WHAT IS ENERGY ?

1. WHAT IS ENERGY ? Zdeněk Votruba1, zdevo@ieee.org, 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.

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

3. Contents 1.Concept of Energy 2. 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 Physics 1st and 2nd Laws of Thermodynamics Conservation / Dissipation of Energy 4. Energy Transforms Efficiency of Energy Transforms Carnot Cycle 5. Relations(Systemic View): Energy – Mass Energy – Information 6. Energy Releasing, Transmission and Storage 7. Global Energy Balance 8. Sustainability of Energy Use, “Green Energy” 9. Concept of Smart Net Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

4. 1. Concept of Energy Energeia(Energeia) Aristotle´s concept (4th century B.C.), (related toErgon– work) could be translated into English approx. as “being-at-work“. Examples ofenergeiai(energeai) in Aristotle's works are:eudaimonia(eudaimonia) – pleasure / happiness andkinesis(kinesis), translated as movement / motion, or in some contexts change. 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). Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

5. 1. Concept of Energy Energy is aCategory. 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 constant Recommended reading: http://www.ftexploring.com/energy/definition.html http://phet.colorado.edu/en/simulation/energy-skate-park Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

6. 2. Fundamentals of Energy in Physics Energy & 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

7. 2. Fundamentals of Energy in Physics Energy & Work - 2 d  C 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 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

8. 2. Fundamentals of Energy in Physics Energy & Work - 3 The more general definition of mechanical work (for F(t)  const.) is given by the line integral: WC = CF.dx (2) • where: • C is the path traversed by the object; • F is the force vector; and • x 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? Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

9. 2. Fundamentals of Energy in Physics Energy & Work - 3 • 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. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

10. 2. Fundamentals of Energy in Physics Energy & Work - 4 The work done on the object (System) is equal to the change of (kinetic) energy. E2 – E1 = E = W (4) E E2 W= E2 – E1 E1 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

11. 2. Fundamentals of Energy in Physics Related Variables - 1 • 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= abPdt(6) • P is scalar variable Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

12. 2. Fundamentals of Energy in Physics Related Variables - 2 • EvEnergy density (volumetric – by volume): Ev=DE/DV (7) Evis scalar variable • EmEnergy 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

13. 2. Fundamentals of Energy in PhysicsUnits - 1 (SI - Multiplicationfactors) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

14. 2. Fundamentals of Energy in PhysicsUnits -2 Energy, Work E, W: Basic unit SI: J……Joule The work done when the point of application of a force of1 newton is displaced through a distance of 1 meter in the direction of the force,ore.g.: The work required to produce 1W for 1 s. Alternative (non SI) units: eV (electronvolt)1 eV = 1.602176487(40)×10−19J (orapprox. 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

15. 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

16. 2. Fundamentals of Energy in PhysicsUnits- 4 Power P Basic 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-1respectively. WHY ? Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

17. 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 (vc) 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= I2/2(10)  For more bodies and also for both rotation and translation the kinetic energy is the additive entity. • For v  c: Ek = mc2 - 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

18. 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

19. 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

20. 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

21. Relations of kinetic and potential energy -exercise1Kittel Ek K(x) ; Ep  U(x) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

22. Relations of kinetic and potential energy –exercise - 2Kittel Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

23. Relations of kinetic and potential energy –exercise -3Kittel Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

24. Relations of kinetic and potential energy –exercise 4Kittel Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

25. Relations of kinetic and potential energy –exercise 5Kittel Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

26. Relations of kinetic and potential energy –exercise 6 Kittel Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

27. Electric energy -1 Ep= ½CU2 = ½QU (15) C A/d Ev=DE/DV /d2 ____________________________ Where: U … potential difference (voltage) V A…surface of capacitor plate m2 C…capacitance F d…thickness of the dielectric …permitivity of the dielectric Q…electric charge As How to increase the amount of stored energy? Electrostatic energy: (potential energy) capacitor Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

28. Electric energy-2 • Ep = ½LI2 = ½ I(16) • Where: • L… inductance H • I… electric current A • …magnetic flux Wb, i.e. V.s •  = SB.dS ; • In the persistent state (superconductivity) the current and magnetic field are stored • How to increase the amount of stored energy? 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

29. Electric energy-3 Electric Energy Heat Transformation (dissipation) Resistor R  (Ohms law: u = R.i )  W=abpdt(work converted to heat) (17) p (t)…power W ; t…time s p (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

30. Energy of electromagnetic wave -1 P = E × H* Paverage= ½E0H0 W/m2 (SunEarth surface 1.37 kW/m2) Direction of P vector is the same as transmission direction Radiation 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) (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

31. Energy of electromagnetic wave -2 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-1 h = ħ/2….Planck constanth = 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 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

32. Energy of thermal radiation-1 Planck law Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

33. Energy of thermal radiation-2 Stefan – Boltzmann law E=Prad t(20) Prad ST4(nonlinearity!) For energy exchange of 2 bodies: Pex S(T14– T24)(21) S…surface T…absolute temperature …Stefan – Boltzmann constant http://phet.colorado.edu/en/simulation/blackbody-spectrum Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

34. 3. Energy and Ordering 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. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

35. Entropy, 2nd Law of Thermodynamics Entropy is quantitative logarithmic measure of disorder or Systems missing information. (22) kB is Boltzmann constant Pi 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 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

36. Entropy, 1st Law of Thermodynamics 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. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

37. 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

38. Temperature 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 constant T…absolute temperature K kelvin This relation serves as the definition of (absolute) temperature. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

39. 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

40. Temperature, State equation of ideal gas • 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 idealgas: pV = NkBT (26) • http://phet.colorado.edu/en/simulation/gas-properties Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

41. 4. Energy Transforms • 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? Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

42. Heat Engine • 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. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

43. Heat Engine; Carnot Cycle; Efficiency An ideal heat engine utilizes reversible Carnot cycle: http://galileo.phys.virginia.edu/classes/109N/more_stuff/flashlets/carnot.htm 2nd 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 engine TC…….. Absolute temperature of colder reservoir (sink) TH…….. Absolute temperature of hotter reservoir (source) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

44. Efficiency, Examples Carnot(SUN – EARTH) = 1- 300/6000 = 0,95 Carnot(theor. CE) = 1- 300/1500 = 0.8 Carnot(green CE) = 1- 300/600 = 0,5 Carnot(HB P CE)= 1- 290/310 = 0,06 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

45. 5. Mass – Energy Relations Fundamental mass – energy relation is the Einstein principle of equivalence: E= mc2; (28) m… rest mass c… 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. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

46. Mass – Energy Relations, Real Energy Densities Homework: Specify energy density of Hydrogen EM assuming: (1) nuclear fusion of He (most important reaction in SUN) (2) burning. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

47. E-I relation 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 bit Emin….corresponding minimum of dissipated energy kB … Boltzmann constant T…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)    165 Upper limit of (29) relation does not exist. (1 bit can switch off / on for example 1GW PowerStation) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

48. E-I relationM-E-I equivalence hypothesis 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. E M I Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

49. 6. Energy storage and transmission • 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. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics

50. Energy storage • 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 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Control and Telematics