Modern Engineering Thermodynamics

4.6 Mechanical Work Modes of Energy Transport 109
L
Area A
p
F
± F
x
dx
Area A
x
± dx
(a) Moving system boundary
(c) Elastic work
Wire frame
T
dΘ
b
x
Film
± dx
± F
Moving slider
(b) Shaft work
(d) Surface tension work
FIGURE 4.5
Four classical types of mechanical work.
or
ð 1
W 2 Þ mechanical
=
Z x2
x1
ð F ! applied by the system Þ .d x ! −
Z x2
x1
ð F ! applied on the system Þ .d x ! (4.24)
Note that our sign convention requires that work done by the system be positive, while work done on the system
be negative.
In thermodynamics, the four classical types of mechanical work (Figure 4.5) are
1. Moving system boundary work.
2. Rotating shaft work.
3. Elastic work.
4. Surface tension work.
These are very important work modes in engineering analysis and the following material provides a detailed
discussion of their major characteristics.
4.6.1 Moving System Boundary Work
Whenever a system boundary moves such that the total volume of the system changes, moving system boundary
work occurs. This is sometimes called expansion or compression work, and it has wide application in mechanical
power technology. In this case, the force is applied by the system through the pressure p (see Figure 4.5a), so
! ! !
F = p A and F . d ! x = pA ! .d ! x = pdV, where p is the pressure acting on the system boundary, ! A is the area vector
(defined to be normal to the system boundary and pointing outward), d ! x is the differential boundary movement,
and dV is the differential volume ! A .d ! x : Consequently,
and for moving boundary work,
ðdWÞ moving
= pdV (4.25)
boundary
Moving boundary work:
ð 1
W 2 Þ moving
boundary
=
Z 2
1
pdV (4.26)
EXAMPLE 4.3
The sealed, rigid tank shown in Figure 4.6 contains air at 0.100 MPa and 20.0 °C. The tank is then heated until the pressure
in the tank reaches 0.800 MPa. Determine the mechanical moving boundary work produced in this process.
(Continued )