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 place to another place.
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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Energy is additive
An isolated system has a fixed sum 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
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•
•
•
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
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•
•
•
•
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
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•
•
•
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 frequency 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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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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https://flowcharts.llnl.gov/archive.html
What you need to know about energy, The National Academies.
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Wasted energy
Yang, Stabler, Journal of Electronic Materials. 38, 1245 (2009)
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System
• A system can be any part of the world.
• The rest of the world is called the surroundings of the system.
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Experimental setup
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A fixed number of H2O molecules
Cylinder
Frictionless, perfectly sealed piston
Weights
Fire
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Isolated system
(isolated system) = (a fixed number of H2O molecules in the cylinder) + (weights) + (fire).
• An isolated system does not interact with the rest of the world.
• Inside the isolated system, energy flows from one part of the system (weights or fire) to another (water).
Isolated system
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Closed system
(closed system) = (a fixed number of H2O molecules in the cylinder).
• The closed system does not exchange matter with its surroundings.
• The closed system exchange energy with its surroundings.
• Weights transfer energy to the closed system by work.
• Fire transfers energy to the closed system by heat.
closed
system
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Thermal system
(not a standard terminology)
(thermal system) = (fixed amount of water) + (fixed set of weights)
• The thermal system does not exchange matter with its surroundings.
• The thermal system does not exchange energy by work with its surroundings.
• The thermal system exchanges energy by heat with its surroundings.
• The system is said to be in thermal contact with its surroundings.
Enthalpy
• (Internal energy of the thermal system) = (internal energy of water) + (potential energy of weights)
• Draw a free-body diagram of the piston. Balance forces acting on the piston: mg = PA
• (Potential energy of weights) = mgh = PAh = PV
• (Internal energy of the thermal system) = U + PV.
• U, P, V are all properties of water, so that (U + PV) is also a property of water.
• Give the quantity (U + PV) a symbol H, and call H = U + PV the enthalpy of water.
thermal system
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Adiabatic system
(not a standard terminology)
(adiabatic system) = water + fire
• The adiabatic system does not exchange matter with its surroundings.
• The adiabatic system does not exchange energy by heat with its surroundings.
• The adiabatic system exchanges energy by work with its surroundings.
• The system is said to be in adiabatic contact with the surroundings.
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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Change the state of a closed system
in two ways
• A closed system does not exchange matter with the rest of the world.
• The closed system exchanges energy with the rest of the world in two ways.
thermal contact
exchange energy by heat
adiabatic contact
exchange energy by work
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Adiabatic work
Variations of Joule’s experiment
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The first law of thermodynamics
To make energy conserved, we discover a form of energy: internal energy.
• Name the states of a closed system using a set of independent properties.
• Internal energy of the closed system, U, is a property (i.e., a function of state) of
the closed system.
• Experimental determination of internal energy. Insulate the closed system to
make an adiabatic system. When we do work Wadiabatic to the adiabatic system,
the system changes from state A to state B, and the change in internal energy
equals the adiabatic work, U(B) – U(A) = Wadiabatic.
• Experimental determination of heat. Now let the closed system interact with
the rest of the world by both adiabatic contact and thermal contact. When the
closed system changes from state A to state B, in general, U(B) – U(A) does not
equal the work W. The difference defines heat, U(B) – U(A) = W + Q.
• Work and heat are not properties of the closed system.
• The art of measuring internal energy and heat is known as calorimetry.
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Force-displacement work
(Isolated system) = (weights) + (ideal spring)
(closed system) =( ideal spring)
• Displacement: x.
• Force acting on the spring by the weights: F.
• work done to the spring by the weights: Fdx.
Isolated system
closed system
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Pressure-volume work
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External force acting on the piston: F
height of the cylinder occupied by the gas: z
Work done by the external force: -Fdz
Volume: V. dV = Adz
Pressure due to external force: p = F/A.
work done by the external to the closed system: - Fdz = - pdV.
Work done in a process: integrate –pdV along the path
state
process
state
closed
system
F
z
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Voltage-charge work
• Charge in the battery: Q
• Voltage acting on the bulb by the battery: V.
• work done to the bulb by the battery: VdQ.
closed system
bulb
conductor of
negligible resistance
current I
voltage V
battery
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Mechanisms of
transferring energy by work
Identify a macroscopic quantity
• Displacement x
• Volume V
• Charge Q
The change in energy associated with such a macroscopic
quantity is called a type of work
• 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.
conduction
convection
radiation
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Pure substance
P, V,T,U
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 of the system
• A property is a function of state.
• Intensive properties: temperature, pressure.
• Extensive properties, volume, energy, enthalpy.
P
state
V
Equations of state
• Use two properties (e.g., pressure P and volume V) as
independent properties to specify (i.e., name) all states.
• Any other property is a function of the two properties. T(P,V)
and U(P,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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Energy has many forms.
Convert energy from one form to another form.
Energy is additive.
Transfer energy from one place to another place.
Discover new form of energy by making the energy of any isolated system conserved.
The energy of a closed system changes as energy transfers by work and heat.
The first law defines internal energy and heat in terms of experimental measurements.
Calorimetry is the art to measure internal energy and heat.
Represent states of a pure substance on planes of various properties.
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