CHAPTER
3
Energy Transfer by
Heat, 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
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FIGURE 3-9
Specifying the
directions of
heat and work.
Formally:
Qin and Wout
are positive,
Qout and Win
are negative
3-1
Heat 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 Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide ‹#›
Work
Processes
P1
State 1
Process line, or path
P3
P2
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
State 2
Chapter 3 Module 1 Slide ‹#›
Work
Electrical Work
• We = VI
• so We = VIΔt if V and I are constant.
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide ‹#›
Work
Mechanical Work
W  F  d s
F
m
ds
s
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide ‹#›
Work
Quasi – equilibrium processes,
best case.
Work at a system
boundary...
There must be a force acting on the boundary.
The boundary must move.
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide ‹#›
Work
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 3-19
A gas does a
differential amount
of work Wb as it
forces the piston to
move by a
differential amount
ds.
3-2
Work transfer at a boundary
Surroundings
System
W>0
W< 0
System Boundary
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide ‹#›
Work
Work of Expansion
p  p gas  pambient
Wb  
x2
x1
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
pAdx
Chapter 3 Module 1 Slide ‹#›
Work
Work of Expansion: p-dV work
V2
Wb  
V1
dV  Adx
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
pdV
p  p(V )
Chapter 3 Module 1 Slide ‹#›
Work
Evaluating a equilibrium
expansion process
p  p(V )
p
p1
p2
V1
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
V2
V = Ax
Chapter 3 Module 1 Slide ‹#›
Work
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 3-20
The area under
the process
curve on a P-V
diagram
represents the
boundary work.
3-3
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 3-22
The net work
done during a
cycle is the
difference
between the
work done by
the
system and the
work done on
the system.
3-4
PROCESSES
INVOLVING
IDEAL GASES
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide ‹#›
Processes Involving Ideal Gases
Polytropic processes...
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide ‹#›
Processes Involving Ideal Gases
The polytropic process:
n
PV =Const.
State 1
p
State 2
V
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide ‹#›
Processes Involving Ideal Gases
Assumptions
• Changes in KE and PE
are zero
• Quasistatic process
• Polytropic process
• Ideal gas
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide ‹#›
Processes Involving Ideal Gases
Expression for work:
V2
W1 2,by   PdV
V1
V2
  P (V )dV
V1
Process equation:
PV  C1  PV
n
1 1
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
n
Chapter 3 Module 2 Slide ‹#›
Processes Involving Ideal Gases
Evaluating the integral:
W1 2,by
C1

dV
V1 V n
P2V2  P1V1

1 n
V2
Note that n cannot equal one, which is the general case.
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide ‹#›
Processes Involving Ideal Gases
For the special case when n = 1:
W1 2,by
C1

dV
V1 V
 V2
 P1 V1 ln
V
 1
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
V2



Chapter 3 Module 2 Slide ‹#›
Processes Involving Ideal Gases
Polytropic processes
p
Isothermal Process
(n = 1)
p1
p2
p2
T1
n>1
T2
V1
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
V2
V
Chapter 3 Module 2 Slide ‹#›
Processes Involving Ideal Gases
Alternative expressions for W1-2
W1 2
W1 2
mR
T2  T1 , n  1

1 n
 V2 
 m RT ln , n  1
 V1 
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide ‹#›
Processes Involving Ideal Gases
Constant pressure
processes...
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide ‹#›
Processes Involving Ideal Gases
Constant pressure process
• Consider as a limiting case of the
general polytropic process.
• P = Constant
• Evaluation of the work integral
V2
W13   PdV  P(V2  V1 )
V1
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide ‹#›
Processes Involving Ideal Gases
Constant pressure, constant temperature
and polytropic processes:
P
1
P = Constant
(n = 0)
Isobaric process
n 1
n 1
2
V
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 2 Slide ‹#›
Processes Involving Ideal Gases
Shaft 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
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 3 Module 1 Slide ‹#›
Work