egr 334 lecture 02 work and energy
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8/11/2019 EGR 334 Lecture 02 Work and Energy
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Chapter 2
Lecture 02:
Work and Energy
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Today’s Objectives:
• Be able to distinguish between work and energy.• Be able to calculate Kinetic Energy• Be able to calculate Potential Energy• Be able to calculate Work done by an acting force• Be able to calculate Power
• Be able to calculate Work done by gases undergoing changesof state.• Be able to explain the concept of Internal Enegy
Reading Assignment:
Homework Assignment:
• Read Chap 2. Sections 1-5
From Chap 2: Problems 6, 20, 24, 32
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Work, Heat, and Energy
Energy is conserved, but can be converted to different types
Ways to Transfer Energy Into or Out of A System
Work – transfers by applying a force and causing adisplacement of the point of application of the force.
Mechanical Waves – allow a disturbance to propagatethrough a medium.
Heat – is driven by a temperature difference between tworegions in space.
Matter Transfer – matter physically crosses the boundaryof the system, carrying energy with it.
Electrical Transmission – transfer is by electric current. Electromagnetic Radiation – energy is transferred byelectromagnetic waves
W = PE = KE = U
3Sec 2.1: Reviewing Mechanical Concepts of Energy
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Thermodynamics “Work”
“Work is done by a system onits surroundings if the soleeffect on everything external
to the system could have been done by raising (ordropping) a weight.”
Physics definition of work is W = F sBut, in thermodynamics often we are working with
fluids (non-solids), so we need a broader definition.
4Sec 2.2: Broadening Our Understanding of Work
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Joule’s Experiment (1845-Salford, England)
Joule dropped a known mass and measured the change intemperature of the water.
The experiment was conducted in the basement of his family’s brewery, where there was a constant ambient temperature.
The friction of the water molecules rubbing together caused thetemperature to increase.
5Sec 2.2: Broadening Our Understanding of Work
Joule’s Equipment - Manchester
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Work Sign Convention
W > 0 : Work done BY the system
W < 0 : Work done ON the system
6Sec 2.2.1: Sign Convention
Sign is not inherently important, but this is the convention.
W < 0 : Work done ON the system
(System is compressed)
W > 0 : Work done BY the system
(System expands)
f
i
V
V PdV W
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Power = Rate of Energy Transfer
Book’s convention: Dot above symbol represents the rate.
7Sec 2.2 .2: Power
The rate of work can be expressed as
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Work Properties
Work is NOT a property of a system like V , T , or E .Work occurs when the system undergoes a process.
8Sec 2.2 : Work
A differential of a property is exact.
V
f
i
V
f iV
V dV V V The differential of work depends upon the path.
f
i
V
V W pdV
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But, work depends on the process.
9Sec 2.2 : Work
For “Bobby” work
depends on the path,
since friction is a non-
conservative force.
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So, we need to have a PV relationship for
the process.
10Sec 2.2 : Work
The process of changing volume is NOTnecessarily in equilibrium.
- He balloon popping, gas does not
instantly mix with air- Gas cylinder rupture, pressure inside ishigher then outside for some time, t
For this class, we will used an idealized process, that arecompletely reversible. We call this type of process
- quasi-equilbirium
- quasi-static
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11Sec 2.2 : Work
Consider a box initially divided in half.
- Initially, one is filled with gas, the other a vacuum.
- The divider is then removed.
- The gas takes some time to fill the new volume.
During that time, there are different local values for Pin the volume. There is also likely some heat
generated, as the process is irreversible.
Non-quasi-static Process
V V V
Thermodynamics ≠ Kinetics
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12Sec 2.2 : Work
Now we move the wall slowly, such that the gas is able to
adjust instantly. This is a reversible quasi-static process.
Quasi-static
V V V V
V V V V
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Example (2.34): Air contained within a piston-cylinder assemblyundergoes three processes in series. Evaluate W .
Process 1-2: Compression at constantpressure from p1=10 psi, V 1=4.0 ft3 to state 2
Process 2-3: Constant volume heating to state 3, where p3=50 psi
Process 3-1: Expansion to the initial state, during which the p-V relationship is pV = constant .
psi P
13
V
3 ft V
4
10
50
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14
S d i O d di f
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Energy
Physics energy typesKinetic Energy: Energy of objects in motion
Potential Energy: Energy of objects in a field (g,E,B)
Internal Energy
SpringChemical
Pressure
15Sec 2.3: Broadening Our Understanding of Energy
Pressure can be a form of energy if P > P atm
P atm
P Thus, the general energy
equation is
E PE KE U
6
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Example Problem (2.37) A 10 V battery supplies a constant current of0.5 amp to a resistance for 30 min.
a) Determine the resistance, in ohms. b) For the battery, determine the amount
of energy transfer to work, in kJ.
16
Solution:
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Example Problem (2.31)
Air contained within a piston-cylinder assembly is slowly heated. Asshown in Fig P2.31, during the process the pressure first varies linearly with volume and then remains constant. Determine the total work inkJ.
17
150
100
P (kPa)
V (m3)0.0700.0450.030
50
1
2 3
Solution:
8
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End of Lecture 02
• Slides that follow show solutions to Exampleproblems.
18
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Example (2.34): Air contained within a piston-cylinder assemblyundergoes three processes in series. Evaluate W.
Process 1-2: Compression at constant pressure from P1=10 psi, V1=4.0 ft3
to state 2
19
psi P
3 ft V 4
10
50
12
3
2
112 2 1
1 1 3 3 2 3
12 3 1
3
3 3
2
P
since:
:
104 0.8
50
V
V
W PdV V V
PV PV and V V
P then V V V
P
psiV ft ft
psi
Process 1-2: Isobaric Process
BTU ft psiW
f lb ft BTU
in
ft 92.548.010
778
1443
12 2
2
20
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Example (2.34): Air contained within a piston-cylinder assemblyundergoes three processes in series. Evaluate W.
Process 2-3: Constant volume heating to state 3, where P3=50 psiProcess 3-1: Expansion to the initial state, during which the P-Vrelationship is PV = constant.
20
psi P
3 ft V
4
10
50
12
3
Process 2-3: Isovolumetric Process
002323
W V
21
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Example (2.34): Air contained within a piston-cylinder assemblyundergoes three processes in series. Evaluate W.
Process 2-3: Constant volume heating to state 3, where P3=50 psiProcess 3-1: Expansion to the initial state, during which the P-Vrelationship is PV = constant.
21
psi P
3 ft V
4
10
50
12
3Process 3-1: Isothermic Process
3
11
3
1
3
lnC31 V
V V
V
V
V dV
V
C PdV W
23
3 2
14443
31 7780.810 4 ln
11.9
f
f t ft BTU
ft lb ft inW psi ft
BTU
3
1ln1131 V
V V P W
22
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Example Problem (2.37) A 10 V battery supplies a constant current of0.5 amp to a resistance for 30 min.
a) Determine the resistance, in ohms. b) For the battery., determine the amount
of energy transfer to work, in kJ.
22
Solution: Electrical Work Principle
elec P VI elec elecW P t therefore: V = 10 V I = 0.5 A Δt =30 min
(10 )(0.5 ) 5elec
P VI V A W
60 1 / 1(5 )(30 min)
1 min 1 1000elec
s J s kJ W W
W J
then
0.15elec
W kJ
23
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Example Problem (2.31)
Air contained within a piston-cylinder assembly is slowly heated. As shown inthe figure, during the process the pressure first varies linearly with volume
and then remains constant. Determine the total work in kJ.
23
150
100
P (kPa)
V (m3)0.0700.0450.030
50
1
2 3Solution: B
A
V
A B
V
W p dV
Conceptually, this representsthe area of the P-V plotunderneath the process lines.
2
1
1 2 _
V
PV trapezoid
V
W p dV A 3
2
2 3 _ rectangle
V
PV
V
W p dV A 31
(100 150)(0.045 0.030)2
kPa m 3(150)(0.070 0.045) kPa m
23 1 / 1
1.875 1.8751 1
kN m kJ kPa m kJ
kPa kN m
2
3 1 / 13.75 3.75
1 1
kN m kJ kPa m kJ
kPa kN m
1 3 1 2 2 3 1.875 3.75 5.625total W W W W kJ