In

thermodynamics,

**work** performed by a system is the quantity of

energy transferred by the system to another
due to changes in the external parameters of the system. If these
changes happen in a

reversible way, then the
performed work does not lead to a change of the

entropy. 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

### 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*.
Specifically, according to Carnot:

### 1845

In 1845,
the English physicist James Joule wrote
a paper *On the mechanical equivalent of heat* for the
British Association meeting in Cambridge. In this work, he reported his best-known
experiment, 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 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.

## 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 driving a piston-head out of a cylinder
against an external force. This is in contrast to

**heat** energy, which is 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 slightly more general than
that of mechanical work because it includes other types of energy
transfers as well. The electrical work required to move a charge
against an external electrical field can be measured, as can the
work required to move heat against a temperature gradient. An
extremely important fact to understand is that thermodynamic work
need not have any mechanical component to be considered such.

## Mathematical definition

According 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 minus work

*δW* done

*by* the system:

- dU = \delta Q - \delta W.\;

The 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, and not
upon the path taken. In contrast, the Greek

delta's (

*δ*‘s) 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, 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.

## 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

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

The above equation of the Work is valid for

reversible process of

closed system.

Like all work functions, PV work is

path-dependent. 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).

In other words, from a mathematical point of view, đW is not an

exact one-form.
The line-through is merely a flag to warn us there is actually no
function (

0-form) W which is the

potential of đW. If there were, indeed, this
function W, we should be able to just use

Stokes Theorem to evaluate this putative
function, the potential of đW, 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.

PV work is often measured in the (non-SI) units of
litre-atmospheres, where 1 L·atm = 101.325 J.The mathematical
equation for the thermodynamical substance depends on the
weight,mass and temperature of the thermodynamical substance.

## 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: 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.

## See also

## References