Modern Engineering Thermodynamics

6.3 Conservation of Energy and Conservation of Mass Equations for Open Systems 171
Note that the ke and pe terms in Example 6.1 amount respectively to only 0.14% and 0.0015% of the total mass flow
energy. This is because the specific enthalpy of steam (and most vapors) usually has a large numerical value, while the specific
kinetic and potential flow energies for most engineering problems usually have much smaller values when converted into
the same units. 2
2 Actually, because of the form of the first law of thermodynamics, we normally compare values of the change in enthalpy, Δh, with the changes in ke, Δke,
and pe, Δpe. Here, too, we find that Δh usually dominates.
6.3 CONSERVATION OF ENERGY AND CONSERVATION
OF MASS EQUATIONS FOR OPEN SYSTEMS
To obtain a general working formula for the first law of thermodynamics for open systems, we begin by constructing
a general energy rate balance (ERB) equation for these systems. The general open system energy rate
balance is given by Eq. (4.22) as
_Q − _W + _E mass
flow
= _E G
where the rate of gain of total system energy _E G is given by Eq. (4.9) as
_E G = d
U + m
V 2 + mgZ/g c
dt 2g c
and the mass flow energy transports are given by Eq. (6.2) as
where
_E mass
flow
system
= ∑ _mðh + ke + peÞ − ∑ _mðh + ke + peÞ
inlet
outlet
ðkeÞ inlet = V2 inlet
2g c
and
ðkeÞ outlet = V2 outlet
2g c
ðpeÞ inlet
= gZ inlet
g c
ðpeÞ outlet = gZ outlet
g c
are the specific kinetic and potential energies of each inlet and outlet flow stream. Combining these equations
gives the general energy rate balance (ERB) for open systems:
General open system energy rate balance
_Q − _W +∑
inlet
= d dt
_mðh + V 2 /2g c + gZ/g c Þ − ∑ _m h+ V 2 /2g c + gZ/g c
outlet
U + mV 2 /2g c + mgZ/g c
system
(6.4)
It must be remembered that the _Q and _W terms in this equation are the net heat and work transport rate terms; that is,
_Q =
∑
all
boundaries
_Q and _W = ∑
all
boundaries
_W (6.5)