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8/3/2019 Lecture 3 Thermodynamics
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Lecture_ 3 Energy Transfer by
Heat, Work, and Mass
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Processes
Process line, or path
State 1
State 2
P1
P 3
P 2
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Interactions
Ma
System f( P k , k =1...N)=0
Surroundings
Mass Flow
Mass FlowWork
Heat
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Mechanical work flow
Motor Electrical Power
System
Boundary
Work Flow
The turning fan
represents the
result of a mechanical work
transfer.
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Energy Transfer
• Energy transfer to/from closed systems – Heat (Q)
– Work (W )
• Energy transfer to/from open systems (control
volumes)
– Heat (Q)
– Work (W )
– Mass flow )( m
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3-1
FIGURE 3-9 Specifying thedirections of
heat and work.
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Heat
• Heat (Q) is the transfer of energy due to atemperature difference
– a system w/o heat transfer is an adiabatic system
– SI units: kJ
• Heat rate, (kJ/s or kW)
• Heat per unit mass, q = Q/m
• Sign convention:
– Q > 0: heat transferred to system from surroundings – Q < 0: heat transferred from system to surroundings
Q
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Heat Transfer Modes
• Conduction – transfer of heat through a material due to random molecular
or atomic motion; most important in solids
• Radiation
– transfer of heat due to emission of electromagnetic waves,usually between surfaces separated by a gas or vacuum
• Convection
– transfer of heat between a solid surface and fluid due to
combined mechanisms of i) fluid conduction at surface; ii)
fluid flow within boundary layer
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Conduction Heat Transfer
• Fourier’s law of conduction:
dx
dT kAQcond
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Convection Heat Transfer
• Newton’s law of “cooling”, or convection:
)( f sconv T T hAQ
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Radiation Heat Transfer
• Stefan-Boltzmann law of radiation (between a
small surface A of emissivity e and large
surroundings):
44
surr srad T T AQ e
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Work
• Work (W ) is the energy transfer associated with aforce acting through a distance:
• Work rate or power
• Work per unit mass, w = W/m
• Sign convention
– W > 0: work done by system on surroundings
– W < 0: work done on system by surroundings
(kJ) sd F W
kW)or(kJ/s V F W
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Work
dsdt ds
dsdV m
dt dV msd F
V d V V
ds
sd F d W d s
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Work
KE W
V V m
msd F W s
s
2121
21
22
21
2
2
2
1
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Work
m
gm
F s
sd F d W d s
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Work
PE KE
ssgmKE sd F s
s
2121
1221
2
1
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Types of Work
• Moving boundary (compression/expansion) work • Shaft work
• Spring work
• Electrical work
• Other forms; work associated with: – Acceleration
– Gravity
– Polarization
– Magnetization
– Solid deformation
– Liquid film stretching
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Moving Boundary Work• Associated with a volume change of a fluid system
(aka compression-expansion work)
2
1
2
1
2
1
PdV W
PAdxFdxW
b
x
x
x
x
FIGURE 3-19 A gas does adifferential amountof work dW b as it
forces the piston tomove by adifferential amountd s.
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3-3
FIGURE 3-20 The area underthe processcurve on a P-V
diagramrepresents theboundary work.
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Moving Boundary Work, cont.
• Expansion: dV > 0, W b > 0
• Compression: dV < 0, W b < 0
• Work processes on P-V diagram:
curvesbetweenarea
)(curve1-2underarea
(-)curve2-1underarea
exp
1
221,exp
2
112,
W W W
PdV W W
PdV W W
compcycle
b
bcomp
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Moving Boundary Work, cont.
• Special cases:
1) if V = constant, W b = 0
2) if P = constant, W b = P(V 2-V 1)
3) if PV n = constant (known as a polytropic process),
)1( ln
)1( 1
1
211
1122
nV
V V PW
nn
V PV PW
b
b
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3-4
FIGURE 3-22 The net workdone during acycle is thedifferencebetween thework done bythesystem and the
work done onthe system.
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Shaft Work
• Associated with a rotating shaft
unit time)persrev' ( 2
s)revolutionof no. ( 2
thenconstant, if
torque)( 2
1
2
1
nnW
nnW
d Frd W
sh
sh
sh
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Spring Work
• Associated with the extension or compression of aspring; if spring is linear, then force obeys Hooke’s
law,
2
1
2
221
2
1
andconstant)spring(
x xk
kxdxW
k kxF
sp
sp
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Electrical Work
• Associated with the motion of electrons due to an
electromotive force
V
V
V V
I W
I t I
N
N sd E N
sd F W
e
e
current)(
voltage)(
charge)electric( 2
1
2
1
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Evaluating work at a
boundary...
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Note: P gas > P ambient
Direction of Motion
x
X p ambient
The gas is the system for analysis.
Force balance at the boundary on the
piston, where the boundary deforms.
p gas
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)0,0,( xF F
c
ambient gas x
g
gm
A p pF
X
P ambient
P gas
dx
The net force on
the piston.
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Total work done
dxF W xd
dx
g
gm A p A pW
x
x
x
x c
ambgas
2
1
2
1
d
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p ambient
p gas > p ambient
X
dxg
gm A p A pW x
x
x
x c
ambgas
2
1
2
1
d
Component of work due
to expansion of the gasWork to raise
the piston
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Work of Expansion
2
1
x
x
e pAdxW
ambiengas p p p
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Work of Expansion: p-dV work
2
1
V
V
e pdV W
AdxdV )(V p p
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Evaluating a equilibrium expansion process
p
V = AxV 1 V 2
p1
p 2
)(V p p
n egra or
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n egra ora quasistatic process
p
V = AxV 1 V 2
p1
p 2
pAdx pdV W e d
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Conservation of Mass
• “Mass can neither be created nor destroyed” – mass and energy can be converted to each other
according to Einstein’s E=mc2, but this effect is
negligible except for nuclear reactions)
• For closed systems, this principle imposes m =constant since mass cannot cross the system
boundary
• For control volumes, the mass entering andleaving the system may be different and must be
accounted for
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Key concepts and terms
Equilibrium process
Kinetic energy
Path-dependent workQuasistatic process
Work at a system boundary
Work transferWork of expansion
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Mass and Volume Flow Rates
• Mass flow rate: fluid mass conveyed per unit time[kg/s]
where V n = velocity normal to area [m/s] = fluid density [kg/m3]
A = cross-sectional area [m2]
A ndAm V
Mass and Volume Flow Rates, cont.
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Mass and Volume Flow Rates, cont.
• For most pipe flows, = constant and the average
velocity (V ) is used:
• Volume flow rate is given by
v
Am
Am ave
V
V
or
v
V V m
AV
then
V
)(V
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Conservation of Mass Principle - Control
Volume
• Net mass transfer during a process is equal to thenet change in total mass of the system during that
process
where i = inlet, e = exit, 1 = initial state, 2 = final state
• in rate form:
• In fluid mechanics, this is often referred to as the
continuity equation
systemei mmmm )( 12
dt
dm
mm
system
ei
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FIGURE 3-48 Schematic forflow work.
Steady-Flow Processes
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Steady Flow Processes
• Steady-flow or steady-state – a condition where allfluid and flow properties, heat rates, and work
rates do not change with time.
– mathematically:
– applied to mass balance:
0dt d
0dt
dmsystem
Steady-Flow Processes, cont.
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Steady Flow Processes, cont.
• Conservation of mass during a steady-flow process:
• If control volume is single-stream (i.e., one inlet, one
exit), then
ei mm
2
22
1
11
21
orv
AV
v
AV
mmm
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Incompressible Flow
• If = constant, then the mass flow is consideredincompressible
– for steady-flow:
– for single-stream, steady-flow:
ei V V
2211
21
or
V V A A
V V
Total Energy of a Flowing Fluid
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Total Energy of a Flowing Fluid
• A flowing fluid contains internal, kinetic, and
potential energies:
• Fluid entering or leaving a control volume has an
additional form of energy known as flow energy,
which represents the work required to “push” the
fluid across a boundary:
gzue
gzum E
2
21
2
21 or ,)(
V
V
mPvPV W flow energyflow
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3-6
FIGURE 3-51
The total energyconsists of three partsfor a nonflowing fluidand four parts for aflowing fluid.
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Total Energy of a Flowing Fluid, cont.
• The total energy of a flowing fluid (on a unit-mass
basis, ) becomes
• Using the definition of enthalpy (h),
Pvgzu 2
21 V
gzh 2
21 V
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Energy Transport by Mass
• Amount of energy transport:
• Rate of energy transport:
)(2
21 gzhmm E
mass V
)( 221 gzhmm E mass V
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FIGURE 3-58
The absorption ofradiation incident on
an opaque surfaceof absorptivity .