Environmental Engineering Reference
In-Depth Information
It is possible to express the relationship between these properties in differential form by noting
that, for a reversible process,
dq
=
Tds
by equation (3.10), so that
Tds
=
de
+
pd
v
(3.17)
=
dh
−
v
dp
(3.18)
=
dh
+
sdT
−
df
(3.19)
3.7
STEADY FLOW
Many thermodynamic systems incorporate components through which a fluid flows at a mass
flow rate
m
that is invariant in time, which we call
steady flow
. That is true for the compressor,
combustor, and turbine of a gas turbine power plant; for the boiler, steam turbine, condenser, and
feed pump of a steam power plant; but not for the cylinder of an automobile engine, where the
flow is intermittent.
6
If the flow is steady, the first law may be expressed in a form that relates the
thermodynamic properties of the inflowing and outflowing fluid streams with the rates
˙
Q
W
and
at which heat is added to and work is done by the fluid within the component in question,
mh
in
+
Q
−
W
mh
out
=˙
˙
(3.20)
where the subscripts
out
and
in
identify the thermodynamic state of the fluid at the outlet and inlet
of the component.
7
For a boiler,
Q
would be the rate at which heat is added to change the water
W
flow to steam; for a steam turbine,
is the mechanical power delivered by the turbine as its shaft
rotates to drive an electric generator or other mechanical load. If we divide equation (3.20) by
˙
m
,
Q/
˙
W/
˙
then
q
m
are the heat and work quantities per unit mass of fluid flowing
through the device; the change in fluid enthalpy
h
out
−
≡
m
and
w
≡
h
in
is then equal to the sum of these terms,
h
out
−
h
in
=
q
−
w
(3.21)
Many power plant components belong to one of two categories: adiabatic (
Q
=
0) devices
that deliver or absorb mechanical power (e.g., turbines, pumps, compressors) or workless (
W
=
0)
heat exchangers in which a fluid is heated or cooled. The combustion chamber of a gas turbine
power plant is an exception to this rule, because it is both adiabatic and workless.
3.8
HEAT TRANSFER AND HEAT EXCHANGE
While the laws of thermodynamics tell us how much work can be generated by adding and sub-
tracting heat from a working fluid, they don't tell us how quickly we can accomplish this task, a
6
When operated at a steady speed, the inflows of fuel and air and outflow of exhaust gas from an automobile
engine may be regarded as steady, so that steady flow equation (3.20) below may be applied.
7
We have omitted in this expression the contributions of the kinetic and potential energies of the fluid, which
in many cases are negligible compared to the other quantities.
