictions of the collective motion of particles from their microscopic behavior, is the field of statistical thermodynamics, a branch of statistical mechanics. Roughly, heat means "energy in transit" and dynamics relates to "movement"; thus, in essence thermodynamics studies the movement of energy and how energy instills movement. Historically, thermodynamics developed out of need to increase the efficiency of early steam engines.

The starting point for most thermodynamic considerations are the laws of thermodynamics, which postulate that energy can be exchanged between physical systems as heat or work. They also postulate the existence of a quantity named entropy, which can be defined for any system. In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of system and surroundings. A system is composed of particles, whose average motions define its properties, which in turn are related to one another through equations of state. Properties can be combined to express internal energy and thermodynamic potentials, which are useful for determining conditions for equilibrium and spontaneous processes.

With these tools, thermodynamics describes how systems respond to changes in their surroundings. This can be applied to a wide variety of topics in science and engineering, such as engines, 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 economics to name a few.

## 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 created the world's first ever vacuum (known as the Magdeburg 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 Irish 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. 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 a bone 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. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.

Their work led 127 years later to Sadi Carnot, the "father of thermodynamics", who, in 1824, published Reflections on the Motive Power of Fire, a discourse on heat, power, and engine efficiency. The paper outlined the basic energetic relations between the Carnot engine, the Carnot cycle, and Motive power. This marks the start of thermodynamics as a modern science.

The term thermodynamics was coined by James Joule in 1849 to designate the science of relations between heat and power. 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. 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.

## The laws of thermodynamics

In thermodynamics, there are four laws of very general validity, and as such they do not depend on the details of the interactions or the systems being studied. Hence, they can be applied to systems about which one knows nothing other than the balance of energy and matter transfer. Examples of this include Einstein's prediction of spontaneous emission around the turn of the 20th century and current research into the thermodynamics of black holes.

The four laws are:

If two thermodynamic systems are separately in thermal equilibrium with a third, they are also in thermal equilibrium with each other.

The change in the internal energy of a closed thermodynamic system is equal to the sum of the amount of heat energy supplied to the system and the work done on the system.

The total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value.

As a system asymptotically approaches absolute zero of temperature all processes virtually cease and the entropy of the system asymptotically approaches a minimum value; also stated as: "the entropy of all systems and of all states of a system is zero at absolute zero" or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".

Express the equality of certain relations between flows and forces in thermodynamic systems out of equilibrium, but where a notion of local equilibrium exists.

## Thermodynamic potentials

As can be derived from the energy balance equation (or Burks' equation) on a thermodynamic system there exist energetic quantities called thermodynamic potentials, being the quantitative measure of the stored energy in the system. The five most well known potentials are:

Internal energy $U,$
Helmholtz free energy $A=U-TS,$
Enthalpy $H=U+PV,$
Gibbs free energy $G=U+PV-TS,$
Grand potential $Phi_\left\{G\right\}=U-TS-mu N,$

Other thermodynamic potentials can be obtained through Legendre transformation. Potentials are used to measure energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. Internal energy is the internal energy of the system, enthalpy is the internal energy of the system plus the energy related to pressure-volume work, and Helmholtz and Gibbs energy are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.

## Classical thermodynamics

Classical thermodynamics is the original early 1800s variation of thermodynamics concerned with thermodynamic states, and properties as energy, work, and heat, and with the laws of thermodynamics, all lacking an atomic interpretation. In precursory form, classical thermodynamics derives from chemist Robert Boyle’s 1662 postulate that the pressure P of a given quantity of gas varies inversely as its volume V at constant temperature; i.e. in equation form: PV = k, a constant. From here, a semblance of a thermo-science began to develop with the construction of the first successful atmospheric steam engines in England by Thomas Savery in 1697 and Thomas Newcomen in 1712. 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).

## Statistical thermodynamics

With the development of atomic and molecular theories in the late 1800s and early 1900s, thermodynamics was given a molecular interpretation. This field is called statistical thermodynamics, which can be thought of as a bridge between macroscopic and microscopic properties of systems. Essentially, statistical thermodynamics is an approach to thermodynamics situated upon statistical mechanics, which focuses on the derivation of macroscopic results from first principles. It can be opposed to its historical predecessor phenomenological thermodynamics, which gives scientific descriptions of phenomena with avoidance of microscopic details. The statistical approach is to derive all macroscopic properties (temperature, volume, pressure, energy, entropy, etc.) from the properties of moving constituent particles and the interactions between them (including quantum phenomena). It was found to be very successful and thus is commonly used.

## Chemical thermodynamics

Chemical thermodynamics is the study of the interrelation of heat with chemical reactions or with a physical change of state within the confines of the laws of thermodynamics. 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, in which he showed how thermodynamic processes could be graphically analyzed, by studying the energy, entropy, volume, temperature and pressure of the thermodynamic system, in such a manner to determine if a process would occur spontaneously. During the early 20th century, chemists such as Gilbert N. Lewis, Merle Randall, and E. A. Guggenheim began to apply the mathematical methods of Gibbs to the analysis of chemical processes.

## Thermodynamic systems

An important concept in thermodynamics is the “system”. Everything in the universe except the system is known as surroundings. A system is the region of the universe under study. A system is separated from the remainder of the universe by a boundary which may be imaginary or not, but which by convention delimits a finite volume. The possible exchanges of work, heat, or matter between the system and the surroundings take place across this boundary. Boundaries are of four types: fixed, moveable, real, and imaginary.

Basically, the “boundary” is simply an imaginary dotted line drawn around a volume of something when there is going to be a change in the internal energy of that something. Anything that passes across the boundary that effects a change in the internal energy of the something needs to be accounted for in the energy balance equation. That something can be the volumetric region surrounding a single atom resonating energy, such as Max Planck defined in 1900; it can be a body of steam or air in a steam engine, such as Sadi Carnot defined in 1824; it can be the body of a tropical cyclone, such as Kerry Emanuel theorized in 1986 in the field of atmospheric thermodynamics; it could also be just one nuclide (i.e. a system of quarks) as some are theorizing presently in quantum thermodynamics.

For an engine, a fixed boundary means the piston is locked at its position; as such, a constant volume process occurs. In that same engine, a moveable boundary allows the piston to move in and out. For closed systems, boundaries are real while for open system boundaries are often imaginary. There are five dominant classes of systems:

1. Isolated Systems – matter and energy may not cross the boundary
2. Adiabatic Systems – heat must not cross the boundary
3. Diathermic Systems - heat may cross boundary
4. Closed Systems – matter may not cross the boundary
5. Open Systems – heat, work, and matter may cross the boundary (often called a control volume in this case)

As time passes in an isolated system, internal differences in the system tend to even out and pressures and temperatures tend to equalize, as do density differences. A system in which all equalizing processes have gone practically to completion, is considered to be in a state of thermodynamic equilibrium.

In thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than systems which are not in equilibrium. Often, when analysing a thermodynamic process, it can be assumed that each intermediate state in the process is at equilibrium. This will also considerably simplify the situation. Thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state are said to be reversible processes.

## Thermodynamic parameters

The central concept of thermodynamics is that of energy, the ability to do work. As stipulated by the first law, the total energy of the system and its surroundings is conserved. It may be transferred into a body by heating, compression, or addition of matter, and extracted from a body either by cooling, expansion, or extraction of matter. For comparison, in mechanics, energy transfer results from a force which causes displacement, the product of the two being the amount of energy transferred. In a similar way, thermodynamic systems can be thought of as transferring energy as the result of a generalized force causing a generalized displacement, with the product of the two being the amount of energy transferred. These thermodynamic force-displacement pairs are known as conjugate variables. The most common conjugate thermodynamic variables are pressure-volume (mechanical parameters), temperature-entropy (thermal parameters), and chemical potential-particle number (material parameters).

## Thermodynamic instruments

There are two types of thermodynamic instruments, the meter and the reservoir. A thermodynamic meter is any device which measures any parameter of a thermodynamic system. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the zeroth law states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by James Maxwell in 1872, asserts that it is possible to measure temperature. An idealized thermometer is a sample of an ideal gas at constant pressure. From the ideal gas law PV=nRT, the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called a barometer may also be constructed from a sample of an ideal gas held at a constant temperature. A calorimeter is a device which is used to measure and define the internal energy of a system.

A thermodynamic reservoir is a system which is so large that it does not appreciably alter its state parameters when brought into contact with the test system. It is used to impose a particular value of a state parameter upon the system. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon any test system that it is mechanically connected to. The earth's atmosphere is often used as a pressure reservoir.

It is important that these two types of instruments are distinct. A meter does not perform its task accurately if it behaves like a reservoir of the state variable it is trying to measure. If, for example, a thermometer were to act as a temperature reservoir it would alter the temperature of the system being measured, and the reading would be incorrect. Ideal meters have no effect on the state variables of the system they are measuring.

## Thermodynamic states

When a system is at equilibrium under a given set of conditions, it is said to be in a definite state. The state of the system can be described by a number of intensive variables and extensive variables. The properties of the system can be described by an equation of state which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant

## Thermodynamic processes

A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. Typically, each thermodynamic process is distinguished from other processes, in energetic character, according to what parameters, as temperature, pressure, or volume, etc., are held fixed. Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a conjugate pair. The seven most common thermodynamic processes are shown below:

1. An isobaric process occurs at constant pressure.
2. An isochoric process, or isometric/isovolumetric process, occurs at constant volume.
3. An isothermal process occurs at a constant temperature.
4. An adiabatic process occurs without loss or gain of heat.
5. An isentropic process (reversible adiabatic process) occurs at a constant entropy.
6. An isenthalpic process occurs at a constant enthalpy.
7. A steady state process occurs without a change in the internal energy of a system.