An attempt to take ideas about Energy and Conservation from several disciplines and form an integrated organization.
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An attempt to take ideas about Energy and Conservation from several disciplines and form an integrated organization.
Statements about energy from various sources: 1. There are many forms of energy: wind, water, sun, potential, chemical, electrical, nuclear, light, motion, heat, mechanical, internal, external, atomic, nuclear, molecular, gravitational, bond energy, bonding energy, sound energy etc. Energy can change from one form to another. Energy is Conserved 2. Potential Energy can be stored in an atom or nucleus or molecule or by gravity or in a battery 3. Work: Force times Distance= KE= 1/2 mv 2 PE= mgh 4. In an exothermic reaction heat is given off by a chemical reaction. The energy comes from substances involved. 5. Electricity often turns into heat 6. A windmill can turn wind energy into electrical energy 7. Nuclear energy is very large and comes from the nucleus! Both fission and fusion produce energy. 8. Potential energy is in a form you often cannot see.
Where does the confusion about energy come from? 1. Why is it work to push on a wall? We get tired! Books say no work is done! 2. Do these topics have any conceptual similarities as we teach them. Biology (sun energy, cell energy, chemical energy, potential energy), Physics (mechanics:gravitational potential energy and kinetic energy, frictional heat energy), thermodynamics: heat transfer, nuclear and electrical energy), Chemistry (thermochemistry, bond energy, nuclear energy, heat of reaction, heat of fusion and evaporation and in all areas The Law of Conservation of Energy 3. How do you describe how energy is stored in molecules and bonds and the nucleus? 4. In an exothermic reaction where exactly does the heat come from? At the atomic level what is the same for all exothermic reactions? 5. What is the connection between mass and energy? 6. How is electrical energy related to the equations of Mechanics in Physics? 7. How are all the different Forms of Energy..mentioned in most texts …..related? Are there really so many different forms of energy? 8. How is Work done actually related to PE, KE, heat, electricity ? 9. How is Binding Energy related to energy given off in nuclear reactions? Is Binding Energy a form of energy? 10. What do all the forms of Potential Energy have in common?
Definitions that prove consistent throughout the curriculum: 1. Work is the Transfer of Energy from one form or condition to another. Mass=Energy is always Conserved in all interactions 2. There are 3 forms of energy: kinetic, potential and electromagnetic. (Mass is converted into Energy via E= Δ mC 2 ) 3. Kinetic energy may assume the form of Macroscopic 1/2 MV 2 or Microscopic Heat. (Heat in or out can be calculated) 4. Potential energy is associated with the relative positions between bodies. Most common: Since all molecules and atoms and opposite charged ions attract each other …Potential Energy goes UP when attracting bodies move away from each other and goes down when they approach…at least until they get to their bond distance in which case repulsion becomes greater than attraction. Ultimately all losses PE involve mass being converted into energy. 5. Electromagnetic energy refers to any of the electromagnetic spectrum.
Examples of sources of potential energy in systems 1. Gravitational: Masses attract the earth…when moved further away PE goes up. 2. Electrostatic A. Electrical: When electrons are moved from protons PE goes up; when electrons are moved closer together PE goes up. …as in charging a capacitor etc. B. Chemical: Anytime PE goes up: Sum of attracting bodies get further apart and repelling bodies get closer together. It often is difficult to see all of this but if you analyze simple systems you can see it at work. 4. Nuclear: In any exothermic nuclear reaction…be it fusion or fission it can be shown that potential energy goes down because attracting bodies are getting closer…the nuclear force of attraction is much larger than the electrostatic forces of repulsion. Potential energy can be shown in graphical form for ALL changes….not just chemical reactions.
1/2 M V 2 Kinetic Potential Electromagnetic Heat For now EM is left out of the scheme. Within each category energy can go from one body to another AC B Can include Mass: E= MC 2 Macroscopic KE Microscopic KE D A and B CD
1/2 M V 2 Kinetic Potential Electromagnetic Heat Within each category energy can go from one body to another A C B 1. Expanding gases cool: B to C Compress gases: C to B 2. Water evaporates and cools: B to C Water condenses: C to B 3. Wax freezes on your finger: C to B Wax melts: B to C 4. Car brakes to a stop: A to B Engine accelerates car: B to A 5. Exothermic chem reaction: C to B Endothermic chem reaction: B to C 6. Bullet shot from gun: C to B & A Car bounces down on springs: A to C 7. Car coasts up a hill: A to C Car coasts down a hill: C to A 8. Driver brakes down a hill: C to A & B Car brakes going up a hill: A to B & C 9. Pendulum: C to A and A to C Eventually: all ends up as B 10. Drop a book on the table: C to A to B Pour hot water into cold: B to B 11. Lift a rock:C body to C gravity Push on the wall: C to B 12. Pool balls collide: A ball 1 to A ball 2 A mass compresses a spring: C gravity to C spring 13. Battery lights light bulb: C to B etc Electric motor: C electrical to A and B Can include Mass: E= MC 2
Conversions within a category 1. Potential Energy: a. Chemical PE -----Electrical PE: Battery charging capacitor b. Gravitational PE-----Spring PE: A mass set atop a spring compresses it. c. Chemical PE -----Gravitational PE: Lift a box 2. Kinetic Energy a. Microscopic KE: Heat flows from hot to cold b. Macroscopic KE: Two billiard balls collide. 3. Electromagnetic Energy a. Fluorescence: UV changed to Visible light
Student questions: 1. How does compressing a gas increase PE when molecules are actually getting closer together? Attracting forces are not a factor in increasing gas pressure….work must be done on the gas to compress it. 2. How does compressing a spring increase PE: Moving atoms either side of their equilibrium position will increase the PE within the solid…attraction results in more PE when its stretched and repulsion results in more PE when compressed.
Thermochemistry 1. Hot water is mixed with cold water: H = MC T= KE change Δ H hot water + Δ H cold water = ZERO [ (35g)(1cal/gC)(T 2 - 80C)] + [(19g)(lcal/gC)(T 2 - 24C )] = 0 T 2 = 60 C Kinetic energy falls Kinetic energy falls Kinetic energy rises Energy Conserved For example: Suppose 35ml of 80C water is mixed with 19ml of 24C water. What is the resulting temperature? (60 C) Heat energy is transferred from hot object to a cooler one. HOT COLD
Determining the Specific Heat of Iron 2 Heat a 1.0 kg mass in water to about 80 c. Place 200 ml tap water in a styrafoam cup, measure temp. and insert mass. Kg T1 Water = 22.2C T1 iron = 81.2 C heat 0 = heat lost by Fe + heat gained by water 0 = mc Δ t iron + mc Δ t water 0 = (1000g) (C Fe ) (T 2 -81.2C) + (200g) (1cal/gC) (T 2 -22.2C) 200.0 ml water Measure T 2 : Insert the final temperature and solve for C Fe
Thermochemistry 20g of wax at 80C in mixed with 50ml of water at 25C. What is the final temp? Fd = Δ PE + Δ KE (macroscopic) + Heat 0 = (Mass H fusion wax) + [(Mwax Cwax T) + (M Cwater T)] 0= [(20g)( - 20cal/g)] + [(20g)( 0.1cal/gC)(T 2 - 80C)] + [(50g)(1cal/gC)(T 2 - 25C)] Heat of fusion is (-) PE goes down cools heats 0 = ( - 400) + 2T 2 + ( - 160 ) + ( + 50T 2 ) + ( - 1250 ) 0 = - 1810 + 52 T 2 T 2 = 35 C 0 = ( - ) + 0 + + ( - ) + ( + ) Liquid Hot Wax Water Solid Hot Wax
Some examples 1. Going from solid oxygen to nucleons. PE solid Liquid Gas Atom s Nucleons 1 2 3 4 6 1-2. O2(s) + energy --- O2(L) 2-3. O2(L) + energy ----- O2( g ) 3-4. O2(g) + energy ---- 2 O(g) 4-5 O(atom) + Energy ----- O(ion) + 8 electrons 5-6 O(ion) + Energy ---- 8 protons + 8 neutrons 5 Ion s Endothermic Exothermic Δ PE + Δ KE = 0 up down Δ PE + Δ KE = 0 down up Getting further apart Getting closer together
O O O O O O O O O PE KE Total Energy Heat Ice Melt Ice Heat Water Vaporize Water Heat Vapor Decompose water Heat atoms Ionize atoms Heat ionz Nucleons Ice…to....nucleons thru heating * * * * * solid liquid gas atoms ions nuceons *= phase change
Demonstration Have a student insert one finger into 60F liquid wax and another into 60F water. Essentially both will feel the same. Now remove both fingers: the wax gets hotter as it freezes and the water gets cooler as it evaporates. PE Water Wax Liquid Gas Liquid solid PE Heat AbsorbedHeat given off
Ice in Water ICE 0 C Water Heat from the water is used to (1) melt the ice and (2) warm the resulting ice water. heat
Thermochemistry Example: Add 5.0 g of ice at 0C to 100ml of water at 25C. What is the final temp? Δ H = mC(specific heat) Δ T = Δ KE Δ H = m (H f ) ….heat of fusion = Δ PE Δ H ice =(5.0g) (+80 cal/g) H 25C water =(100g)(1cal/gC)(T 2 -25C) H ice water =(5.0g)(1cal/gC)(T 2 -0C) Δ H total =(100g)(1cal/gC)(T 2 -25C) + 5.0g)(1cal/gC)(T 2 -0C)+ 5.0g) (+80 cal/g) = 0 KE goes down + KE goes up + PE goes up = 0 Δ KE + Δ KE + Δ PE = 0 ( - ) ( + ) ( + ) Conservation of Energy 100T 2 - 2500 + 5T 2 - 0 + 400 = 0 Final Temp = 20C (Use +80 when PE rises and -80 when PE falls; when a substance freezes the attracting particles get closer together and PE goes down. This also happens with water but because of hydrogen bonding its less obvious to see….ice floats) warm water cools cool water heats ice melts
A Simple Chemical Reaction C (g) + 0 2 (g) ------ CO 2(g) + heat PE + KE C + OO O O PE Coordinate O 2 + C C + O + O CO 2 ……………………. Atoms are closer together
Hydrogen gas + chlorine gas ==== hydrogen chloride gas PE Coordinate ……………………………………………… …………………………….. H + H H2H2 Cl + Cl Cl 2 Exo Endo H + H + Cl + Cl 2H = H 2 + heat 2Cl = Cl 2 + heat 2H + 2Cl = 2HCl + heat H 2 + Cl 2 = 2HCl + heat Exo Endo H2H2 Cl 2 PE average Exo The Net reaction is Exothermic because the bond distances between hydrogen and chlorine are smaller than between hydrogen-hydrogen or chlorine-chlorine…PE is down.
Putting Na0H in water heats the water PE KE (temp) before after before after Na0H Water PE KE Since the water heats up the reaction is called exothermic
Exothermic Reactions A. 2.0g (0.050mol) of Na0H are put into 300ml of water at 22C and the temperature rises 2.5C. What happened to the Potential energy of the Na0H? Fd = Δ PE + Δ KE (macroscopic) + Heat 0 = Δ PE + 0 + heat 0= Δ PE + mC Δ T 0= Δ PE + (300g)(1cal/gC)( + 2.5C) chemical PE is lost and KE transferred to the water Δ PE= - 750 calories The reaction is EXOTHERMIC! B. 0.10mol of Ammonium Chloride dissolves in 250ml of water and the temp drops from 24C to 21C. What is the H of the reaction? Fd = Δ PE + Δ KE (macroscopic) + Heat 0 = Δ PE + 0 + mC Δ T 0= Δ PE + (5g)(1cal/gC)(21C - 24C) KE is lost by the water and converted to PE in the chemical system 0= Δ PE + ( - 15cal) Δ H = + 15cal or + 150cal/mol ENDOTHERMIC!
Line Spectra : Δ PE + Δ Electromagnetic energy = 0 down up Energy levels in a hydrogen atom PE N=1 N=2 N=3 N=4 0 Ionization UV Visible light IR Average distance from nucleus PE As the attracting electron gets further from the nucleus the PE goes up 0= Δ PE + Δ EM energy
Ionization Level 1st e Calcium 2, 8, 2 1st Electron …Outermost 2nd Electron 3rd Electron Ionization energy increases as electrons closer to the nucleus are reached. Rise in PE corresponds to more work needed to be done to remove it.
External Work Done on a Body changes to Kinetic Energy (macroscopic) Kinetic Energy (microscopic) Potential Energy
Mechanics 1. Work in mechanics (F d) is an usually is an instance where external energy is transferred to a system. 2. Most texts show equations like: Fd = KE or Fd=PE Fd=mgh Fd= 1/2 mv 2 This leads to an incomplete understanding of just what is going on. The equations are really: External work Fd= mg Δ h and Fd= Δ KE = 1/2 mv 2 2 - 1/2 mv 1 2 3. A system that consistently works in mechanics is: Work = change in PE + change in KE + heat generated Fd = Δ PE + Δ KE (macroscopic) + Heat F Δ d = mg Δ h + (1/2 mv 2 2 -1/2 mv 1 2 ) + heat F Δ d = mg Δ h + (1/2 mv 2 2 -1/2 mv 1 2 ) + F friction d Which is the same as 0 = F d + Δ PE + Δ KE + heat
F Δ d = mg Δ h + (1/2 mv 2 2 - 1/2 mv 1 2 ) + F friction d 0 = ( - ) + (0) - (0) + ( + ) Suppose a 2.0 kg block at rest slides down a frictionless ramp 25 cm high and out on a horizontal surface upon which there was a friction force of 4.0N. Where does the block stop? No external work is done. Zero = 0 = [(2.0kg)(9.8N/kg)(-0.25m)] + [0 - 0] + [4.0N)(d)] d=+1.23m Mechanics Suppose a 2.0 kg block at rest slides down a frictionless ramp 25 cm high and out on a horizontal surface upon which there was a friction force of 4.0N. Where does the block stop? No external work is done.
Mechanics Suppose YOU lifted a 3.0kg block vertically upward 9.0 meters and let it slide down an incline upon which the constant force of friction was 15N. What would be the speed of the block after it had slid a distance of 4.0 meters 15m down the incline and dropped a vertical distance of 3.0 meters? Only consider the starting and ending points involved F Δ d = mg Δ h + (1/2 mv 2 2 - 1/2 mv 1 2 ) + F friction d (+) (-) zero (+) (3.0)(9.8)(+9.0) = (3.0)(9.8)(-3.0) + ( 1/2 (3.0)( v 2 2 ) - ( 0 ) + (15)(4.0) + 265 J = - 88.2J + 1.5 V 2 2 + +60J V 2 = 14 m/s
The curious example of taking energy from something by pushing on it. Applied Force Motion FD = Δ PE + Δ KE + heat From the dot product we get negative work…which \ means we are taking energy out instead of putting it in. 0 = - FD + Δ PE + Δ KE + heat 0 = -[-FD] + 0 + Δ KE + 0 Frictionless 4N KE 1 = 40 J 10 m 0= +(4)(10) + KE 2 - KE 1 0= +40 J + 0 - 40J 40 J of some form of energy must be created from the lost KE; we know we did work …in fact as much work is done stopping it as was done getting it going.
The amount of work we did took energy from the block and therefore that amount of energy must be vented via heat from our bodies. This term does not appear in the equation for the same reason as when we push on a wall and get tired we are actually working on the air….its gaining energy…but this equation cant be used to measure the energy gained by the air. We can calculate the energy gained by the air in the above case with reason. If you did 40 J of work lifting a rock you would do 40 J of work setting it gently back down. In setting it down the rock loses 40 J of PE and you lose 40 J of heat….explaining your sense of getting tired.
Potential Energy changes to KE (macroscopic) KE (microscopic) Other form of PE
Electricity: Δ V=IR and EL = IR V1QV1Q V2QV2Q PE R -+ L=length of resistance Δ VQ= Δ VIt ELQ=VIt= change in PE PE Ohms Law Electric Field
Electricity A 1.5v battery delivers 0.30amps to a toy car for 5.0 s and the 1.0kg car goes from rest to 2.0 m/s in that time. How much energy is wasted as heat? Change of electrical potential energy is: Δ VIt or( Power x time) Δ V is really Vlost in all equations using ohms law: V=IR F Δ d = Δ VIt + (1/2 mv 2 2 - 1/2 mv 1 2 ) + F friction d zero = V lost I t + 1/2mV 2 2 - 0 + heat 0 = (-1.5)(2.0)(5.0) + (0.5)(1.0)(3.0) 2 - 0 + heat 0 = -15J + +4.5J + heat battery lost 15J car gained 4.5J gained heat 10.5J Fd = Δ PE + Δ KE (macroscopic) + Heat
The Role of Mass The Rest Mass particles have is simply the work done in separating them against their mutual attraction after they are created Richard Feynman This implies that when particles that attract each other are moved closer and PE goes down…energy must be given off and MASS MUST BE LOST. In the case of burning a mol of carbon to carbon dioxide the amount of KE (= to loss of PE) is equivalent to 5x10 -9 g. In normal chemical reactions this mass loss is not measurable.
Potential Energy changes to KE (microscopic)
Binding Energy: The energy required to take apart attracting bodies…it is not energy stored in the atom. In a Nuclear Reaction enough PE is lost that the mass loss is measurable…unlike chemical reaction.
Nuclear Fission and Fusion Fusion : 8 protons + 8 neutrons ------- 1 oxygen nucleus + ENERGY Nucleons moving closer together with the attracting Nuclear Force of Attraction means the PE is going down greatly.. Energy given off is opposite of Binding Energy The electrostatic PE goes up but the amount of energy is insignificant Fission : A nucleus splits and becomes pieces whose binding energy is greater. PE 8 protons 8neutrons A nucleus Binding Energy: Energy required to take something apart Exothermic Individual protona and neutrons U235 Kr and Ba BE Exothermic Going from Lower Binding Energy to Higher is Exothermic PE FISSION 235.12517AMU 236.90814 AMU16.12752 AMU 16.0000 AMU MC 2 E= Even less mass If a reaction moves toward more binding energy/nucleon then PE may go down and energy must be given off: exothermic Δ PE + Δ KE =0 down up Δ
Nuclear Fusion and The Death of a Star Nucleons Hydrogen Helium Iron Heavy elements Gravitational attraction produces enough heat to begin fusion of H to He in the sun. Actually in the processs of being formed in the collapse of Hatoms the Gravitational PE dropsand a great deal of heat is produced. This heat causes the fusion to take place which produces another dropin PE and even more heat. (physics books refer to Binding Energy per nucleon to explain what happens.) When H fuel is expended further collapse of the sun in which PE drops even more produces a great deal more heat and begins the fusion of He to elements up to iron. When He fuel is gone the sun collapses under the force of gravity and Gravitational PE goes down even more which further raises the temperature BUT the next fusion reaction to heavier elements is endothermic so there is not enough KE to cause fusion…in a sun 100x our sun the collapse continues rapidly and a great burst of heat is given off as the sun core density becomes VERY large….a supernova has produced enough energy to fuse the heavier elements in the periodic chart and incidently produce the mass difference between products and reactants. Mass loss PE (As gravitationally attractive bodies get closer together their PE drops.) Δ PE + Δ KE = 0
Water PE Liquid Solid When water freezes..attracting bodies get closer together and PE goes down just like everything else. However, ice floats. How can the density get less but molecules get closer together? The strongest bonding in water is hydrogen bonding…in the process of freezing the bonds involved in hydrogen bonding do get closer together as the same time the average distance between molecules get larger…dispersion force energy actually does go up a little. WATER Unique properties