Page 75 - Modern physical chemistry

64 The First Law for Energy

In thennodynarnics, one qeneralizes this fonn. Any energy added to a system that
can be represented as the scalar product of a generalized force and a generalized dis-
placement is identified as work.
Always present when the volume changes is the work of compression or expansion.
Consider a fluid enclosed by a cylinder and a movable piston, as figure 4.1 shows. Let
the surroundings exert pressure on the piston, while the area of the piston is A. The cor-
responding force on the piston is PexA-. When the piston moves distance -dz, the work
done is
[4.2]
Also, consider a rectangular solid subject to external pressure Pex, as figure 4.2 shows.
The work done on compressing the solid a small amount is
[4.3]

For any other configuration, the work of compression is similarly

dw=-P ex dV. [4.4]
When the change is carried out reversibly, the internal pressure does not differ appre-
ciably from the external pressure and
dw=-PdV. [4.5]

z

,'" ------- ... "
FIGURE 4.1 Cylinder fitted with a piston confining a fluid.

y
,
,'x
,
,
, ,
FIGURE 4.2 Rectangular solid that expands dx in the
Ix x direction, dy in the y direction, and dz in the z
direction.