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Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1 , [email protected] , VŠE / CEMS-MIM-BLOCK SEMINAR; Prague ´11-09-06 1 Czech Technical University in Prague, Faculty of Transportation Sciences, dept. of Control and Telematics, Konviktská 20, Praha 1, CZ 110 00, Czech Republic.

Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, [email protected],

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Page 1: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Czech Technical University in Prague

Faculty of Transportation Sciences  Department of Control and Telematics

WHAT IS ENERGY ?

Zdeněk Votruba1, [email protected],

VŠE / CEMS-MIM-BLOCK SEMINAR; Prague ´11-09-06

1 Czech Technical University in Prague, Faculty of Transportation Sciences, dept. of Control and Telematics, Konviktská 20, Praha 1, CZ 110 00, Czech Republic.

Page 2: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Abstract

Fundamentals of the concept of energy are reviewed.

The aim is to unify the knowledge of students and emphasize the essential context.Attention is also paid to the energy balance of the Earth and to the concepts of sustainable / green energy.

Key Words: Work, Energy, Power, Energy density, Energy Transformation, Conservation and/or Degradation of Energy, Entropy, Ordering, Efficiency, Carnot cycle, Energy resources, Green Energy, Smart grid

Page 3: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Contents1. Concept of Energy2. Fundamentals of Energy in Physics:

Energy and Work, Related Variables (Power, Energy Density, etc.); Units; Kinetic and Potential Energy; Energy of (Chemical or Nuclear) Bonds; Electric

Energy; Energy of Fields, Energy of (Electromagnetic) Waves; Radiation

3. Energy and Ordering: Temperature, Enthalpy, Entropy

Selected Parts of Thermodynamics / Statistical Physics1st and 2nd Laws of ThermodynamicsConservation / Dissipation of Energy

4. Energy Transforms Efficiency of Energy Transforms Carnot Cycle

5. Relations (Systemic View): Energy – MassEnergy – Information

6. Energy Releasing, Transmission and Storage7. Global Energy Balance8. Sustainability of Energy Use, “Green Energy” 9. Concept of Smart Net

Page 4: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

1. Concept of Energy

Modern concept of Energy is based on ideas of G. Leibniz (approx. 1700) who introduced “vis viva“ (living force), defined as the product of the mass of an object and its velocity squared.

An important contributors to this concept were as well: I. Newton, T. Young (he was possibly the first to use the term

"energy" instead of vis viva). G. G. Coriolis (introduced “kinetic energy“), W. Rankine (“potential energy“), W. Thomson (-Lord Kelvin- formulated the laws of thermodynamics). Consequently R. Clausius, W. Nerst and J.W. Gibbs explained backgrounds of chemical processes. This achievement also led to an introduction of the concept of entropy by R. Clausius.

A. Einstein explained the principle of energy-mass equivalence.Links to the concept of information established L. Brillouin (1956).

Energeia (Energeia) Aristotle´s concept (4th century B.C.), (related to Ergon – work) could be translated into English approx. as “being-at-work“. Examples of energeiai (energeai) in Aristotle's works are: eudaimonia (eudaimonia) – pleasure / happiness and kinesis (kinesis), translated as movement / motion, or in some contexts change.

Page 5: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

1. Concept of Energy

Energy is a Category. It is quite difficult to define Categories - frequent approach being to state significant features:

Energy (E): the capacity / ability of a physical system to perform

work (or the work itself)® scalar entity® integral of the motion E – conservation significant

consequence of the translational symmetry of time; implied by the empirical fact that the rules of the System, e.g. the laws of physics do not change with time itself.

® E / t - conjugation® Indirectly measureable (?)® quantifiable to the constantRecommended reading:http://www.ftexploring.com/energy/definition.htmlhttp://phet.colorado.edu/en/simulation/energy-skate-park

Page 6: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

2. Fundamentals of Energy in PhysicsEnergy & Work - 1

Work (Def. Encyclopaedia Britannica):

work,  in physics, measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement.

Why this smart definition is of limited use for us?

Recommended explanatory reading:

http://physics.info/work/

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 7: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

2. Fundamentals of Energy in PhysicsEnergy & Work - 2

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Work: W= F.d = F d cos        (1)Where: W is work – a scalar quantity; is the angle between the vector of force F (constant)

and the displacement vector d; Dot ( .) means scalar (dot) product.

F

d

C

Page 8: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

2. Fundamentals of Energy in PhysicsEnergy & Work - 3

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

The more general definition of mechanical work (for F(t) const.) is given by the line integral:

WC = CF.dx

where:C is the path traversed by the object;F is the force vector; andx is the position vector.• The notion of force is often related with the concept of

(force) vector field. Give some of them!

• The calculation of WC is path-dependent cannot be differentiated to give F.dx.

Is there any possibility of a nonzero force doing zero work?

(2)

Page 9: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

2. Fundamentals of Energy in PhysicsEnergy & Work - 3

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

• Work done by a torque can be calculated in a similar manner. The arc length s can be calculated from the angle of rotation (expressed in radians) as s = r , and the (vector) product F x r is equal to the torque . Hence, a constant torque does work as follows:

W= (3)

• The work done by a force acting on an object depends on the choice of reference frame, because displacements and velocities are dependent on the reference frame in which the observations are being made.

Page 10: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

2. Fundamentals of Energy in PhysicsEnergy & Work - 4

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

E

E1

E2

W= E2 – E1

 The work done on the object (System) is equal to the change of (kinetic) energy.

E2 – E1 = E = W (4)

Page 11: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

2. Fundamentals of Energy in PhysicsRelated Variables - 1

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

• Power is the rate at which work (W) is performed or Energy (E) converted (released / transformed /dissipated / thermalized)

P = dW/dt; or P = dE/dt (5)

It also means that work done in time interval t a,b is:

W= a

bP dt (6)

P is scalar variable

Page 12: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

2. Fundamentals of Energy in PhysicsRelated Variables - 2

Ev Energy density (volumetric – by volume):

Ev =DE/DV (7)

Ev is scalar variable

Em Energy density by mass, also Specific

Energy:

Em =DE/ D m (8)

EM is scalar variable

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 13: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

2. Fundamentals of Energy in PhysicsUnits - 1 (SI - Multiplication factors)

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 14: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

2. Fundamentals of Energy in PhysicsUnits -2

Energy, Work E, W: Basic unit SI: J……JouleThe work done when the point of application of a force of 1 newton is displaced through a distance of 1 meter in the direction of the force, or e.g.: The work required to produce 1W for 1 s.

Alternative (non SI) units: eV (electronvolt) 1 eV = 1.602176487(40)×10−19 J (or

approx. 160 zepto J) is equal to the amount of kinetic energy gained by an electron when it accelerates through an electric potential difference of one volt

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 15: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

2. Fundamentals of Energy in PhysicsUnits -3

kWh (kilowatt-hour) is defined as the power of 1kW continuously acting for 1 hour

Exact definition: 1kWh = 3.6 MJ kcal (kilocalorie) - approx. equivalent of energy needed

to increase the temperature of a kilogram of water by 1 °C ;

Exact definition: 1 kcal = 4.184 kJ Btu (British Thermal Unit) – approx. the amount of

energy needed to heat 1 pound (0.454 kg) of water from 39 to 40 ° F (3.8 to 4.4° C)

Exact definition: 1Btu = 1.055056 kJ (approx. 1kJ)

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 16: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

2. Fundamentals of Energy in PhysicsUnits - 4

Power PBasic unit SI: W……Watt, i.e.: Joule per second

W = J/s VA (voltampere)

Alternative (non SI) units:

HP….horsepower (this unit was originally introduced to compare the output of engines with the power of draft horse) Exact definition: 1HP = 0.735 kW

Energy density EV, Em:Use SI units only, i.e.: Joule per cubic meter J m-3 , and Joule per kilogram J kg-1 respectively.

WHY ?

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 17: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Kinetic energy

The kinetic energy of an object is the energy which it possesses due to its motion.

Non-rotating rigid body with mass m and velocity v (vc) in the chosen frame of reference has kinetic energy:

Ek = mv2/2 = p2/2m ; where impulse p = mv (9)

Rotating rigid body with moment of inertia I and angular velocity in the chosen frame of reference has kinetic energy of rotation: Ekr = I2/2 (10)

For more bodies and also for both rotation and translation the kinetic energy is the additive entity.® For v c: Ek = mc2 - mc2 where = (1-v2/c2)-1/2 (11)

® Can you specify another types of kinetic energy? Czech Technical University in Prague - Faculty of Transportation Sciences

Department of Control and Telematics

Page 18: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Potential energy

® Potential Energy is the Energy stored in a System resulting from the configuration of Systems components, or from the position in force field.

® Potential energy is a function of the Systems State® This type of energy also has the capacity to do

work on its own. ® It is also capable of changing into other forms of

energy. ® There are various types of potential energy, each

associated with a particular type of force field and/or forces associated with Systems components configuration.

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 19: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Potential energy - Examples

Elastic potential energy:= potential energy of an elastic body (for example a spring) that is deformed under the tension or compression. It arises as a consequence of a force that tries to restore the object to its original shape, (which is often the electromagnetic force between the atoms and molecules that constitute the object). If the stretch is released, the energy is transformed into kinetic energy. In the simplest case of a spring (F = - kx);

Ep= - F.dx = = --kxdx = kx2/2 +const. (12) Gravitational potential energy := potential energy

associated with the field of gravity. It has a number of practical uses, notably the generation of hydroelectricity. Local approx.: F = mg ; Ep = mgh + const. (13)

Newton approx.: Ep = - Mm/r + const. (14)Czech Technical University in Prague - Faculty of Transportation Sciences

Department of Control and Telematics

Page 20: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Potential energy – Examples 2

Electric / magnetic potential energy Chemical binding energy:= form of potential energy

related to the structural arrangement of atoms / molecules. This energy can be transformed to other forms of energy by chemical reactions. For example when a fuel is burned the chemical energy is converted to heat, same is the case with digestion of food metabolized in an organism. Green plants transform solar electromagnetic energy to chemical energy through the process of photosynthesis.

Nuclear binding energy := energy of the particles inside an atomic nucleus. - Fission / fusion.

Fusion: Sun: 4Mt/s (H He) releasing electromagnetic radiation

Can you specify another types of potential energy?

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 21: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Relations of kinetic and potential energy -exercise1Kittel

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Ek K(x) ; Ep U(x)

Page 22: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Relations of kinetic and potential energy –exercise - 2Kittel

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 23: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Relations of kinetic and potential energy –exercise -3Kittel

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 24: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Relations of kinetic and potential energy – exercise 4Kittel

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 25: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Relations of kinetic and potential energy –exercise 5Kittel

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 26: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Relations of kinetic and potential energy –exercise 6 Kittel

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 27: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Electric energy -1

Electrostatic energy:

(potential energy)

capacitor

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Ep= ½CU2 = ½QU (15)

C A/dEv =DE/DV /d2 ____________________________Where: U … potential difference (voltage) V A…surface of capacitor plate m2C…capacitance F d…thickness of the dielectric…permitivity of the dielectricQ…electric charge AsHow to increase the amount of stored energy?

Page 28: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Electric energy -2

Electromagnetic energy

Potential energy of the magnetic field, which is generated by (?) electric current

Inductance L

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Ep = ½LI2 = ½ I (16)

Where:L… inductance HI… electric current A…magnetic flux Wb, i.e. V.s

= S B.dS ;

In the persistent state (superconductivity) the current and magnetic field are storedHow to increase the amount of stored energy?

Page 29: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Electric energy -3

W=ab pdt (work converted to

heat) (17)

p (t)…power W ; t…time sp (t) = u(t).i(t) = Ri2(t) =u2(t)/R

__________________________

For constant current and voltage:

W= P.t; P= U.I =RI2 =U2/R

__________________________

For alternate - harmonic current (phasors):

W= P.t; P = U.I.cos

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Electric Energy Heat

Transformation (dissipation)

Resistor R (Ohms law: u = R.i )

Page 30: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Energy of electromagnetic wave -1

(kinetic energy?)

E=P .S.t (18)

t…time

S…surface perpendicular to wave transmission

P…Poynting vector

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

P = E × H* Paverage = ½E0H0 W/m2

(Sun Earth surface 1.37 kW/m2)

Direction of P vector is the same as transmission directionRadiation pressure prad = paverage /c Pa = N/m2

is the pressure exerted upon any surface exposed to electromagnetic radiation (Sun Earth surface prad = 4.6 Pa)

Page 31: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Energy of electromagnetic wave -2

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Utilizing “Wave – corpuscular dualism“

Concept of Photon (particle with zero rest mass and with the velocity of the light - c)

E = N Ephoton ; Ephoton = h = ħ (19)

= /2 …. frequency Hz = s-1h = ħ/2….Planck constant h = 6,626 069 57(29) x 10-34 J.s

Example : Photon of green light; wavelength 555 nm, = 540 THz; Ephoton = 3.58×10−19 J. For N := (Avogadro number) = 6.022×1023 of photons E =216 kJ

Page 32: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Energy of thermal radiation-1

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Plancklaw

Page 33: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Energy of thermal radiation-2

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Stefan – Boltzmann lawE=Prad t (20)

Prad ST4 (nonlinearity!)

For energy exchange of 2 bodies:Pex S(T1

4 – T2

4) (21)

S…surfaceT…absolute temperature…Stefan – Boltzmann constant http://phet.colorado.edu/en/simulation/blackbody-spectrum

Page 34: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

3. Energy and Ordering

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Energy in Systems depends on the ordering of the parts (subsystems).For small number of subsystems this feature do not cause serious problems. But in frequent physical / engineering Systems the number of parts is enormous, typical quantity being Avogadro number 6.022×1023 parts/molecules, e.g. There is no chance to calculate such system in detail as the majority of information on system is missing we are able to calculate / measure / control either highly ordered systems, or to tackle with the lack of information, i.e. with uncertainty (for example utilizing state variables). The effect of missing information has serious applications results – disordered energy being of less use. It is for example the case of heat thermal energy. Energy is conserved but it can be degraded / dissipated / thermalized.

Page 35: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Entropy, 2nd Law of Thermodynamics

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Entropy is quantitative logarithmic measure of disorder or Systems missing information. (22)

kB is Boltzmann constantPi is probability that System is in the i-th microstate Far reaching 2nd Law of Thermodynamics stating that Entropy in closed System is non-decreasing function of time is based on the concept of entropy. Even in open systems there is at least certain tendency to Entropy increase which could eventually been compensated by Energy or information (i.e. negative entropy) flow.

1,380 65 x 10-23 J K-1

Page 36: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Entropy, 1st Law of Thermodynamics

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

1st Law of Thermodynamics is an equivalent of the Law of Energy Conservation (heat specific form of energy).

The equilibrium (i.e. most probable) state of a system maximizes the entropy because we have not to disposal any information about the initial conditions except for the conserved variables maximizing the entropy minimizes our knowledge about the details of the System.

Page 37: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Enthalpy

Enthalpy is a measure of the total energy of a thermodynamic system.

(23)

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 38: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Temperature

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Kinetic energy of single particle is:

EK=½mv2 (9a)

Mean energy of an ensemble of particles is:

ĒK = ½kBT for each degree of freedom (24)

http://en.wikipedia.org/wiki/File:Translational_motion.gif

kB… Boltzmann constantT…absolute temperature K kelvinThis relation serves as the definition of (absolute) temperature.

Page 39: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Temperature

Temperature has some significant features:• In classical macro-systems absolute temperature is always

positive Two Systems of different temperatures brought into

thermal connection, (conductive or radiative), exchange heat (accompanied by changes of other state variables). Left isolated from other systems, the two connected systems eventually reach a state of thermal equilibrium in which no further changes occur. Then temperatures of both systems fluctuate around the same value. (0th Law of Thermodynamics)

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 40: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Temperature, State equation of ideal gas

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

1/T =dS / dE (25)

(The rate of entropy increase with respect to energy is equal to reciprocal of temperature.)Conversions of temperature units :

State equation of ideal gas: pV = NkBT (26)

http://phet.colorado.edu/en/simulation/gas-properties

Page 41: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

4. Energy Transforms

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Energy can be transformed from one form to the another.While the transformation of the energy forms in the directions:ordered ordered;ordered less ordered,can proceed (in principle) without losses, i.e. with efficiency approaching to one,the transformation of energy in the direction: less ordered highly ordered form is always in principle lossy.This is the consequence of 2nd Law of thermodynamic

Question: How these losses correspond to the principle of energy conservation?

Page 42: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Heat Engine

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Heat engine:= system that converts thermal energy (i.e. heat) to mechanical work.

It does this by bringing a working substance from a high temperature state to a lower temperature state.

A heat "source" generates thermal energy that brings the working substance in the high temperature state TH.

The working substance generates work in the “active body" of the engine while transferring heat to the colder „sink" until it reaches a cold temperature state TC.

During this process part of the thermal energy is converted into mechanical work by exploiting the properties of the working substance.

The working substance is usually a gas or liquid.

Page 43: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Heat Engine; Carnot Cycle; Efficiency

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

An ideal heat engine utilizes reversible Carnot cycle: http://galileo.phys.virginia.edu/classes/109N/more_stuff/flashlets/carnot.htm2nd Law of thermodynamics No real heat engine have better efficiency then reversible engine with Carnot cycle

Carnot = 1- TC/TH (27)

Carnot …efficiency of Carnot engineTC…….. Absolute temperature of colder reservoir (sink)TH…….. Absolute temperature of hotter reservoir (source)

Page 44: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Efficiency, Examples

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Carnot (SUN – EARTH) = 1- 300/6000 = 0,95Carnot (theor. CE) = 1- 300/1500 = 0.8Carnot (green CE) = 1- 300/600 = 0,5Carnot (HB P CE) = 1- 290/310 = 0,06

Page 45: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

5. Mass – Energy Relations

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Fundamental mass – energy relation is the Einstein principle of equivalence:

E= mc2; (28)m… rest massc… speed of light in vacuum.

This relation gives 9. 1016 J / kg 100 PJ / kg. This relation is of almost none practical value as it presumes full annihilation of rest mass (matter / antimatter) into photons. Such transformation is not practically feasible in our environment (except of accelerators).In real reactions, both nuclear and chemical, just a minor part of mass can be transformed into energy (mass defect).Mass can be considered an excellent form of energy storage.

Page 46: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Mass – Energy Relations, Real Energy Densities

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Homework: Specify energy density of Hydrogen EM assuming: (1) nuclear fusion of He (most important reaction in SUN) (2) burning.

Page 47: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

E-I relation

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Fundamental information – energy relation (i.e. definition of the minimum energy dissipated in single irreversible operation with elementary information - bit) for macrosystems is the Brillouin equivalence:

Ie Emin= kBT (29)

Ie…elementary irreversible logic operation bitEmin ….corresponding minimum of dissipated energykB … Boltzmann constantT…absolute temperature… coefficient whose value depends on the pre- defined acceptable probability (p) of error. For: p=0,5 = ln2 0.7

p=10-19 (moderate value) 165Upper limit of (29) relation does not exist. (1 bit can switch off / on for example 1GW PowerStation)

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E-I relation M-E-I equivalence hypothesis

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reverse direction of (29) means that sufficient amount of information I resulting in entropy decrease (measured rather in T bits, then in bits), can efficiently substitute large amount of energy (Smart organization Energy savings).

Existence of binary equivalences (M – E) , (I – E) respectively provokes speculations about the validity of ternary equivalence M-E-I. This relation in general remains till now a fruitful hypothesis.

M

E

I

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6. Energy storage and transmission

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Energy storage means retention of energy in time, while the energy transfer means distribution of energy in space and time. Energy can be stored both in the form of potential and kinetic one. Give examples!Performance indicators (What does it mean?) of energy storage are as follows:• Energy storage density (both volumetric and mass) MAX.• Losses during storage MIN.• Efficiency of transformation (if any) MAX (i.e. 1)• Security (What is it?) MAX• Expenses of Energy or equivalent MIN.• Environmental impacts (What is it?) MIN.

Page 50: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Energy storage

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

• The requirement for energy storage density has historically been of strong value. This has led in the past to the preference of "fuels" utilization for this purpose.

• From our point of view it means the use of the binding energy of the substance (mass) and the subsequent release of this energy in the chemical (nuclear) reaction - burning.

Give examples!The weaknesses of this approach lie in the fact that the relevant energy transforms are mostly "via heat" and thus they have a fundamentally less efficiency and usually also more substantial impact on the environment. Therefore an interest is focused (again) on reversible hydro-electric power stations.Specific demands arise for Energy stores in vehicles. http://www.lss.fd.cvut.cz/publikace/prednasky-prezentace/seminare-z-elektromobility/101111_sadil_zasobnikyenergie.pdf

Page 51: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Energy storage - plot of Energy Densities

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 52: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Energy storage and transmission

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Reversible Hydroelectric Power StationDlouhé stráně 2x 325 MW; : 1350-825 m

Page 53: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Energy storage and transmission

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 54: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Energy Transmission

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Performance indicators of energy transmission are similar:• Energy transmission density (both volumetric and mass)

MAX.• Losses during transmission MIN.• Efficiency of transformation (if any) MAX (i.e. 1)• Security (What is it?) MAX• Expenses of Energy or equivalent MIN.• Environmental impacts (What is it?) MIN.• Speed of transmission MAX (?)Frequent kind of energy transmission is the transport of substance (mass) in which the energy is bonded.Give examples!Specific features have the transmissions of electricity, electromagnetic energy respectively (CO2 laser – 10.2m).Discuss!

Page 55: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Energy and Transport The consumption of energy for transportation reaches in developed

countries (including the Czech Republic) about 30% of the total energy consumption.

In the Czech Republic the road transportation consumes from this quantity more than 90%.

These facts, together with requirements on safe storing of this energy with high efficiency and high mass and volume density underline the high strategic significance of the energy basis for road transportation

In the area of road transportation many significant changes arise at present. All of them are related to the concept of so called Green Energy, considered as the complex of factors, taking into account the necessity of reaching more efficient and life conditions less affecting energy sources and kinds of its use. The reasons for these changes are many and they all have various significance. Examples: Electromobility (EV;HEV), Hydrogen mobility.

Discuss!

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 56: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Energy and Transport

1. The expected trends are influenced by following factors especially:

2. exhausting of fossil fuels reserves.

3. Price instability of oil. Oil price and partially also natural gas price are almost equally sensitive to global economic situation However, in global, the prices are still increasing. New oil / gas wells are continuously being found, but these are still more expensive for exploiting. This concerns especially the deep see wells.

4. Environmental requirements: The necessity to suppress negative impacts of road transport, either local or global is widely accepted. This concerns not only the emissions of sulfur oxides, nitrogen, CO and hydro-carbonates but in these days also the emissions of green-house gases (incl. CO2), dust particles and aerosols.

5. Scientific development

6. Energy security: In Central Europe the sources of oil and natural gas are localized mainly in countries with instable or even unfriendly political regimes.

7. Strategic role of new technologies (China, India…)  Czech Technical University in Prague - Faculty of Transportation Sciences

Department of Control and Telematics

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6. Global Energy Balance - Qualitatively

An essential condition of sustainability (of the life on Earth) is minimization of deviations from long – term energy balance of our planet.

Significant items of this balance are as follows:

Inputs: Solar irradiation; Gravity effects

Outputs: Thermal radiation of Earth

Stored energies: Fossil fuels; Radioactive materials; kinetic energy of tectonic processes; Energy of Earth rotation; Innate heat of Earth.

Nevertheless, the most important is the radiation balance

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 58: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Global Energy Balance- overview

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 59: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Global Energy Balance – Inputs quantitatively

The total solar flux of energy entering the Earth's atmosphere 174PW. This flux consists of: Solar radiation (99.97%, 173 PW 340 W m−2)

The solar flux averaged over just the sunlit half of the surface is approx. 680 W m−2

Total Solar radiation slightly varies (approx. 0.1% over a solar cycle)

Geothermal energy (0.025%; 45 TW; 0.08 W m−2)

This is both innate Earth's heat and heat produced by radioactive decay

Tidal energy (0.002%, 3TW; 0.0059 W m−2) Waste heat from fossil fuels consumption (0.007%,

13 TW; 0.025 W m−2)

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 60: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Global Energy Balance –Outputs quantitatively

The average reflectivity of the Earth is about 0.3, 30% of the incident radiation is reflected into space, while 70% is absorbed and reradiated as infrared ( max ?). The contributions

from geothermal and tidal power sources are so small that they can be omitted.

30% of the incident energy is reflected, consisting of: 6% reflected from the atmosphere

20% reflected from clouds

4% reflected from the ground (land, water and ice)

The remaining 70% of the incident energy is absorbed:

When the Earth is at thermal equilibrium, the same 70% that is absorbed is reradiated: 64% by the clouds and atmosphere 6% by the ground

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 61: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Global Energy Balance –Human perspective Abbott

Human Global power needs 15 TW (?)

Fossil fuels power dissipated 13 TWDiscuss consequences!

Renewable sources:

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 62: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Global Energy Balance –Human perspective Abbott

Fossil fuels depleting – example:“This graph shows the Hubbert curve, indicating that world oil resources are on track to critically deplete within 40 years. While this figure is hotly debated, what is clear is that oil has a host of useful industrial applications and to irreversibly burn oil jeopardizes the future.“

Discuss!Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

The vertical scale is in arbitrary relative units.

Page 63: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Global Energy Balance –Human perspective Abbott

Consolidated utility time CUT (???)

CUT:= All energy demands hypothetically realized only on specified source

http://phet.colorado.edu/en/simulation/nuclear-fission

Discuss Nuclear fusion and fission in detail!

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 64: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Sustainability of Energy Use; Green Energy

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Efficiency of Energy Use (incl. Energy saving) + Renewable Energy ® Sustainable Energy (SE) energy that meets the needs of

the present without compromising the ability of future generations

® Renewable Energy replenish able energy within a human lifetime + it causes no long-term damage to the environment

® Green Energy (GE) := subset of sustainable energy can be extracted, generated, and/or consumed without any significant (?) negative impact to the environment

® Specify examples of SE and GE; discuss !http://en.wikipedia.org/wiki/Sustainable_energyhttp://phet.colorado.edu/en/simulation/molecules-and-light

Page 65: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Smart Grid

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Fusion of information + power energy networks into a wholeIntelligence, omni-directionality, flexibility, re-structuralization, graceful degradation, self healing, clusteringhttp://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5768087http://en.wikipedia.org/wiki/Smart_grid

Page 66: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

NIST model of Smart Grid

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 67: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

Conclusions

Wise, efficient and inventive control of energy flows and transforms is a challenge for near future both in the global and regional scales as it is crucial condition for sustainable evolution of human society on Earth.

This task demands deeper knowledge of physics, technology, transportation, control, cybernetics, Systems theory and Social sciences.

Understanding the concept of Energy is an important initial step to this goal.

Thank you !

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

Page 68: Czech Technical University in Prague Faculty of Transportation Sciences Department of Control and Telematics WHAT IS ENERGY ? Zdeněk Votruba 1, zdevo@ieee.org,

References

Abbott…D. Abbott: Keeping the Energy Debate Clean… Proceedings IEEE, Jan. 2010, pp. 42 – 66

Kittel et. al.… Ch.Kittel, W. D. Knight, M.A. Ruderman

Mechanics, Berkeley physics Course, McGraw- Hill book company 1962

Internet resources are cited locally

Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics