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WELCOME TO THE FINAL EXAM REVIEW
The final exam is Mon, Apr 29, at 6:00 pm
(same room as your midterm exams)
Review sessions: Thurs, 4/25, 7:00 pm
and Fri, 4/26, 1:00 pm in 2005 Smith.
Drop in: Mon, Apr 29, 2:00 – 5:30 in 2005
Smith
Be sure to bring a calculator to the exam!
Using ratios to convert units The equality 1 hour = 60 min can be written in 2 ways:
1 hour or 60 min
60 min 1 hour
1,609 meters = 1 mile can be written:
1,609 meters or 1 mile
1 mile 1,609 meters
Example: Convert 60 miles per hour into meters per second. Choose ratios that cancel the unwanted units (hours and miles).
sec1
meters27
sec600,3
hour1x
mile1
meters609,1x
hour1
miles60
Use a ratio to make a comparison
Example: How many kilograms of natural gas equal
the energy content of 1 kilogram of hydrogen gas?
(1 kg natural gas) x (14.2 x 107 J) = 2.6 kg gas
(5.5 x 107 J) 1 kg hydrogen kg hydrogen
Arrange the ratios to cancel the unwanted units (joules)
and give an answer in the desired units (kg natural gas/ kg
hydrogen)
Use a ratio to find efficiency
Efficiency = Useful energy out
Total energy in
What is the efficiency of an energy conversion that
requires 600 joules of energy in to produce 450 joules
of useful energy?
Efficiency = Useful energy out = 450 joules = 0.75
Total energy in 600 joules
Using equations, step #1:
Near each number in a problem, write the letter that
stands for that variable. Examples:
500F = T for temperature
10 kg = M for mass
If you’re not sure of the variable letter, write the word:
temperature or mass.
You can guess most of the variable letters because they
are the first letter of the word:
E = energy t = time, P = power
It is worth the time it takes to write the variable letters!
Using equations, step #2: Look on the equation sheet for an equation with the same
letters.
Most of the equations are grouped by topic. Before the exam, become familiar with the arrangement of the equations. This will save you time when looking for an equation.
Write down the equation.
Underline the variable to wish to find. What quantity does the problem ask you to find? Hint: the units of the 5 answer choices give you a clue.
It’s worth the time it takes to write down the equation!
Using equations, step #3: Rearrange the equation variables so the variable you
underlined is by itself on one side of the equation.
S = D becomes S x t = D t S = D becomes t = D t S Rule: If you move a variable from the numerator, it goes
down into the denominator. If you move a variable from the denominator, it goes up into the numerator.
It’s worth the time it takes to write rearrange the equation!
Using equations, step #4:
Substitute numbers from the problem for each variable.
Note: Some equations include a constant.
Examples: c, h, k
You can find the values for these constants on the
equation sheet.
Note: Sometimes a problem gives more information that
you need. You may not need to use all of the information
given.
When you DON’T need an equation
Exponential growth N = B x 2t and decay N = B x 1/2t
problems can be worked without an equation.
Example: The dandelions in my yard double every 2
days. Today there are 1,500. How many were there 6
days ago?
today 1,500
2 days ago 750
4 days ago 375
6 days ago 188
When you DON’T need an equation
Radiocarbon dating problems use the exponential
decay of carbon-14. Work them without an equation.
Example: The carbon-14 in a fossil bone is 1/32 of the
amount when the organism died. How old is the
bone? The carbon-14 half life = 5,730 years.
1 = 1 x 1 x 1 x 1 x 1 = 1
32 2 2 2 2 2 25
5 half lives x 5,730 yrs = 28,650 yrs
half life
Number of half lives
When you don’t need an equation:
specific heat and heat capacity
Example: The specific heat of a plastic is 1.3 cal/gram oC.
How much heat is required to heat 50 grams of plastic from
25 oC to 35 oC?
1.3 cal x 50 grams x (35 – 25) oC = 650 cal
gram oC
Example: The heat capacity of concrete is 50 cal/gram.
How much heat is required to raise the temperature of a
1 kg piece of concrete by 1oC?
50 cal x 1,000 grams = 50,000 cal
gram
When you don’t need an equation:
specific heat and latent heat
Example: How many calories are required to turn 60 grams
of water at 75 oC into steam at 100 oC.
The specific heat water is 1.0 cal/gram oC.
The latent heat of vaporization is 540 cal/gram
1.0 cal x 60 grams x (100 – 75) oC = 1,500 cal
gram oC
540 cal x 60 grams = 32,400 cal
gram
Add to find the total heat: 1,500 + 32,400 = 33,900 cal
Alternate Forms of Energy
The following is a summary of periods 20-26. About ½
of the final exam questions will cover these periods.
Solar energy (electromagnetic radiation from the
Sun)
Water energy (including tidal and geothermal)
Wind energy
Biomass energy
Radiant energy (electromagnetic radiation)
Radiant energy results from vibrations of charges.
As the charges vibrate, they produce waves of energy.
Waves of electromagnetic radiation travel at a speed of
3 x 108 (300,000,000) meters/second in a vacuum.
Wavelength, period, and frequency
• The wave’s period is the time it takes to complete one cycle.
• The wave’s frequency is how often it completes a cycle.
Wave Length
Wave Length
Distance
Wave
Period
Wave
Period
Time
Lower frequency Higher frequency
Wave speed and frequency
s = f L
s = speed at which radiant energy travels
(meters/sec or mi/sec)
f = frequency (cycles/sec, or Hertz)
L = wavelength (in meters, miles, or feet)
frequency = 1/period
Frequency is measured in Hertz (Hz)
1 Hz = 1 cycle/second
Fusion in stars: the proton-proton chain Stars smaller than 1.2 times the mass of the Sun use a
hydrogen-burning proton-proton chain as their primary fusion process.
1) two hydrogen nuclei (protons) fuse to form a nucleus of deuterium.
1H + 1H 2H + e+ + ne (+1.44 MeV)
2) Deuterium fuses with another hydrogen to form an isotope of helium called tritium.
2H + 1H 3He + g (+ 5.49 MeV)
3) Two tritium fuse to form a stable helium nucleus plus two hydrogen nuclei.
3He +3He 4He + 1H + 1H (+12.86 MeV)
Fusion Fission
Combining of Breaking apart of nucleons or large nuclei small nuclei
Exothermic Exothermic
Total number of nucleons
Energy in the early universe The Universe began with an explosion: The Big Bang.
As the Universe expanded and cooled, increasingly
complicated structures formed.
The energy per photon can be found from the
temperature:
E = 3 k T
with
E = energy (in joules or electron volts eV)
k = Boltzman’s constant = 1.38 x 10 – 23 J/K
or 8.62 x 10 – 5 eV/K
T = temperature (in kelvin)
Hubble’s constant
Hubble’s Law: The speed of a galaxy increases in
direct proportion to its distance from an observer.
The recessional velocity of an object is the rate at
which it appears to be moving away.
The Hubble constant (Ho) is the slope of the graph of
velocity of galaxies vs. their distance.
The inverse of the Hubble constant, (1/Ho) gives an
estimate of the age of the Universe.
Formation of chemical elements
Most of the hydrogen, helium and lithium in the
Universe was created during the Big Bang.
Carbon is formed when two alpha particles fuse to
form an unstable isotope of beryllium. 4He + 4He 8Be (– 0.1 MeV)
If a 3rd alpha is added before the beryllium nucleus
decays back into two alphas, carbon is formed. 8Be + 4He 12C (+ 7.4 MeV)
Formation of heavy elements
Elements through iron are formed when stars more massive than 5 times the mass of the Sun collapse violently.
Increasingly massive elements are fused until iron is produced.
Elements heavier than iron are formed when large stars collapse one last time and explode violently in a type II supernova.
Enough energy is released to begin endothermic fusion reactions of heavy elements.
These reactions require both activation energy and energy to produce the endothermic reaction.
Doppler effect A stationery light source emits waves of light uniformly in all directions.
If the same light source moves to the right, the wavelengths are no longer evenly spaced.
Light from a receding source
has longer wavelengths, and the
light is shifted to the red end of
the spectrum.
The redshift of distance stars
shows they are moving away
from the Earth.
Spread of waves over time
Hertzsprung-Russell diagram of stars
www.ucsd.edu/archive/public/tutorial/images/hr_local.gif&imgrefu
Source: http://imagine.gsfc.nasa.gov/Images/basic/xray/supernova_cycle.gif&imgref
Focusing radiant energy
Light reflected from concave and convex mirrors.
Focus
A Concave Mirror Focuses
Radiant Energy
A Convex Mirror Spreads
Radiant Energy
Focusing radiant energy
Light passes through concave and convex lenses.
A Concave Lens Spreads
Radiant Energy
Focus
A Convex Lens Focuses
Radiant Energy
Orientation of a solar collector
In the northern hemisphere, solar
collectors face south.
In winter, the collector angle
equals the latitude + 15o.
In summer, the collector angle
equals the latitude - 10o.
40o
15o
10o
Columbus, OH in winter
Columbus, OH in summer
Features of a solar house Deciduous trees or a roof overhang on the south side of a
house to shade windows from the direct sun in the summer, but allow the sun to shine in through windows in the winter when the sun is lower.
Embankments and non-deciduous trees on the north side of the house to block winter winds.
A thermal mass may be used to store solar energy gathered during the day for use at night when the temperature drops.
Rooftop solar collectors to supplement the heating system and to generate electricity.
Fiber optic light pipes to bring outside light into the interior of the house.
Insulation of walls and attic to reduce heat transfer.
Vents to exhaust hot air from the house.
Solar cells
Solar cells use the photoelectric effect to produce
electricity.
When electrons in the cell absorb photons of radiant
energy, some electrons have enough energy to
escape from their atom and form an electric current.
_
Output
Voltage
+
Light Rays
When an electron in a solar cell absorbs a photon with
sufficient energy, the electron can escape from the atom’s
electron cloud.
These unbound electrons form an electric current.
Photon
Time 1: A photon is absorbed by an electron.
Time 2: The electron escapes from the atom.
Energy of a photon
The energy of a photon is related to the frequency and
wavelength.
E = h f = (h c)/L
E = energy of a photon (joules)
h = is a constant = 6.63 x 10– 34 joule sec
f = frequency (Hertz)
c = speed of radiant energy = 3 x 10 8 m/s
L = wavelength (meters).
Power from a solar cell
The power generated by a solar cell depends on…
• the amount of solar insolation striking the cell
• the size (area) of the cell
• the efficiency of the solar cell
P = I x A x Eff
where
P = power (in watts)
I = solar insolation ( in watts/meter2)
A = area of collector (in meters2)
Eff = the efficiency of the solar cell
Source: http://www.education.noaa.gov/Freshwater/Water_Cycle.html
The Earth’s water cycle
Water from oceans, lakes, rivers, and the soil evaporates
when radiation from Sun warms the Earth’s surface.
Water vapor rises, is cooled, and condenses on dust
particles, forming clouds.
When clouds become saturated, precipitation falls as rain
or snow.
Precipitation eventually runs back into lakes and oceans
and the cycle repeats.
Latent heat of vaporization is removed from the
atmosphere when water evaporates and is added when
water vapor condenses.
Solar energy drives the water cycle.
Energy from ocean tides
• The moon’s gravitational force causes the oceans to form two bulges, one on each side of the Earth.
• As the Earth spins on its axis, land bordering the oceans passes through both bulges each day.
• This produces two high tides and two low tides per day.
• The gravitational attraction between the Earth and the moon causes the water on the side facing the moon to be pulled toward the moon.
• On the opposite side of the Earth, water tries to continue moving away from the Earth, forming a bulge.
http://en.wikipedia.org/wiki/File:
Tide_overview.svg
Tidal generators
http://www.alternative-energy-news.info/technology/hydro/tidal-power/
Electricity from geothermal energy
• Heat in the Earth’s core is the result
of radioactive decay.
• Thermal energy is conducted from
the core through the Earth’s mantle.
• This thermal energy can produce the
steam needed to turn generator
turbines
• This type of geothermal energy is
available only in geologically
unstable areas, such as volcanically
active Iceland. http://en.wikipedia.org/wiki/File:Old
_Faithfull-pdPhoto.jpg
Consequences of melting glaciers Mountain glaciers will disappear, many before 2050.
Billions of people depend on glacial melt water.
Consequences:
Glacial melt water is the primary source of the water
used to generate hydropower. Other energy sources
will be needed to replace this hydropower.
Much irrigation water comes from lakes that are
replenished by glacial melt water.
Other sources of drinking water will be needed.
Many glacial lake dams could fail, flooding valleys.
Energy from wind
Wind pattern due to
convection of warm air
from the equator to the
high latitudes.
Wind pattern due to convection
AND the Coriolis force of the
rotating Earth.
http://oceanservice.noaa.gov/education/kits/currents/0
5currents1.html
Daytime: Warm air
rises above the
land. Cool air over
the water flows
toward the land.
Night: Warm air
rises above the
water. Cool air
over the land flows
toward the water.
http://www.prh.noaa.gov/hnl/kids/activities.php
Wind turbines
The moving blades turn a shaft connected to a generator. This motion spins magnets near coils of wire.
Best locations: shorelines flat plains, and mountain ridges.
Advantages: A renewable resource, no atmosphere pollution
Blades are fatal to birds, bats, and insects.
Objections to the noise of the spinning blades and appearance of the large towers.
http://upload.wikimedia.org/wikipedia/common
s/1/14/Wind_turbine_Holderness.jpg&imgref
250 feet
Fuel from biomass
Biomass: plant material or animal waste used as a fuel.
Bioethanol is ethyl alcohol that is distilled from plant
material, such as corn, sugar cane or switchgrass.
Biodiesel is produced from vegetable oils and animal fats,
such as used cooking oil.
Adding ethanol to gasoline reduces the amount of fossil
fuel needed.
Alcohol combustion may produce less soot than oil.
The CO2 released by the burning biofuel is equal to the
uptake of CO2 from the atmosphere by the plants that
produced the biofuel.
Thus, biofuel is considered carbon neutral.
Carbon cycle
http://upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Carbon_cycle.jpg/460px-
Carbon_cycle.jpg&imgref
The carbon budget The carbon budget is the balance of the carbon exchanges
between carbon sinks and sources.
A carbon sink is a component of the carbon cycle that absorbs and stores more carbon than it releases.
A carbon source emits more carbon than it absorbs.
The oceans are the largest active carbon sink on the planet.
Human influence on the carbon budget
1) combustion of fossil fuel
2) deforestation
3) acid rain has makes sea water more acidic
4) the manufacture of concrete
Energy Advantages Disadvantages
Fossil Plentiful (at least for now) and inexpensive
greenhouse gases, acid rain, soot. Non-renewable
Biomass plentiful, inexpensive, renewable
Soot. (No net carbon dioxide is released.)
Wind Inexpensive to operate, renewable
Expensive to install, noisy, affects scenic vistas, can harm birds
Tidal Renewable. No atmospheric pollution
Limited locations. Can change aquatic ecosystem
Hydro-electric
Renewable. No atmospheric pollution
Dams can change the aquatic ecosystem
Nuclear No atmospheric pollution Thermal pollution. Possible nuclear accidents. Storage of radioactive waste.
Geother-mal
Limited atmospheric pollution.
Large quantities available only in areas with hot rock close to the surface.
Solar No atmospheric pollution. Renewable
Low efficiency, expensive, not always available.
• OR
K = the thermal conductivity
(J/s m oC or BTU inch/hour foot2 oF)
A = the cross sectional area (meters2 or feet2)
T = temperature (oC or oF)
L = thickness (meters or inches)
R = insulation value = L/K
L
Thot Tcold
AreaHeat flow
time
dtransferreenergyflowHeat
L
TTAK
t
E coldhot )(
R
TTA
t
E coldhot )(
The cost of using electricity
Electric companies charge for electricity in units of
kilowatt hours (kWh).
One kilowatt hour = 1,000 watts of power provided for
one hour.
To find the number of kilowatt hours,
1) divide watts by 1,000 to find kilowatts
2) multiply kilowatt by the number of hours of use.
To find the cost of using electricity, multiply the
kilowatt hours by the cost per kilowatt-hour
Payback time How long it takes to recover the cost of purchasing a more
expensive appliance from the savings in energy.
• The total cost of using an appliance is the purchase price plus the cost of operation:
Total cost = purchase price + (cost/year x # of years)
• An energy-efficient dishwasher costs $80 more than a less efficient dishwasher.
• The energy-efficient dishwasher saves $20 each year in operating costs.
• What is the payback time for the dishwasher?
additional cost = $80 x 1 year = 4 years savings each year $20
FOR THE FINAL EXAM…
The final exam is Mon, Apr 29, at 6:00 pm
(same room as your midterm exams)
Review sessions: Thurs, 4/25, 7:00 pm and Fri, 4/26, 1:00 pm in 2005 Smith.
Drop in: Mon, Apr 29, 2:00 – 5:30 in 2005 Smith
Be sure to bring a calculator to the exam!
