   #copyright

Work (thermodynamics)

2007 Schools Wikipedia Selection. Related subjects: General Physics

                                        Thermodynamic potentials
                                      Internal energy               U(S,V)
                                Helmholtz free energy      A(T,V) = U − TS
                                             Enthalpy      H(S,P) = U + PV
                                    Gibbs free energy G(T,P) = U + PV − TS

   In thermodynamics, thermodynamic work is the quantity of energy
   transferred from one system to another. It is a generalization of the
   concept of mechanical work in mechanics. In the SI system of
   measurement, work is measured in joules (symbol: J). The rate at which
   work is performed is power.

History

   Joule's apparatus for measuring the mechanical equivalent of heat.
   Enlarge
   Joule's apparatus for measuring the mechanical equivalent of heat.

1824

   The modern-day definition of work, i.e. "weight lifted through a
   height", was originally defined in 1824 by thermodynamicist Sadi Carnot
   in his famous paper Reflections on the Motive Power of Fire.
   Specifically, according to Carnot:


   Work (thermodynamics)

     We use here motive power (work) 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.


   Work (thermodynamics)

1845

   In 1845, the English physicist James Joule read a paper On the
   mechanical equivalent of heat to the British Association meeting in
   Cambridge. In this work, he reported his best-known experiment, that in
   which the work 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 friction and agitation of action the
   paddle-wheel on the body of water caused heat to be generated which, in
   turn, increased the temperature of water. Both the temperature ∆T
   change 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.

Overview

   According to the First Law of Thermodynamics, it is useful to separate
   changes to the internal energy of a thermodynamic system into two sorts
   of energy transfers. Work refers to forms of energy transfer, which can
   be accounted for in terms of changes in the macroscopic physical
   variables of the system, for example energy which goes into expanding
   the volume of a system against an external pressure, by say driving a
   piston-head out of a cylinder against an external force. This is in
   distinction to heat energy carried into or out of the system in the
   form of transfers in the microscopic thermal motions of particles.

   The concept of thermodynamic work is a little more general than that of
   mechanical work, because it also includes other energy transfers, i.e.
   for example electrical work, the movement of charge against an external
   electrical field to charge up a battery say, which may or may not
   necessarily be thought of as strictly mechanical in nature.

Mathematical definition

   As stipulated to the First Law of Thermodynamics, any net increase in
   the internal energy U of a thermodynamic system must be fully accounted
   for, in terms of heat δQ entering the system less work δW done by the
   system:

          dU = \delta Q - \delta W\;

   The Roman letter d indicates that internal energy U is a property of
   the state of the system, so changes in the internal energy are exact
   differentials - they depend only on the original state and the final
   state, not the path taken. In contrast the Greek δs in this equation
   reflect the fact that the heat transfer and the work transfer are not
   properties of the final state of the system. Given only the initial
   state and the final state of the system, all one can say is 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 summarised by saying
   that heat and work are not state functions of the system.

Pressure-volume work

   Chemical thermodynamics studies PV work, which occurs when the volume
   of a fluid changes. PV work is represented by the following
   differential equation:

          dW = -P dV \,

   where:
     * W = work done on the system
     * P = external pressure
     * V = volume

   Therefore, we have:

          W=-\int_{V_i}^{V_f} P\,dV

   Like all work functions, PV work is path-dependent. (The path in
   question is a curve in the Euclidean space specified by the fluid's
   pressure and volume, and infinitely many such curves are possible.)
   From a thermodynamic perspective, this fact implies that PV work is not
   a state function. This means that the differential dW is an inexact
   differential; to be more rigorous, it should be written đW (with a line
   through the d).

   From a mathematical point of view, that is to say, dW is not an exact
   one-form. This line through is merely a flag to warn us there is
   actually no function ( 0-form) W which is the potential of dW. If there
   were, indeed, this function W, we should be able to just use Stokes
   Theorem, and evaluate this putative function, the potential of dW, 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; work presupposes a path.

   PV work is often measured in the (non-SI) units of litre-atmospheres,
   where 1 L·atm = 101.3 J.

Free energy and exergy

   The amount of useful work which can be extracted from a thermodynamic
   system is discussed in the article Second Law of Thermodynamics. Under
   many practical situations this can be represented by the thermodynamic
   Availability or Exergy function. Two important cases are thermodynamic
   systems where the temperature and volume are held constant in which the
   measure of "useful" work attainable reduces to the Helmholtz free
   energy function; and systems where the temperature and pressure are
   held constant in which the measure of "useful" work attainable reduces
   to the Gibbs free energy.

   Retrieved from "
   http://en.wikipedia.org/wiki/Work_%28thermodynamics%29"
   This reference article is mainly selected from the English Wikipedia
   with only minor checks and changes (see www.wikipedia.org for details
   of authors and sources) and is available under the GNU Free
   Documentation License. See also our Disclaimer.
