CHAPTER 3 THE FIRST LAW
3.4 DEFORMATIONWORK 69
a phase transition from solid to liquid (Sec.2.2.2). We can carry out the heat transfer by
placing the system in thermal contact with an external water bath at a higher temperature
than the equilibrium temperature, which will cause a temperature gradient in the system and
the melting of an amount of solid proportional to the quantity of energy transferred.
The closer the external temperature is to the equilibrium temperature, the smaller are
the temperature gradients and the closer are the states of the system to equilibrium states.
In the limit as the temperature difference approaches zero, the system passes through a
sequence of equilibrium states in which the temperature is uniform and constant, energy is
transferred into the system by heat, and the substance is transformed from solid to liquid.
This idealized process is anequilibriumphase transition, and it is a reversible process.
3.4 Deformation Work
This and the four following sections (Secs.3.5–3.8) describe some spontaneous, irreversible
processes with various kinds of work and illustrate the concept of a reversible limit for the
processes that have such a limit.
Thedeformationof a system involves changes in the position, relative to the local frame,
of portions of the system boundary. At a small surface element of the boundary, the work
of deformation is given in general by the expression^8
∂w DF surcos (^) ds (3.4.1)
whereF suris the magnitude of the contact force exerted by the surroundings on the surface
element, ds is the infinitesimal displacement of the surface element in the local frame, and
(^) is the angle between the directions of the force and the displacement. If the displacement
is entirely parallel to thexaxis, the expression becomes equivalent to that already given by
Eq.3.1.1on page 57 :∂wDFxsurdx.
3.4.1 Gas in a cylinder-and-piston device
A useful kind of deformation for the development of thermodynamic theory is a change in
the volume of a gas or liquid.
As a model for the work involved in changing the volume of a gas, consider the arrange-
ment shown in Fig.3.4on the next page. A sample of gas is confined in a cylinder by a
piston. Thesystemis the gas. The piston is not part of the system, but its position given by
the variablexdetermines the system’s volume. Movement of the piston to the right, in the
Cxdirection, expands the gas; movement to the left, in the xdirection, compresses it.
We will find it instructive to look in detail at the forces acting on the piston. There are
three kinds: the forceFgasexerted in theCxdirection by the gas; an external forceFextin
the xdirection, which we can control in the surroundings; and a frictional forceFfricin
the direction opposite to the piston’s velocity when the piston moves.
The friction occurs at the seal between the edge of the piston and the cylinder wall.
We will assume this seal is lubricated, and thatFfricapproaches zero as the piston velocity
approaches zero.
(^8) From Eq.G.6.10on page 498.