ENERGY
I am teaching Engineering Thermodynamics using the textbook by Cengel and Boles.
A few figures in the slides are taken from that book, and most others are found online.
Similar figures can be found in many places.
I went through these slides in two 90-minute lectures.
Zhigang Suo, Harvard University
Energy
The world has many parts: stars, planets, animals, molecules, electrons, protons...
The parts move relative to one another, and interact with one another.
The motion and interaction carry energy.
Energy is a fundamental concept.
We don’t know how to define energy in more fundamental concepts.
But we do know how to measure and calculate energy.
That is all that matters.
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Potential energy
m
When a mass m is lifted by a distance z,
The energy increases by
State 2
z
mgz.
We call this energy the potential energy.
m
state 1
3
Kinetic energy
velocity v
stationary
m
m
state 1
state 2
From the stationary state to a state of velocity v, the energy increases by
1
mv2
2
We call this energy the kinetic energy.
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Zero-sum game
1
mv2 + mgz = constant
2
state 1
velocity = 0
height = 0
h
1
mv2 - mgh = 0+0
2
state 2
state 2
velocity = v
height = -h
state 1
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Newton’s second law
dv
a=
dt
ma = f
dz
v=
f = -mg
dt
dv
m + mg = 0
dt
dv
m v + mgv = 0
dt
z
mg
ö
d æ1
2
ç mv + mgz ÷ = 0
dt è 2
ø
1
mv2 + mgz = constant
2
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Vocabulary
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•
•
•
Forms of energy (kinetic energy and potential energy)
Conversion of energy from one form to another form.
Transfer of energy from one part of the system to another part.
Conservation of energy. When kinetic energy and potential energy
convert to each other, their sum is fixed. Really?
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Joule’s discovery
1
mv2 + mgz
2
decreases
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Internal Energy
Isolated system
(isolated system) = fluid + paddle + weight
(internal energy) + (kinetic energy) + (potential energy) = constant
1
U + mv2 + mgh = constant
2
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Internal energy and molecular motion
Even when a tank of water is stationary at a macroscopic scale,
water molecules undergo rapid and ceaseless motion.
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A game-changing idea
The principle of the conservation of energy
A new zero-sum game
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•
•
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An isolated system has a fixed amount of energy.
What if energy of all known forms is not conserved?
Discover another form of energy to make energy conserve.
But what qualifies as a new form of energy?
Anything that can convert to a known form of energy.
Sounds like a self-fulfilling prophesy. It is.
My view on the principle of the conservation of energy follows, I believe, Feynman.
Read his tale of “Dennis the Menace”. http://www.feynmanlectures.caltech.edu/I_04.html
The Feynman’s Lectures on Physics ought to be required reading for all engineers.
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Elastic energy
•
•
•
•
Gradually add weights from different heights to pull the spring.
When the length of the spring is x, the amount of weights to maintain the length of the spring is F(x).
When the length increases by dx the potential energy of the weights reduces by F(x)dx.
The total reduction of the potential energy of the weights is
x
ò F ( x ) dx
•
•
•
•
•
0
The same amount of energy is added to the spring as elastic energy.
The spring is a lattice of atoms. The elastic energy is stored in the stretched atom bonds.
How do I know? Gradually remove the weights to place them back to the original heights.
(Isolated system) = weights + spring.
(energy of the system) = (potential energy of the weights) + (elastic energy of the spring) = constant
Isolated system
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Force-length curve
Ideal spring
Force, F
Force, F
loading
loading
x
ò F ( x ) dx
unloading
0
Elongation, x
Elongation, x
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Force-length curve
dissipative spring
Force, F
loading
energy dissipated
by the spring
unloading
Elongation, x
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Force-length curve
dissipative spring
(isolated system) = weights + spring + (insulated room)
(potential energy of the weights) + (elastic energy of the spring) + (internal energy of the room) = constant
Force, F
loading
energy dissipated
by the spring
unloading
Elongation, x
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Electrical energy
(isolated system) = battery + bulb + (insulated room)
(chemical energy of the battery) + (internal energy of the bulb) + (internal energy of the room) = constant
Energy per unit time (power) going out the battery = VI
Isolated system
bulb
conductor of
negligible resistance
current I
voltage V
battery
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Convert chemical energy to electrical energy
lithium-ion battery
Electron 
wire
Lithium-ion

electrolyte
electrode
•
•
•
•
electrode
Electrodes host lithium atoms.
(lithium atom) = (lithium ion) + (electron)
Electrolyte conducts lithium ions.
Wire conducts electrons.
Electromagnetic energy
n w
• n: number of photons
• » 10-34 J × s Planck’s constant
• w frequncy of the electromagnetic wave
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Surface energy of liquid
• Molecules on surface have different energy from those in the interior.
• When the area of surface increases, more molecules come to the surface.
• The extra energy of the surface is proportional to the area of the surface:
U =ssA
• ss is the surface energy (per unit area).
dU = Fdx
2s sbdx = Fdx
2s sb = F
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Energy is an over-rated concept and an
over-used word. The word tells you nearly
nothing about the process.
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•
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Chemical energy
Elastic energy
Kinetic energy
Potential energy
Thermal energy
…..
Does the inventor of this toy really get helped by all these words? I don’t think so.
Do these words help us understand how this toy work? Not really.
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Convert energy from one form to another
kinetic
potential
light
electrical
chemical
nuclear
thermal
kinetic
turbine
falling object
solar
sail
motor
explosion
atomic bomb
steam engine
potential
rising object
seesaw
atomic bomb
balloon
light
triboluminescence
electrical
generator
hydro-electric
chemical
electric
pump
light bulb
chemoluminescence
atomic bomb
fire
photoelectricity
electrical
circuit
discharge
battery
nuclear power
station
thermoelectricity
photosynthesis
charge
battery
chemical
reaction
atomic bomb
chemical
reaction
nuclear
reaction
nuclear
thermal
friction
falling object
radiator
radiator
fire
atomic bomb
heat
exchanger
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https://flowcharts.llnl.gov/
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Wasted energy
Yang, Stabler, Journal of Electronic Materials. 38, 1245 (2009)
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What you need to know about energy, The National Academies.
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One experiment, many ways to look at it
Isolated system
Experimental setup
• A fixed number of H2O molecules
• Cylinder
• Frictionless, perfectly sealed piston
• Weights
• Fire
System
• A system can be any part of the world.
• The rest of the world is called the surroundings of the system.
Isolated system
• An isolated system does not interact with the rest of the world.
• No exchange of matter. Seal the cylinder.
• No exchange of energy. Jam the piston. Insulate the cylinder.
• Do whatever necessary to prevent the rest of the world from affecting the
system.
• Here, (isolated system) = (a fixed number of H2O molecules in the cylinder) +
(weights) + (fire).
• Within the isolated system, energy flows from one part of the system (weights
or fire) to another (water).
closed
system
Closed system
• The system exchange energy with its surroundings.
• The system does not exchange matter with its surroundings.
• Here, (closed system) = (a fixed number of H2O molecules in the cylinder).
• Weights transfer energy to the system by work.
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• Fire transfers energy to the system by heat.
System
thermal system
(thermal system) = (fixed amount of water) + (fixed set of weights)
• (Internal energy of the thermal system) = (internal energy of water) +
(potential energy of weights)
• H = U + PV.
• H is call the enthalpy of water.
(adiabatic system) = water + fire
• The system exchange energy with its surroundings.
• The system does not exchange matter with its surroundings.
• Here, (closed system) = (a fixed number of H2O molecules in the
cylinder).
• Weights transfer energy to the system by work.
• Fire transfers energy to the system by heat.
adiabatic system
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Systems interact with
the rest of the world in various ways
Exchange matter
Exchange energy
by work
Exchange energy
by heat
Open system
yes
yes
yes
Isolated system
no
no
no
Closed system
no
yes
yes
Thermal system
no
no
yes
Adiabatic system
no
yes
no
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Adiabatic work changes internal energy
Variations of Joule’s experiment
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From isolated system to closed system
(Isolated system) = (weights) + (ideal spring)
(closed system) =( ideal spring)
• Force acting on the spring by the weights: F(x).
• work done to the spring by the weights: F(x)dx.
• Change in the elastic energy of the spring: dU = F(x)dx.
Isolated system
closed system
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Electrical Work
work per unit time (power) going out the battery = VI
closed system
bulb
conductor of
negligible resistance
current I
voltage V
battery
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Transfer energy to a closed system
in two ways
(closed system) = (fixed number of water molecules)
thermal contact
transfer energy by heat
adiabatic contact
transfer energy by work
• The two ways cause the same change in state.
• Internal energy is a property of the closed system.
• Work and heat are not properties of the closed system.
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Mechanisms of
transferring energy by work
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Force-displacement, Fdx
Pressure-volume, PdV.
Voltage-charge, VdQ.
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Mechanisms of
transferring energy by heat
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Conduction. Energy flows via waves of atomic vibration. Matter does not flow
Convection. Matter flows, energy flows with it.
Radiation. Light, electromagnetic wave. With or without matter.
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The first law of thermodynamics
• For all adiabatic processes between two states of a
closed system, the net work done is the same
regardless of the nature of the closed system and the
details of the process.
• Determine the change in internal energy by adiabatic
process, DU = W.
• For a closed system, in general DU is not equal to W.
• The difference defines heat, DU = W + Q.
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Pure substance
Thermodynamic states of the system
• Add a little heat and add a little weight to the closed system
• Isolate the system.
• The system isolated for a long time approaches a
thermodynamic state of equilibrium.
• The states of the system has two independent variations.
Thermodynamic properties (variables) of the system
• A property is a function of state.
• Intensive properties: temperature, pressure.
• Extensive properties, volume, energy, enthalpy.
Equations of state
• Use two properties as independent variables to specify (i.e.,
name) all states. TV
• Once the values of the two properties are fixed, a state of
the system is fixed.
• Any other property is a function of the two properties. P(T,V)
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Internal energy of a pure substance
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Internal energy U is an extensive property.
Internal energy per unit mass, u = U/m
For a state outside the dome, u(P,T)
For a state inside the dome, u = xuf + (1-x)ug.
P = 0.1 MPa
T
u
uf
u
ug
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Enthalpy of a pure substance
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Enthalpy H is an extensive property.
Enthalpy per unit mass, h = H/m
For a state outside the dome, h(P,T)
For a state inside the dome, h = xhf + (1-x)hg.
Latent heat hgf = hg - hf
P = 0.1 MPa
T
u
hf
h
hg
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Choices of two independent variables
5 variables (PTvuh), 10 choices
a
P
critical
point
liquid
a
gas
T
a
T
T
liquid
gas
u
liquid
P = 0.1 MPa
gas
gas
P = 0.1 MPa
liquid
u
h
v
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Three phases
u
gas
liquid
solid
v
intensive-intensive
extensive-intensive
extensive-extensive
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Summary
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Forms of energy.
Convert energy from one form to another form.
Energy is additive.
Transfer energy from one place to another place.
The energy of an isolated system is conserved.
The energy of a closed system changes when heat and work are come
from the rest of the world.
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