History
1824
Work, i.e. "weight ''lifted'' through a height", was originally defined in 1824 by Sadi Carnot in his famous paper '' Reflections on the Motive Power of Fire'', where he used the term ''motive power'' for work. Specifically, according to Carnot:We use here motive power to express the useful effect that a motor is capable of producing. This effect can always be likened to the elevation of a weight to a certain height. It has, as we know, as a measure, the product of the weight multiplied by the height to which it is raised.
1845
In 1845, the English physicistOverview
Conservation of energy
A pre-supposed guiding principle of thermodynamics is the conservation of energy. The total energy of a system is the sum of its internal energy, of its potential energy as a whole system in an external force field, such as gravity, and of its kinetic energy as a whole system in motion. Thermodynamics has special concern with transfers of energy, from a body of matter, such as, for example a cylinder of steam, to the surroundings of the body, by mechanisms through which the body exerts macroscopic forces on its surroundings so as to lift a weight there; such mechanisms are the ones that are said to mediate ''thermodynamic'' work. Besides transfer of energy as work, thermodynamics admits transfer of energy asNearly reversible transfer of energy by work in the surroundings
In the surroundings of a thermodynamic system, external to it, all the various mechanical and non-mechanical macroscopic forms of work can be converted into each other with no limitation in principle due to the laws of thermodynamics, so that the energy conversion efficiency can approach 100% in some cases; such conversion is required to be frictionless, and consequently adiabatic.F.C.Andrews ''Thermodynamics: Principles and Applications'' (Wiley-Interscience 1971), , p.17-18. In particular, in principle, all macroscopic forms of work can be converted into the mechanical work of lifting a weight, which was the original form of thermodynamic work considered by Carnot and Joule (see History section above). Some authors have considered this equivalence to the lifting of a weight as a defining characteristic of work. For example, with the apparatus of Joule's experiment in which, through pulleys, a weight descending in the surroundings drives the stirring of a thermodynamic system, the descent of the weight can be diverted by a re-arrangement of pulleys, so that it lifts another weight in the surroundings, instead of stirring the thermodynamic system. Such conversion may be idealized as nearly frictionless, though it occurs relatively quickly. It usually comes about through devices that are not simple thermodynamic systems (a simple thermodynamic system is a homogeneous body of material substances). For example, the descent of the weight in Joule's stirring experiment reduces the weight's total energy. It is described as loss ofWork done by and on a simple thermodynamic system
Work done on, and work done by, a thermodynamic system need to be distinguished, through consideration of their precise mechanisms. Work done on a thermodynamic system, by devices or systems in the surroundings, is performed by actions such asProcesses not described by macroscopic work
One kind of heat transfer, through direct contact between a closed system and its surroundings, is by the ''microscopic'' thermal motions of particles and their associated inter-molecular potential energies.G.J. Van Wylen and R.E. Sonntag, ''Fundamentals of Classical Thermodynamics'', Chapter 4 - ''Work and heat'', (3rd edition) Microscopic accounts of such processes are the province of statistical mechanics, not of macroscopic thermodynamics. Another kind of heat transfer is by radiation.Prevost, P. (1791). Mémoire sur l'equilibre du feu. ''Journal de Physique'' (Paris), vol 38 pp. 314-322.Planck, M. (1914). ''The Theory of Heat Radiation'', second edition translated by M. Masius, P. Blakiston's Son and Co., Philadelphia, 1914. Radiative transfer of energy is irreversible in the sense that it occurs only from a hotter to a colder system, never the other way. There are several forms of dissipative transduction of energy that can occur internally within a system at a microscopic level, such as friction including bulk and shear viscosityRayleigh, J.W.S (1878/1896/1945). ''The Theory of Sound'', volume 2, Dover, New YorkOpen systems
For an open system, the first law of thermodynamics admits three forms of energy transfer, as work, as heat, and as energy associated with matter that is transferred. The latter cannot be split uniquely into heat and work components. One-way convection of internal energy is a form a transport of energy but is not, as sometimes mistakenly supposed (a relic of the caloric theory of heat), transfer of energy as heat, because one-way convection is transfer of matter; nor is it transfer of energy as work. Nevertheless, if the wall between the system and its surroundings is thick and contains fluid, in the presence of a gravitational field, convective circulation within the wall can be considered as indirectly mediating transfer of energy as heat between the system and its surroundings, though the source and destination of the transferred energy are not in direct contact.Fictively imagined reversible thermodynamic "processes"
For purposes of theoretical calculations about a thermodynamic system, one can imagine fictive idealized thermodynamic "processes" that occur so slowly that they do not incur friction within or on the surface of system; they can then be regarded as virtually reversible. These fictive processes proceed along paths on geometrical surfaces that are described exactly by a characteristic equation of the thermodynamic system. Those geometrical surfaces are the loci of possible states of thermodynamic equilibrium for the system. Really possible thermodynamic processes, occurring at practical rates, even when they occur only by work assessed in the surroundings as adiabatic, without heat transfer, always incur friction within the system, and so are always irreversible. The paths of such really possible processes always depart from those geometrical characteristic surfaces. Even when they occur only by work assessed in the surroundings as adiabatic, without heat transfer, such departures always entail entropy production.Joule heating and rubbing
The definition of thermodynamic work is in terms of the changes of the system's extensive deformation (and chemical constitutive and certain other) state variables, such as volume, molar chemical constitution, or electric polarisation. Examples of state variables that are not extensive deformation or other such variables are temperature and entropy , as for example in the expression . Changes of such variables are not actually physically measureable by use of a single simple adiabatic thermodynamic process; they are processes that occur neither by thermodynamic work nor by transfer of matter, and therefore are said occur by heat transfer. The quantity of thermodynamic work is defined as work done by the system on its surroundings. According to the second law of thermodynamics, such work is irreversible. To get an actual and precise physical measurement of a quantity of thermodynamic work, it is necessary to take account of the irreversibility by restoring the system to its initial condition by running a cycle, for example a Carnot cycle, that includes the target work as a step. The work done by the system on its surroundings is calculated from the quantities that constitute the whole cycle.Lavenda, B.H. (2010). ''A New Perspective on Thermodynamics'', Springer, New York, , pp. 117–118. A different cycle would be needed to actually measure the work done by the surroundings on the system. This is a reminder that rubbing the surface of a system appears to the rubbing agent in the surroundings as mechanical, though not thermodynamic, work done on the system, not as heat, but appears to the system as heat transferred to the system, not as thermodynamic work. The production of heat by rubbing is irreversible; historically, it was a piece of evidence for the rejection of the caloric theory of heat as a conserved substance.Lavenda, B.H. (2010). ''A New Perspective on Thermodynamics'', Springer, New York, , page 20. The irreversible process known as Joule heating also occurs through a change of a non-deformation extensive state variable. Accordingly, in the opinion of Lavenda, work is not as primitive concept as is heat, which can be measured by calorimetry.Lavenda, B.H. (2010). ''A New Perspective on Thermodynamics'', Springer, New York, , page 120. This opinion does not negate the now customary thermodynamic definition of heat in terms of adiabatic work. Known as a thermodynamic operation, the initiating factor of a thermodynamic process is, in many cases, a change in the permeability of a wall between the system and the surroundings. Rubbing is not a change in wall permeability. Kelvin's statement of the second law of thermodynamics uses the notion of an "inanimate material agency"; this notion is sometimes regarded as puzzling.Lavenda, B.H. (2010). ''A New Perspective on Thermodynamics'', Springer, New York, , page 141. The triggering of a process of rubbing can occur only in the surroundings, not in a thermodynamic system in its own state of internal thermodynamic equilibrium. Such triggering may be described as a thermodynamic operation.Formal definition
In thermodynamics, the quantity of work done by a closed system on its surroundings is defined by factors strictly confined to the interface of the surroundings with the system and to the surroundings of the system, for example, an extended gravitational field in which the system sits, that is to say, to things external to the system. A main concern of thermodynamics is the properties of materials. Thermodynamic work is defined for the purposes of thermodynamic calculations about bodies of material, known as thermodynamic systems. Consequently, thermodynamic work is defined in terms of quantities that describe the states of materials, which appear as the usual thermodynamic state variables, such as volume, pressure, temperature, chemical composition, and electric polarization. For example, to measure the pressure inside a system from outside it, the observer needs the system to have a wall that can move by a measurable amount in response to pressure differences between the interior of the system and the surroundings. In this sense, part of the definition of a thermodynamic system is the nature of the walls that confine it. Several kinds of thermodynamic work are especially important. One simple example is pressure–volume work. The pressure of concern is that exerted by the surroundings on the surface of the system, and the volume of interest is the negative of the increment of volume gained by the system from the surroundings. It is usually arranged that the pressure exerted by the surroundings on the surface of the system is well defined and equal to the pressure exerted by the system on the surroundings. This arrangement for transfer of energy as work can be varied in a particular way that depends on the strictly mechanical nature of pressure–volume work. The variation consists in letting the coupling between the system and surroundings be through a rigid rod that links pistons of different areas for the system and surroundings. Then for a given amount of work transferred, the exchange of volumes involves different pressures, inversely with the piston areas, forSign convention
In the early history of thermodynamics, a positive amount of work done ''by'' the system on the surroundings leads to energy being lost from the system. This historical sign convention has been used in many physics textbooks and is used in the present article.Schroeder, D. V. ''An Introduction to Thermal Physics'', 2000, Addison Wesley Longman, San Francisco, CA, , p. 18 According to the first law of thermodynamics for a closed system, any net change in the internal energy ''U'' must be fully accounted for, in terms of heat ''Q'' entering the system and work ''W'' done by the system: : An alternate sign convention is to consider the work performed ''on'' the system by its surroundings as positive. This leads to a change in sign of the work, so that . This convention has historically been used in chemistry, and has been adopted by most physics textbooks.Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', (1st edition 1968), third edition 1983, Cambridge University Press, Cambridge UK, , pp. 35–36. This equation reflects the fact that the heat transferred and the work done are ''not'' properties of the state of the system. Given only the initial state and the final state of the system, one can only say what the total change in internal energy was, not how much of the energy went out as heat, and how much as work. This can be summarized by saying that heat and work are not state functions of the system. This is in contrast to classical mechanics, where net work exerted by a particle is a state function.Pressure–volume work
Pressure–volume work (or ''PV'' work) occurs when the volume of a system changes. ''PV'' work is often measured in units of litre-atmospheres where . However, the litre-atmosphere is not a recognized unit in the SI system of units, which measures ''P'' in Pascal (Pa), ''V'' in m3, and ''PV'' in Joule (J), where 1 J = 1 Pa·m3. ''PV'' work is an important topic inPath dependence
P–V work is path-dependent and is, therefore, a thermodynamic process function. In general, the term is not an exact differential. The statement that a process is quasi-static gives important information about the process but does not determine the P–V path uniquely, because the path can include several slow goings backwards and forward in volume, slowly enough to exclude friction within the system occasioned by departure from the quasi-static requirement. An adiabatic wall is one that does not permit passage of energy by conduction or radiation. TheOther mechanical types of work
There are several ways of doing mechanical work, each in some way related to a force acting through a distance. In basic mechanics, the work done by a constant force ''F'' on a body displaced a distance s in the direction of the force is given by : If the force is not constant, the work done is obtained by integrating the differential amount of work, :Rotational work
Energy transmission with a rotating shaft is very common in engineering practice. Often the torque ''T'' applied to the shaft is constant which means that the force ''F'' applied is constant. For a specified constant torque, the work done during ''n'' revolutions is determined as follows: A force ''F'' acting through a moment arm ''r'' generates a torque ''T'' : This force acts through a distance ''s'', which is related to the radius ''r'' by : The shaft work is then determined from: : The power transmitted through the shaft is the shaft work done per unit time, which is expressed as :Spring work
When a force is applied on a spring, and the length of the spring changes by a differential amount ''dx'', the work done is : For linear elastic springs, the displacement ''x'' is proportional to the force applied : where ''K'' is the spring constant and has the unit of N/m. The displacement ''x'' is measured from the undisturbed position of the spring (that is, when ). Substituting the two equations :, where ''x''1 and ''x''2 are the initial and the final displacement of the spring respectively, measured from the undisturbed position of the spring.Work done on elastic solid bars
Solids are often modeled as linear springs because under the action of a force they contract or elongate, and when the force is lifted, they return to their original lengths, like a spring. This is true as long as the force is in the elastic range, that is, not large enough to cause permanent or plastic deformation. Therefore, the equations given for a linear spring can also be used for elastic solid bars. Alternately, we can determine the work associated with the expansion or contraction of an elastic solid bar by replacing the pressure ''P'' by its counterpart in solids, normal stress in the work expansion : : where ''A'' is the cross sectional area of the bar.Work associated with the stretching of liquid film
Consider a liquid film such as a soap film suspended on a wire frame. Some force is required to stretch this film by the movable portion of the wire frame. This force is used to overcome the microscopic forces between molecules at the liquid-air interface. These microscopic forces are perpendicular to any line in the surface and the force generated by these forces per unit length is called the surface tension ''σ'' whose unit is N/m. Therefore, the work associated with the stretching of a film is called surface tension work, and is determined from : where is the change in the surface area of the film. The factor 2 is due to the fact that the film has two surfaces in contact with air. The force acting on the moveable wire as a result of surface tension effects is , where ''σ'' is the surface tension force per unit length.Free energy and exergy
The amount of useful work which may be extracted from a thermodynamic system is determined by the second law of thermodynamics. Under many practical situations this can be represented by the thermodynamic availability, orNon-mechanical forms of work
Non-mechanical work in thermodynamics is work caused by external force fields that a system is exposed to. The action of such forces can be initiated by events in the surroundings of the system, or by thermodynamic operations on the shielding walls of the system. The non-mechanical work of force fields can have either positive or negative sign, work being done by the system on the surroundings, or ''vice versa''. Work done by force fields can be done indefinitely slowly, so as to approach the fictive reversible quasi-static ideal, in which entropy is not created in the system by the process. In thermodynamics, non-mechanical work is to be contrasted with mechanical work that is done by forces in immediate contact between the system and its surroundings. If the putative 'work' of a process cannot be defined as either long-range work or else as contact work, then sometimes it cannot be described by the thermodynamic formalism as work at all. Nevertheless, the thermodynamic formalism allows that energy can be transferred between an open system and its surroundings by processes for which work is not defined. An example is when the wall between the system and its surrounds is not considered as idealized and vanishingly thin, so that processes can occur within the wall, such as friction affecting the transfer of matter across the wall; in this case, the forces of transfer are neither strictly long-range nor strictly due to contact between the system and its surrounds; the transfer of energy can then be considered as by convection, and assessed in sum just as transfer of internal energy. This is conceptually different from transfer of energy as heat through a thick fluid-filled wall in the presence of a gravitational field, between a closed system and its surroundings; in this case there may convective circulation within the wall but the process may still be considered as transfer of energy as heat between the system and its surroundings; if the whole wall is moved by the application of force from the surroundings, without change of volume of the wall, so as to change the volume of the system, then it is also at the same time transferring energy as work. A chemical reaction within a system can lead to electrical long-range forces and to electric current flow, which transfer energy as work between system and surroundings, though the system's chemical reactions themselves (except for the special limiting case in which in they are driven through devices in the surroundings so as to occur along a line of thermodynamic equilibrium) are always irreversible and do not directly interact with the surroundings of the system. Non-mechanical work contrasts with pressure–volume work. Pressure–volume work is one of the two mainly considered kinds of mechanical contact work. A force acts on the interfacing wall between system and surroundings. The force is that due to the pressure exerted on the interfacing wall by the material inside the system; that pressure is an internal state variable of the system, but is properly measured by external devices at the wall. The work is due to change of system volume by expansion or contraction of the system. If the system expands, in the present article it is said to do positive work on the surroundings. If the system contracts, in the present article it is said to do negative work on the surroundings. Pressure–volume work is a kind of contact work, because it occurs through direct material contact with the surrounding wall or matter at the boundary of the system. It is accurately described by changes in state variables of the system, such as the time courses of changes in the pressure and volume of the system. The volume of the system is classified as a "deformation variable", and is properly measured externally to the system, in the surroundings. Pressure–volume work can have either positive or negative sign. Pressure–volume work, performed slowly enough, can be made to approach the fictive reversible quasi-static ideal. Non-mechanical work also contrasts with shaft work. Shaft work is the other of the two mainly considered kinds of mechanical contact work. It transfers energy by rotation, but it does not eventually change the shape or volume of the system. Because it does not change the volume of the system it is not measured as pressure–volume work, and it is called isochoric work. Considered solely in terms of the eventual difference between initial and final shapes and volumes of the system, shaft work does not make a change. During the process of shaft work, for example the rotation of a paddle, the shape of the system changes cyclically, but this does not make an eventual change in the shape or volume of the system. Shaft work is a kind of contact work, because it occurs through direct material contact with the surrounding matter at the boundary of the system. A system that is initially in a state of thermodynamic equilibrium cannot initiate any change in its internal energy. In particular, it cannot initiate shaft work. This explains the curious use of the phrase "inanimate material agency" by Kelvin in one of his statements of the second law of thermodynamics. Thermodynamic operations or changes in the surroundings are considered to be able to create elaborate changes such as indefinitely prolonged, varied, or ceased rotation of a driving shaft, while a system that starts in a state of thermodynamic equilibrium is inanimate and cannot spontaneously do that. Thus the sign of shaft work is always negative, work being done on the system by the surroundings. Shaft work can hardly be done indefinitely slowly; consequently it always produces entropy within the system, because it relies on friction or viscosity within the system for its transfer.Münster, A. (1970), ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London, , p. 45. The foregoing comments about shaft work apply only when one ignores that the system can store angular momentum and its related energy. Examples of non-mechanical work modes include * Electric field work – where the force is defined by the surroundings' '' voltage'' (the electrical potential) and the generalized displacement is change of spatial distribution of ''Gravitational work
Gravitational work is defined by the force on a body measured in a gravitational field. It may cause a generalized displacement in the form of change of the spatial distribution of the matter within the system. The system gains internal energy (or other relevant cardinal quantity of energy, such as enthalpy) through internal friction. As seen by the surroundings, such frictional work appears as mechanical work done on the system, but as seen by the system, it appears as transfer of energy as heat. When the system is in its own state of internal thermodynamic equilibrium, its temperature is uniform throughout. If the volume and other extensive state variables, apart from entropy, are held constant over the process, then the transferred heat must appear as increased temperature and entropy; in a uniform gravitational field, the pressure of the system will be greater at the bottom than at the top. By definition, the relevant cardinal energy function is distinct from the gravitational potential energy of the system as a whole; the latter may also change as a result of gravitational work done by the surroundings on the system. The gravitational potential energy of the system is a component of its total energy, alongside its other components, namely its cardinal thermodynamic (e.g. internal) energy and its kinetic energy as a whole system in motion.See also
*References
{{DEFAULTSORT:Work (Thermodynamics) Thermodynamics