chapter 3 energy transfer by heat, work, and mass
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CHAPTER
3
Energy Transfer byHeat, Work, and Mass
Heat Transfer
• Heat, means heat transfer.– Energy transfer driven by temperature difference– always hotter to cooler
• Adiabatic – no heat transfer– same as isothermal?
• Symbols used:– Q and q– Q
• Caloric?
Work
• Energy transfer not driven by a temperature difference. Examples– Rising piston– rotating shaft– electric wire crossing the system boundaries
• Symbols used:
• W and w
• W
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
3-1
FIGURE 3-9Specifying the directions ofheat and work.
Formally:Qin and Wout
are positive,Qout and Win
are negative
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide 5Work
Heat and WorkHeat and Work
• Both heat and work are boundary phenomena.
• Systems possess energy, but not heat or work.
• Both are associated with a process, not a state.
• Both are path functions– Magnitudes depend on paths as well as end states
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide 6Work
ProcessesProcesses
Process line, or pathProcess line, or path
State 1State 1
State 2State 2
P1
P3
P2
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide 7Work
Electrical WorkElectrical Work
• We = VI
• so We = VIΔt if V and I are constant.
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide 8Work
Mechanical WorkMechanical Work
sdFW
mm
F
sd
s
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide 9Work
Work at a system Work at a system boundary...boundary...
There must be a force acting on the boundary.
The boundary must move.
Quasi – equilibrium processes,best case.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
3-2
FIGURE 3-19A gas does a differential amount of work Wb as it forces the piston to move by a differential amount ds.
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide 11Work
Work transfer at a boundaryWork transfer at a boundary
SystemSystemSurroundingsSurroundings
W > 0W > 0
W< 0W< 0
System BoundarySystem Boundary
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide 12Work
Work of ExpansionWork of Expansion
2
1
x
xb pAdxW
ambientgas ppp
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide 13Work
Work of Expansion: p-dV workWork of Expansion: p-dV work
2
1
bV
VpdVW
AdxdV )(Vpp
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide 14Work
Evaluating a equilibrium Evaluating a equilibrium expansion processexpansion process
pp
V = AxV = AxVV11 VV22
pp11
pp22
)(Vpp
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
3-3
FIGURE 3-20The area under the process curve on a P-V diagram represents the boundary work.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
3-4
FIGURE 3-22The net work done during a cycle is thedifference between the work done by thesystem and the work done on the system.
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide 17Processes Involving Ideal Gases
PROCESSES PROCESSES INVOLVING INVOLVING IDEAL GASESIDEAL GASES
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide 18Processes Involving Ideal Gases
Polytropic processes...Polytropic processes...
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide 19Processes Involving Ideal Gases
The polytropic process: PVThe polytropic process: PVnn=Const.=Const.
VV
p State 1
State 2
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide 20Processes Involving Ideal Gases
AssumptionsAssumptions
• Changes in KE and PE Changes in KE and PE are zeroare zero
• Quasistatic processQuasistatic process
• Polytropic processPolytropic process
• Ideal gasIdeal gas
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide 21Processes Involving Ideal Gases
Expression for work:Expression for work:
2
1
2
1
)(
,21
V
V
V
Vby
dVVP
PdVW
Process equation:Process equation:
nn PVCVP 111
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide 22Processes Involving Ideal Gases
Evaluating the integral:Evaluating the integral:
n
VPVP
dVV
CW
V
V nby
11122
1,21
2
1
Note that n cannot equal one, which is the general case.Note that n cannot equal one, which is the general case.
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide 23Processes Involving Ideal Gases
For the special case when n = 1:For the special case when n = 1:
1
211
1,21
ln
2
1
V
VVP
dVV
CW
V
Vby
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide 24Processes Involving Ideal Gases
Polytropic processesPolytropic processes
p p
VV11 VV22 V V
TT11
TT2 2
Isothermal Process Isothermal Process (n = 1) (n = 1)
n > 1 n > 1
pp11
pp22
pp22
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide 25Processes Involving Ideal Gases
Alternative expressions for WAlternative expressions for W1-21-2
1,ln
1,1
1
221
1221
nV
VmRTW
nTTn
mRW
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide 26Processes Involving Ideal Gases
Constant pressure Constant pressure processes...processes...
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide 27Processes Involving Ideal Gases
Constant pressure processConstant pressure process
• Consider as a limiting case of the general Consider as a limiting case of the general polytropic process.polytropic process.
• P = ConstantP = Constant
• Evaluation of the work integralEvaluation of the work integral
)( 1231
2
1
VVPPdVWV
V
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide 28Processes Involving Ideal Gases
Constant pressure, constant temperatureConstant pressure, constant temperatureand polytropic processes:and polytropic processes:
1
2
1n
1n
PP
VV
P = ConstantP = Constant(n = 0)(n = 0)Isobaric processIsobaric process
Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide 29Work
Shaft WorkShaft Work
• Work = F∙d– Replace force with torque, T
– Replace distance with angle rotated = 2πn• where n is number of rotations
• Wsh = T(2πn) or
• Wsh = T(2πn) where n is frequency in Hz