Modern Engineering Thermodynamics

168 CHAPTER 6: First Law Open System Applications
Open system problems are written with their flow stream thermodynamic properties evaluated at inlet and
outlet data monitoring stations. This is done in an attempt to simulate the way in which engineering data are
provided from experimental or field measurements. The bulk properties inside an open system do not normally
change from one equilibrium thermodynamic state to another during the process of interest, as do closed system
bulk properties. In fact, the vast majority of open systems of engineering interest are not in any equilibrium
state, since the thermodynamic properties of the material passing through them are continually changing inside
the system between the inlet and the outlet flow streams. However, most open systems do reach a “steady state”
nonequilibrium operating condition in which the total mass and energy they contain does not change with
time. Any open or closed system can be indefinitely maintained in a steady nonequilibrium state if it has the
proper energy or mass flows passing through it.
In addition, many thermodynamic properties are mathematically defined only for equilibrium conditions. If the
steady state properties within a system do not exhibit large variations between two neighboring points, then
we say that these points are in local thermodynamic equilibrium. The local equilibrium postulate introduced in an
earlier chapter states that a small volume, large enough for the continuum hypothesis to hold, is in local equilibrium
so long as its internal properties do not vary significantly within its borders. This means that the properties
cannot change significantly in a distance on the order of the molecular mean free path at the point in
question. 1 Most nonequilibrium processes of engineering interest obey this postulate. A few systems, such as
those containing shock waves, do not. For example, if rapid explosions occur within a piston-cylinder apparatus
(as in an internal combustion engine) or if the piston speed exceeds the speed of sound in the cylinder, then
the gas in the cylinder is far from equilibrium and an accurate thermodynamic analysis becomes very difficult,
from both a measurement and a theoretical point of view.
6.2 MASS FLOW ENERGY TRANSPORT
Mass flow energy transport occurs whenever mass crosses the system boundary. It consists of two parts. The first
part is the total energy associated with the flow stream mass itself, and the second is the energy required to
push the flow stream mass across the system boundary (this part is often called the flow work). Let an increment
of flow stream mass dm be added to or removed from a system. The total energy dE m associated with dm crossing
the system boundary is given by
dE m = ðu + ke + peÞ dm
Figure 6.1 shows an incremental slug of mass with velocity V crossing a system boundary. The slug’s volumeis
dV = AdL, and its mass is dm = ρ dV = ρA dL, where ρ is the mass density of the slug. In the time increment dt,
Flow stream slug of mass, dm
Pressure
p
dL
Area
A
Slug velocity
V
Center of
gravity
System boundary
Flow stream
height, Z fs
Internal
energy
U
System velocity V sys
System C.G.
height, Z sys
Z = 0
FIGURE 6.1
Open system flow stream and system energies.
1 In air at standard temperature and pressure (STP), the molecular mean free path is approximately 8 × 10 −8 m, or 3 × 10 −6 in.