Work (thermodynamics)

For thermodynamic work, appropriately chosen externally measured quantities are exactly matched by values of or contributions to changes in macroscopic internal state variables of the system, which always occur in conjugate pairs, for example pressure and volume[1] or magnetic flux density and magnetization.

It has, as we know, as a measure, the product of the weight multiplied by the height to which it is raised.In 1845, the English physicist James Joule wrote a paper On the mechanical equivalent of heat for the British Association meeting in Cambridge.

[6] In this paper, he reported his best-known experiment, in which the mechanical power released through the action of a "weight falling through a height" was used to turn a paddle-wheel in an insulated barrel of water.

In this experiment, the motion of the paddle wheel, through agitation and friction, heated the body of water, so as to increase its temperature.

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.

Mechanical work was done by the apparatus of falling weight, pulley, and paddles, which lay in the surroundings of the water.

A quantity of mechanical work, measured as force × distance in the surroundings, that does not change the volume of the water, is said to be isochoric.

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.

It is described as loss of gravitational potential energy by the weight, due to change of its macroscopic position in the gravity field, in contrast to, for example, loss of the weight's internal energy due to changes in its entropy, volume, and chemical composition.

Such energy conversion, through work done relatively rapidly, in a practical heat engine, by a thermodynamic system on its surroundings, cannot be idealized, not even nearly, as reversible.

[12][13] 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.

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 viscosity[17] chemical reaction,[2] unconstrained expansion as in Joule expansion and in diffusion, and phase change.

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.

These fictive processes proceed along paths on geometrical surfaces that are described exactly by a characteristic equation of the thermodynamic system.

Even when they occur only by work assessed in the surroundings as adiabatic, without heat transfer, such departures always entail entropy production.

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.

[21] The irreversible process known as Joule heating also occurs through a change of a non-deformation extensive state variable.

Then for a given amount of work transferred, the exchange of volumes involves different pressures, inversely with the piston areas, for mechanical equilibrium.

[33] 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.

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 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.

This is true as long as the force is in the elastic range, that is, not large enough to cause permanent or plastic deformation.

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 σ = F/A in the work expansion where A is the cross sectional area of the bar.

Two important cases are: in thermodynamic systems where the temperature and volume are held constant, the measure of useful work attainable is the Helmholtz free energy function; and in systems where the temperature and pressure are held constant, the measure of useful work attainable is the Gibbs free energy.

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.

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.

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.

This explains the curious use of the phrase "inanimate material agency" by Kelvin in one of his statements of the second law of thermodynamics.

[37] The foregoing comments about shaft work apply only when one ignores that the system can store angular momentum and its related energy.