In thermodynamics, work performed by a system is energy transferred by the system to its surroundings, due solely to macroscopic forces exerted by the system on its surroundings, where those forces, and their external effects, can be measured. Through suitable passive linkages, the whole of the work done by such forces can lift a weight in the surroundings.
The externally measured forces and external effects may be electromagnetic,Guggenheim, E.A. (1985). Thermodynamics. An Advanced Treatment for Chemists and Physicists, seventh edition, North Holland, Amsterdam, .Jackson, J.D. (1975). Classical Electrodynamics, second edition, John Wiley and Sons, New York, .Konopinski, E.J. (1981). Electromagnetic Fields and Relativistic Particles, McGraw-Hill, New York, . gravitational,North, G.R., Erukhimova, T.L. (2009). Atmospheric Thermodynamics. Elementary Physics and Chemistry, Cambridge University Press, Cambridge (UK), . or pressure/volume or other macroscopically mechanical variables.Kittel, C. Kroemer, H. (1980). Thermal Physics, second edition, W.H. Freeman, San Francisco, . For thermodynamic work, these externally measured quantities are exactly matched by values of or contributions to changes in macroscopic internal state function of the system, which always occur in conjugate pairs, for example pressure and volume or magnetic flux density and magnetization.
By an external system that lies in the surroundings, not necessarily a thermodynamic system as strictly defined by the usual thermodynamic state variables, work can be said to be done on a thermodynamic system. Part of such externally applied work can change the system's state variables other than its temperature and entropy, while the rest of such externally applied work appears to the thermodynamic system as heat transferred to it. The paddle stirring experiments of Joule provide an example, illustrating the concept of isochoric (or constant volume) mechanical work. Such work is not adiabatic, because it occurs through friction in and on the surface of the thermodynamic system. When such externally applied macroscopic mechanical work, described by macroscopic mechanical variables in the surroundings, is done isochorically, it is not thermodynamic work done on the thermodynamic system, as defined here, because it is not pressure–volume work. The external system mixes, and generates friction on and in, the thermodynamic system. An example of a non-mechanical form of externally applied work is Joule heating, which also is not adiabatic, because it occurs through friction as the electric current passes through the thermodynamic system. When it is done isochorically, and no matter is transferred, such an energy transfer is regarded as a heat transfer into the system of interest.
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.
In this experiment, the friction and agitation of the paddle-wheel on the body of water caused heat to be generated which, in turn, increased the temperature of water. Both the temperature change ∆T of the water and the height of the fall ∆h of the weight mg were recorded. Using these values, Joule was able to determine the mechanical equivalent of heat. Joule estimated a mechanical equivalent of heat to be 819 ft•lbf/Btu (4.41 J/cal). The modern day definitions of heat, work, temperature, and energy all have connection to this experiment. In this arrangement of apparatus, it never happens that the process runs in reverse, with the water driving the paddles so as to raise the weight, not even slightly. The doing of such isochoric mechanical work by the device, which lies external to the water, while the energy supplied by the fall of the weight becomes heat passing into the water, is irreversible.
Besides transfer of energy by work, thermodynamics admits transfer of energy as heat. For a process in a Closed system (no transfer of matter) thermodynamic system, the first law of thermodynamics relates changes in the internal energy of the system to those two forms of energy transfer, by work, and as heat. Adiabatic work is done without matter transfer and without heat transfer. In principle, in thermodynamics, for a process in a closed system, quantity of heat transferred is defined by the amount of adiabatic work that would be needed to effect the change in the system that is occasioned by the heat transfer. In experimental practice, heat transfer is often estimated calorimetrically, through change of temperature of a known quantity of calorimetry material substance.
Such conversion may be idealized as nearly frictionless, though it occurs relatively quickly. It usually comes about through devices that are not usually described as simple thermodynamic systems, such as homogeneous bodies of material substances. For example, the descent of the weight in Joule's stirring experiment reduces the weight's total energy. It is usually described as loss of gravitational potential energy by the weight, due to change of its macroscopic position in the gravity field, rather than as loss of the weight's internal energy due for example to changes in its entropy, volume, and chemical composition. Though it occurs relatively rapidly, it may be idealized as nearly reversible.
In contrast, the conversion of heat into work in a heat engine can never exceed the Carnot efficiency, as a consequence of the second law of thermodynamics. Such energy conversion, through work done relatively rapidly, in a practical heat engine, by a thermodynamic system on its surroundings, cannot be idealized, even nearly, as reversible.
Thermodynamic work done by a thermodynamic system on its surroundings is defined so as to comply with this principle. Historically, thermodynamics was about how a thermodynamic system could do work on its surroundings.
In a process of transfer of energy from or to a thermodynamic system, the change of internal energy of the system is defined in theory by the amount of adiabatic work that would have been necessary to reach the final from the initial state, such adiabatic work being measurable only through the externally measurable mechanical or deformation variables of the system, that provide full information about the forces exerted by the surroundings on the system during the process. In the case of some of Joule's measurements, the process was so arranged that heat produced outside the system (in the paddles) by the frictional process was practically entirely transferred into the system during the process, so that the quantity of work done by the surrounds on the system could be calculated as shaft work, an external mechanical variable.Buchdahl, H.A. (1966). The Concepts of Classical Thermodynamics, Cambridge University Press, London, p. 40.Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, , pp. 35–36.
The amount of energy transferred as work is measured through quantities defined externally to the system of interest, and thus belonging to its surroundings. In an important sign convention, preferred in chemistry, work that adds to the internal energy of the system is counted as positive. On the other hand, for historical reasons, an oft-encountered sign convention, preferred in physics, is to consider work done by the system on its surroundings as positive.
Thermodynamic work does not account for any energy transferred between systems as heat or through transfer of matter.
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.
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 does not negate that the now Heat is 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.
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.
There are a few especially important kinds of thermodynamic work.
A simple example of one of those important kinds 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, for mechanical equilibrium. This cannot be done for the transfer of energy as heat because of its non-mechanical nature.Tisza, L. (1966). Generalized Thermodynamics, M.I.T. Press, Cambridge MA, p. 37.
Another important kind of work is isochoric work, that is to say work that involves no eventual overall change of volume of the system between the initial and the final states of the process. Examples are friction on the surface of the system as in Rumford's experiment; shaft work such as in Joule's experiments; stirring of the system by a magnetic paddle inside it, driven by a moving magnetic field from the surroundings; and vibrational action on the system that leaves its eventual volume unchanged, but involves friction within the system. Isochoric mechanical work for a body in its own state of internal thermodynamic equilibrium is done only by the surroundings on the body, not by the body on the surroundings, so that the sign of isochoric mechanical work with the physics sign convention is always negative.
When work, for example pressure–volume work, is done on its surroundings by a closed system that cannot pass heat in or out because it is confined by an adiabatic wall, the work is said to be adiabatic for the system as well as for the surroundings. When mechanical work is done on such an adiabatically enclosed system by the surroundings, it can happen that friction in the surroundings is negligible, for example in the Joule experiment with the falling weight driving paddles that stir the system. Such work is adiabatic for the surroundings, even though it is associated with friction within the system. Such work may or may not be isochoric for the system, depending on the system and its confining walls. If it happens to be isochoric for the system (and does not eventually change other system state variables such as magnetization), it appears as a heat transfer to the system, and does not appear to be adiabatic for the system.
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, but has been adopted in several modern physics textbooks. Quantities, Units and Symbols in Physical Chemistry (IUPAC Green Book) See Sec. 2.11 Chemical Thermodynamics, p. 56.Planck, M. (1897/1903). Treatise on Thermodynamics, translated by A. Ogg, Longmans, Green & Co., London., p. 43.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 of the system. This is in contrast to classical mechanics, where net work exerted by a particle is a state function.
For a process in a closed system, occurring slowly enough for accurate definition of the pressure on the inside of the system's wall that moves and transmits force to the surroundings, described as quasi-static,Herbert Callen (1960/1985), Thermodynamics and an Introduction to Thermostatistics, (first edition 1960), second edition 1985, John Wiley & Sons, New York, , p. 19.Münster, A. (1970), Classical Thermodynamics, translated by E. S. Halberstadt, Wiley–Interscience, London, , p. 24. work is represented by the following equation between differentials:
denotes an infinitesimal increment of work done by the system, transferring energy to the surroundings;
denotes the pressure inside the system, that it exerts on the moving wall that transmits force to the surroundings.Borgnakke, C., Sontag, R. E. (2009). Fundamentals of Thermodynamics, seventh edition, Wiley, , p. 94. In the alternative sign convention the right hand side has a negative sign.
denotes the infinitesimal increment of the volume of the system.
denotes the work done by the system during the whole of the reversible process.
The first law of thermodynamics can then be expressed as
(In the alternative sign convention where W = work done on the system, . However, is unchanged.)
If the process took a path other than an adiabatic path, the work would be different. This would only be possible if heat flowed into/out of the system. In a non-adiabatic process, there are indefinitely many paths between the initial and final states.
In another notation, is written (with a line through the d). This notation indicates that is not an exact form one-form. The line-through is merely a flag to warn us there is actually no function (0-form) which is the potential of . If there were, indeed, this function , we should be able to just use Stokes Theorem to evaluate this putative function, the potential of , at the boundary of the path, that is, the initial and final points, and therefore the work would be a state function. This impossibility is consistent with the fact that it does not make sense to refer to the work on a point in the PV diagram; work presupposes a path.
The shaft work is then determined from:
The non-mechanical work of long-range forces can have either positive or negative sign, work being done by the system on the surroundings, or vice versa. Work done by long-range forces 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.Prigogine, I., Defay, R. (1954). Chemical Thermodynamics, translation by D.H. Everett of the 1950 edition of Thermodynamique Chimique, Longmans, Green & Co., London, p. 43.
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. Also published in 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
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.