For a finite transformation, the work done by the system is obtained by integrating dW
W ¼
Z dW ¼
Z 2
1
pdV ¼
Z 2
1
p
Z
S
dS Á dn
where the integral is taken over the whole process from the initial state ‘1’ to the
final state ‘2’.
The above example of work, the work done by the system as a whole on its
“surroundings” (or the corresponding work on the system by its surroundings), is an
example of external work. Implicit in Fig. 1.4, a work reservoir is assumed and the
piston is connected through a piston rod and additional transmission means to the
work reservoir. A system external work is made up of, in the case of expansion
external work, (1) expansion work against a surrounding thermal-and-pressure
reservoir and (2) useful work which is transmitted and stored in a work reservoir.
Opposite kind of useful work exchange, work extracted from a work reservoir by
the system, is also possible.
Examples of useful work exchange between a system and a mechanical work
reservoir are the rising or lowering of a suspended weight; the winding or
unwinding of a spring; the input or the output of power of a flywheel. (In the case of
electrical work, the charging or discharging of a battery is an example.)
1.8 Calculation of
R pdV for “Quasi-static Processes”
Work (as well as heat in Chaps. 2 and 3) is not a state variable. Change in a
system’s state variable is determined by the initial and final states of the change
independent of the path. In contrast, work done by a system depends not only on the
initial state and the final states but also on the intermediate states, i.e., on the path
connecting the initial state and the final states.
A simple example of work process is the so-called “quasi-static process”,
defined as a process that the path of which can be determined. There are, however,
two different ways of determining the path: One way is, as shown in the figure
(Fig. 1.5), the result of balancing forces acting on a moving piston.
Another way of determining the path of a quasi-static process is through the
removal of closely spaced mechanical constraints as shown in Fig. 1.6. We shall
make a preliminary comment on the two processes in Sect. 1.9 and more detailed
discussion on them in Chap. 6. At this point, it suffices to point out that they are
fundamentally different kinds of quasi-static processes and only the first one
(Fig. 1.5) may be called an internally reversible, quasi-static process (defined in
Chap. 6), an example of such kind is given here.
1.7 Work
17
W ¼
Z dW ¼
Z 2
1
pdV ¼
Z 2
1
p
Z
S
dS Á dn
where the integral is taken over the whole process from the initial state ‘1’ to the
final state ‘2’.
The above example of work, the work done by the system as a whole on its
“surroundings” (or the corresponding work on the system by its surroundings), is an
example of external work. Implicit in Fig. 1.4, a work reservoir is assumed and the
piston is connected through a piston rod and additional transmission means to the
work reservoir. A system external work is made up of, in the case of expansion
external work, (1) expansion work against a surrounding thermal-and-pressure
reservoir and (2) useful work which is transmitted and stored in a work reservoir.
Opposite kind of useful work exchange, work extracted from a work reservoir by
the system, is also possible.
Examples of useful work exchange between a system and a mechanical work
reservoir are the rising or lowering of a suspended weight; the winding or
unwinding of a spring; the input or the output of power of a flywheel. (In the case of
electrical work, the charging or discharging of a battery is an example.)
1.8 Calculation of
R pdV for “Quasi-static Processes”
Work (as well as heat in Chaps. 2 and 3) is not a state variable. Change in a
system’s state variable is determined by the initial and final states of the change
independent of the path. In contrast, work done by a system depends not only on the
initial state and the final states but also on the intermediate states, i.e., on the path
connecting the initial state and the final states.
A simple example of work process is the so-called “quasi-static process”,
defined as a process that the path of which can be determined. There are, however,
two different ways of determining the path: One way is, as shown in the figure
(Fig. 1.5), the result of balancing forces acting on a moving piston.
Another way of determining the path of a quasi-static process is through the
removal of closely spaced mechanical constraints as shown in Fig. 1.6. We shall
make a preliminary comment on the two processes in Sect. 1.9 and more detailed
discussion on them in Chap. 6. At this point, it suffices to point out that they are
fundamentally different kinds of quasi-static processes and only the first one
(Fig. 1.5) may be called an internally reversible, quasi-static process (defined in
Chap. 6), an example of such kind is given here.
1.7 Work
17