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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 mv2 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?
energy definitions.url
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= ΔmC2)
3. Kinetic energy may assume the form of Macroscopic 1/2 MV2 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 systems1. 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 V2
Kinetic Potential Electromagnetic
Heat
For now EM isleft out of the scheme.
Within each categoryWithin each categoryenergy can go from oneenergy can go from onebody to anotherbody to another
A C
B
Can include Mass: E=MC2
Macroscopic KE
Microscopic KE
D
A and B C D
1/2 M V2
Kinetic Potential Electromagnetic
HeatWithin each categoryWithin each categoryenergy can go from oneenergy can go from onebody to anotherbody to another
A C
B
1. Expanding gases cool: B to C Compress gases: C to B2. Water evaporates and cools: B to C Water condenses: C to B3. Wax freezes on your finger: C to B Wax melts: B to C4. Car brakes to a stop: A to B Engine accelerates car: B to A5. Exothermic chem reaction: C to B Endothermic chem reaction: B to C6. Bullet shot from gun: C to B & A Car bounces down on springs: A to C7. Car coasts up a hill: A to C Car coasts down a hill: C to A8. Driver brakes down a hill: C to A & B Car brakes going up a hill: A to B & C9. Pendulum: C to A and A to C Eventually: all ends up as B10. Drop a book on the table: C to A to B Pour hot water into cold: B to B11. Lift a rock:Cbody to Cgravity Push on the wall: C to B12. Pool balls collide: Aball 1 to Aball 2 A mass compresses a spring: Cgravity to Cspring
13. Battery lights light bulb: C to B etc Electric motor: Celectrical to A and B
Can include Mass: E=MC2
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 Hhot water + Δ Hcold water = ZERO
[ (35g)(1cal/gC)(T2 - 80C)] + [(19g)(lcal/gC)(T2 - 24C)] = 0
T2 = 60 C
Kinetic energy fallsKinetic 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 Iron2Heat 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) (CFe) (T2-81.2C) + (200g) (1cal/gC) (T2-22.2C) 200.0 ml water
Measure T2:
Insert the final temperature and solve for CFe
Thermochemistry20g 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)(T2 - 80C)] + [(50g)(1cal/gC)(T2 - 25C)] Heat of fusion is (-) PE goes down cools heats
0 = ( - 400) + 2T2 + ( - 160 ) + ( + 50T2) + ( - 1250 )
0 = - 1810 + 52 T2 T2 = 35 C
0 = ( - ) + 0 + + ( - ) + ( + )
Liquid Hot Wax WaterSolid Hot Wax
Some examples1. Going from solid oxygen to nucleons.
PE
solid
Liquid
Gas
Atoms
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
Ions
Endothermic
Exothermic
Δ PE + Δ KE = 0
up down
Δ PE + Δ KE = 0
down up
Getting fu
rther apart
Getting closer together
O
O
O
O
O
O
O
O
O
PE
KE
TotalEnergy
Heat Ice Melt IceHeat Water
VaporizeWater
HeatVapor
Decomposewater
Heatatoms
Ionizeatoms
Heationz
NucleonsIce…to....nucleons thru heating
*
*
*
*
*
solid
liquid
gasatoms
ions
nuceons
*= phase change
Demonstration Have a student insert one finger into 60F liquid wax and anotherinto 60F water. Essentially both will feel the same.
Now remove both fingers: the wax gets hotter as it freezes and thewater gets cooler as it evaporates.
PE
Water
Wax
Liquid
Gas
Liquid
solid
PE
Heat Absorbed Heat given off
Ice in WaterICE
0 CWater
Heat from the water is used to (1) melt the ice and (2) warmthe resulting ice water.
heat
ThermochemistryExample: 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 (Hf) ….heat of fusion = Δ PE
Δ Hice =(5.0g) (+80 cal/g)H25C water=(100g)(1cal/gC)(T2-25C)
Hice water=(5.0g)(1cal/gC)(T2-0C)
Δ H total =(100g)(1cal/gC)(T2-25C) + 5.0g)(1cal/gC)(T2-0C)+ 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
100T2 - 2500 + 5T2 - 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) + 02 (g) ------ CO2(g) + heat
PE + KE PE + KE
C + O O
O
O
PE
Coordinate
O2 + C
C + O + O
CO2…………………….
Atoms are closer together
Hydrogen gas + chlorine gas ==== hydrogen chloride gas
PE
Coordinate
………………………………………………
……………………………..
H + H
H2
Cl + Cl
Cl2
Exo Endo
H + H + Cl + Cl
2H = H2 + heat 2Cl = Cl2 + heat 2H + 2Cl = 2HCl + heat H2 + Cl2 = 2HCl + heat
Exo Endo
Exo Endo
H2
Cl2
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 ReactionsA. 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 T0= 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 d
i stance from
nu
cle us
PE
PE
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 …Outermost2nd Electron
3rd Electron
Ionization energy increases as electronscloser 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
Mechanics1. 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=1/2mv2
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 mv22 -1/2 mv1
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 mv22 -1/2 mv1
2) + heat
F Δ d = mg Δ h + (1/2 mv22 -1/2 mv1
2) + Ffrictiond
Which is the same as 0 = F d + Δ PE + Δ KE + heat
F Δ d = mg Δ h + (1/2 mv22 - 1/2 mv1
2) + Ffrictiond
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 downan incline upon which the constant force of friction was 15N. What would be thespeed of the block after it had slid a distance of 4.0 meters 15m down the incline anddropped a vertical distance of 3.0 meters? Only consider the starting and ending points involved
F Δ d = mg Δ h + (1/2 mv22 - 1/2 mv1
2) + Ffrictiond
(+) (-) zero (+)
(3.0)(9.8)(+9.0) = (3.0)(9.8)(-3.0) + ( 1/2 (3.0)( v22 ) - ( 0 ) + (15)(4.0)
+265 J = - 88.2J + 1.5 V22 + +60J
V2 = 14 m/s
The curious example of taking energy from somethingby pushing on it. Applied Force
MotionF•D = Δ PE + Δ KE + heatFrom the dot product we get negative work…which \means we are taking energy out instead of putting it in.
0 = - F•D + Δ PE + Δ KE + heat0 = -[-FD] + 0 + Δ KE + 0
Frictionless4N
KE1 = 40 J
10 m
0= +(4)(10) + KE2 - KE1
0= +40 J + 0 - 40J
40 J of some form of energy must be created from thelost 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 bevented via heat from our bodies. This term does notappear 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 can’t be used to “measure” the energy gained by the air. We can calculate the energy gainedby the air in the above case with reason. If you did 40 J of work lifting a rock you would do40 J of work setting it gently back down. In setting itdown the rock loses 40 J of PE and you lose 40 J ofheat….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
V1Q
V2QPE
R
- +
L=length of resistance
Δ VQ= Δ VIt ELQ=VIt= change in PEPE
Ohm’s 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 ohm’s law: V=IR
F Δ d = Δ VIt + (1/2 mv22 - 1/2 mv1
2) + Ffrictiond
zero = Vlost I t + 1/2mV22 - 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 arecreated” Richard Feynman
This implies that when particles that attract each other are moved closer and PE goes down…energy must be given offand 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 5x10-9g.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 PEis lost that the mass loss is measurable…unlike chemical reaction.
Nuclear Fission and Fusion
Fusion: 8 protons + 8 neutrons ------- 1 oxygen nucleus + ENERGYNucleons 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 BE
BE
Exothermic
Going from Lower Binding Energy to Higher
is Exothermic
PEFISSION
235.12517AMU
236.90814 AMU16.12752 AMU
16.0000 AMU
MC2
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 ofbeing 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 sunin which PE drops even more produces a great deal more heat and begins the fusion of He to elements up toiron.
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 tofuse the heavier elements in the periodic chart and incidently produce the mass difference between productsand reactants.
Mass loss
PE
(As gravitationally attractive bodies getcloser together their PE drops.) Δ PE + Δ KE = 0
Water
PE
Liquid
Solid
When water freezes..attracting bodiesget closer together and PE goes downjust like everything else. However, icefloats. How can the density get less butmolecules get closer together?
The strongest bonding in water is hydrogen bonding…in the process offreezing the bonds involved in hydrogenbonding do get closer together as the same time the average distance betweenmolecules get larger…dispersion forceenergy actually does go up a little.
WATER
Unique properties
