work FsF scos (2.1)
where is the angle between the vectors. Work is a scalar, not vector, quantity.
Work has magnitude, but not direction. Figure 2.1 shows a force acting on an
object. In Figure 2.1a, the object is not moving, so the amount of work is zero
(despite the amount of force being exerted). In Figure 2.1b, an object has been
moved, so work was done.
Work has units of joules, like energy. This is not without a reason: work is
a way to transfer energy. Energy is defined as the ability to do work, so it makes
sense that energy and work are described using the same units.
The most common form of work studied by basic thermodynamics involves
the changing volume of a system. Consider Figure 2.2a. A frictionless piston
confines a sample of a gas in an initial volume Vi. The gas inside the chamber
also has an initial pressure pi. Initially, what keeps the piston at a fixed position
is the external pressure of the surroundings,pext.
If the piston moves out, Figure 2.2b, then the system is doing workon the
surroundings. That means that the system is losingenergy in the form of work.
The infinitesimal amount of work dwthat the system does on the surround-
ings for an infinitesimal change in volume dVwhile acting against a constant
external pressure pextis defined as
dwpextdV (2.2)2.2 Work and Heat 25Initial positionFs 0Work 0Fs 0Work 0Initial position
(a) (b)
Figure 2.1 When a force is exerted on an object, no work is done unless the object moves. (a)
Since the wall does not move, no work is done. (b) Work is done because the force is acting
through a distance.pextVi, pi(a)
dw pext dV:
work done by system
on surroundings
(system loses energy)(b)dw pext dV:
work done on system
by surroundings
(system gains energy)(c)
Figure 2.2 (a) A frictionless piston with an enclosed gas is a simple example of how
gases perform work on systems or surroundings. (b) The work is done on the surroundings.
(c) The work is done on the system. The mathematical definition of work remains the same,
however.