CHAPTER 3 THE FIRST LAW
3.5 APPLICATIONS OFEXPANSIONWORK 78
Figure 3.7 Indicator with paper-covered roll at left and pressure gauge at right.a
aRef. [ 111 ], page 104.the area under the solid curve of Fig.3.6between any two points on the curve is equal to
wfor reversible adiabatic expansion or compression. If the direction of the process is to
the right along the path (expansion), the area is positive and the work is negative; but if the
direction is to the left (compression), the area is taken as negative and the work is positive.
More generally, an indicator diagram can be a plot of a work coefficient or its negative
as a function of the work coordinate. For example, it could be a plot of the pressurepbat
a moving boundary as a function ofV. The area under this curve is equal to
R
pbdV, the
negative of expansion work in general (Eq.3.4.8).
Historically, an indicator diagram was a diagram drawn by an “indicator,” an instru-
ment invented by James Watt in the late 1700s to monitor the performance of steam
engines. The steam engine indicator was a simple pressure gauge: a piston moving
in a small secondary cylinder, with the steam pressure of the main cylinder on one
side of the piston and a compressed spring opposing this pressure on the other side. A
pointer attached to the small piston indicated the steam pressure. In later versions, the
pointer was replaced with a pencil moving along a paper-covered roll, which in turn
was mechanically linked to the piston of the main cylinder (see Fig.3.7). During each
cycle of the engine, the pencil moved back and forth along the length of the roll and
the roll rotated in a reciprocating motion, causing the pencil to trace a closed curve
whose area was proportional to the net work performed by one cycle of the engine.3.5.5 Spontaneous adiabatic expansion or compression
Section3.4.1explained that during a rapid spontaneous expansion of the gas in the cylinder
shown in Fig.3.4, the pressurepbexerted by the gas at the moving piston is less than the
pressure at the stationary wall. Consequently the work given byw D
R
pbdV is less