Modern Engineering Thermodynamics

280 CHAPTER 9: Second Law Open System Applications
and
Z
ðS T Þ m = sdm
This equation can also be written as
Z Z
ðS T Þ m = sdm=
s dm Z
dt =
dt
_ms dt
where _m is the mass flow rate crossing the system boundary. Differentiation of this equation with respect to
time yields the mass transport rate term as
_S T
m = _ms
Unlike heat and work transports of entropy, it is customary in mass flow transport to write a more explicit formula
for the net mass flow entropy transport rate as
Entropy transport rate due to mass flow
h i
_S T m
= ∑ _ms −∑ _ms (9.1)
net
in out
where the summations are over all inlet and outlet flow streams (the flow streams normally are pipes or ducts
that convey mass into or out of the system).
9.3 MASS FLOW PRODUCTION OF ENTROPY
Mass flow entropy production is due to mass flow that occurs inside the system. No entropy production is due
solely to mass crossing the system boundary, because it is an imaginary boundary of zero thickness. The two
main sources for this type of internal mass flow entropy production are viscous dissipation and diffusion of
dissimilar chemical species.
Viscous dissipation is really a work mode entropy production mechanism and has already been treated in
Eqs. (7.71) and (7.72). Diffusion of dissimilar chemical species inside the system is an advanced topic not treated
in this text. Consequently, if we neglect diffusion, there is no mass flow production of entropy inside a
system, and
ð _S P Þ m = 0
9.4 OPEN SYSTEM ENTROPY BALANCE EQUATIONS
The general entropy rate balance given by Eq. (7.3) equates the net rate of gain of total entropy by a system _S G
to the sum of the net entropy transport rate into the system _S T plus the net entropy production rate within the
system _S P ,or
_S T + _S P = _S G (7.3)
where
dS
_S G = _S system =
dt system
and the transport and production rates of entropy have been identified as caused by heat transfer, work, and
mass flow, or
and
_S T = ð _S T Þ Q
+ ð _S T Þ W
+ ð _S T Þ m
(9.2)
_S P = ð _S P Þ Q
+ ð _S P Þ W
+ ð _S P Þ m
(9.3)