Transcript Chapter 2 Motion Along a Straight Line Position

FYI: A photon of the "wrong" energy will pass right through the gas
without interacting.
Energy, Power, and Climate Change
FYI: A photon of the "right" energy will be absorbed by the atom, and the
8.9 The Greenhouse Effect
electron will jump to a new energy level.
INTERACTION BETWEEN LIGHT AND ATOMS
Recall
that solar
radiation
strikes
the earth
at a is
FYI:
This process
is called
EXCITING THE
ELECTRON.
The electron
rate
of 1380STATE.
W m-2 or less, the farther from the equator
in
an EXCITED
you are.
FYI: If the "right" photon is of sufficiently large energy, the electron can be
That energy is carried in the form of photons, which
completely
freed
the atom. This is called IONIZATION.
are quanta
offrom
light.
The atmosphere is made up of gases, which are the
first layer of matter that the sun's rays interact
with.
If a photon is at the
precise energy for an
electron to jump to a
different energy level in an
atom, it will be absorbed.
FYI: A photon of the "right" energy will cause the molecule to vibrate with
a larger amplitude. This is called RESONANCE.
Energy, Power, and Climate Change
FYI: Resonant frequencies for molecules tend to be low, so the "right"
8.9
The Greenhouse
Effect
photons are from
the INFRARED
region of the spectrum.
INTERACTION BETWEEN LIGHT AND MOLECULES
Molecules can also absorb light energy.
A relatively useful model of
molecules (in this case diatomic)
N
N
has two masses joined by a spring.
First, we know that there is a potential energy
associated with a spring given by U = (1/2)kx2, where k
is the spring constant (representing how stiff the
spring is) and x is the amount the spring is displaced
from equilibrium.
Second, we know that there is a kinetic energy
associated with moving masses (two of them in this
case). Note that a diatomic molecule has many modes of
motion:
NNN
NNN
Linear Vibration
N
N
Rotation
Translation
FYI: The albedo for snow is one of the highest, and about 0.9 or 90%.
Energy,
and asClimate
Change
Cloud cover
has aboutPower,
the same albedo
snow.
8.9
Greenhouse
Effect
FYI: The albedo
for a The
dark forest
is about 0.1 or 10%.
INTERACTION BETWEEN LIGHT AND SOLIDS
Solids
contain
atoms
which
with each other in
FYI:
The average
albedo
for the
earthinteract
is about 30%.
such a way that electrons do not need to exist in so
few discrete energy levels.
Solids therefore can absorb photons of a very wide
range of energies (and therefore frequencies: E = hf).
The allowable energies of a solid are called bands.
Solids will increase in temperature more readily than
gases because of their increased absorption of photons.
As the solid heatS up it emits low-energy radiation in
the infrared region of the spectrum.
Surfaces of solids, liquids, and clouds absorb and
reflect light.
The ratio of reflected to absorbed light is called the
albedo.
albedo =
reflected light
absorbed light
Albedo
Energy, Power, and Climate Change
8.9 The Greenhouse Effect
INTERACTION BETWEEN LIGHT AND BLACK BODIES
You may recall that black bodies are perfect absorbers
IR radiation
visible radiation
UV radiation
Intensity
of radiation (and also perfect emitters).
Suppose we take our cavity blackbody and place a
detector at the opening, and heat the cavity blackbody
to successively higher temperatures, while measuring
the frequencies of the emitted radiation. We get a
family of graphs that looks like this:
Two trends emerge:
(1) The higher the temperature the greater
the intensity at all wavelengths.
(2) The higher temperature the smaller
the wavelength of the maximum intensity.
1000
maxT = 2.9010-3 mK Wien's
displacement law
2000
3000
Wavelength (nm)
4000
5000
Energy, Power, and Climate Change
8.9 The Greenhouse Effect
POWER OUTPUT OF RADIATING MATTER
Radiation emitted by hot objects is called thermal
radiation.
Recall that the total radiation power emitted is
proportional to T4, where T is the absolute Kelvin
temperature.
P = AeT4
where
FYI: Stefan's Power law
 = 5.6710-8 W/m2K4 Stefan-Boltzmann
constant
A is the surface area of the object,
and e is the emissivity of the object and is a
unitless number between 0 and 1 that depends on the
material emitting the radiation.
FYI: Since all bodies are above absolute zero, all bodies emit thermal
radiation.
Energy, Power, and Climate Change
8.9 The Greenhouse Effect
POWER OUTPUT OF RADIATING MATTER
What is the energy of one photon of 450 nm light?
Using E = hf and c = f we can get E in terms of :
c
hc
f =
Energy of a photon

E =


of wavelength 
(6.6310-34)(3108)
E =
45010-9
E = 4.410-19 J
E = 2.8 eV
1 eV
1.610-19 J
Energy, Power, and Climate Change
8.9 The Greenhouse Effect
POWER OUTPUT OF RADIATING MATTER
What is the wavelength of the most intense radiation
coming from the sun if its surface temperature is 6000
K?
maxT = 2.9010-3 mK
max(6000) = 2.9010-3
max = 48310-9 m = 483 nm
What is the power per square meter emitted by the sun?
Treat the sun like a perfect emitter.
e = 1
P = AeT4
P / A = eT4
P / A = (5.6710-8)(1)(6000)4
P / A = 7.35107 W m-2
FYI: This is 74 MW per
square meter!
Energy, Power, and Climate Change
8.9 The Greenhouse Effect
POWER OUTPUT OF RADIATING MATTER
The radius of the sun is 7108 m. What is the total
power radiated by the sun?
A = r2 = (7108)2 = 1.51018 m2
P / A = 7.35107 W m-2
P = (7.35107 W m-2)A
P = (7.35107)(1.51018)
P = 1.11026 W
FYI: This is 1026 joules
each second!
FYI: The radius of earth is R = 6.4106 m.
Energy, Power, and Climate Change
8.9 The Greenhouse Effect
THE TEMPERATURE OF THE EARTH
Our first model of the effect of the sun's energy on
the temperature of the earth assumes no atmosphere.
Ignoring the atmosphere we will estimate how warm the
earth should be.
The energy per second per
unit area provided by the
sun is 1360 W/m2.
This energy is absorbed only
by half of the earth. Why?
This energy is contained in
1360 W / m2
the disk in heavy yellow,
which has a radius of the
earth.
A = r2 = (6.4106)2 = 1.31014 m2
P = 1360A
P = 1360(1.31014)
P = 1.751017 W
and
6 m.
FYI: TheEnergy,
radius of earthPower,
is R = 6.410
Climate Change
8.9
The
Greenhouse
Effect
FYI: The surface
area of
a sphere
is A = 4r2.
THE TEMPERATURE OF THE EARTH
Since the
albedo
the
earth
is 30%,ofthis
Question:
Whataverage
assumption
did we of
make
about
the emissivity
the
means
that
70%
of
this
power
is
absorbed:
earth?
17 W
Question:P If=the(0.70)1.7510
temperature of the
planet is to remain CONSTANT, at
what rate Pmust
it be emitting
17 W energy if it is absorbing energy at a rate of
=
1.2310
absorbed energy per second
17
1.2310
W?
To calculate the energy absorbed by the earth, we
assume that the whole surface area of the planet is
absorbing this energy. Why?
A = 4r2 = 4(6.4106)2 = 5.21014 m2
From Stefan's power law we can get a handle of the
expected temperature of earth (without atmosphere):
P = AeT4
P = 5.6710-8(5.21014)(1)T4
P = 2.95107T4
1.231017 = 2.95107T4
T4 = 4.17109
FYI: The average temperature
T = 254 K
= -19°C
of the earth is 288 K = +15 C.
FYI: The
absorption of
this radiated
energy
(or TRAPPING
of it) by the
Energy,
Power,
and
Climate
Change
ATMOSPHERE is called THE GREENHOUSE EFFECT, since a
8.9
Greenhouse
Effect
greenhouse also
trapsThe
radiated
energy.
THE EMISSIVITY OF THE EARTH
This estimate is lower than the average temperature of
FYI: The actual emissivity of earth depends on many things - not just the
the earth.
atmosphere. Clouds, ice packs, deserts, forests, lakes, etc. all contribute
We may conclude that other factors contribute to
to a variable emissivity
(and albedo).
increasing
the average
temperature of the earth.
factor contributing
to a higher
surface
temperature
is theby
FYI:
The Another
atmosphere
absorbs some
of the
energy
radiated
the
earth
before
it escapes
space.which produce heat as a
fact that
the earth
contains
radioactiveto
elements
byproduct
In our model
we assumed that
that
of their disintegration.
This is,the
afteremissivity
all, the energywas
behind
of
a block
The earth does NOT have a perfect
volcanoes
andbody.
plate tectonics!
emissivity of 1.
We can estimate the emissivity of earth using the
Stefan power law and the actual temperature of 288 K:
P = AeT4
P = 5.6710-8(5.21014)e(288)4
P = 2.031017e
1.231017 = 2.031017e
e = 0.61
Energy, Power, and Climate Change
8.9 The Greenhouse Effect
ATMOSPHERIC HEAT ABSORPTION
Obviously the atmosphere is the first layer
of earth to be struck by incoming light, and
incoming
so the atmosphere has first dibs on
solar
extracting energy from the sun.
radiation
Different gases in the atmosphere
absorb different frequencies of light this is because of the resonant
20% UV and
properties of each gas.
X-rays
The atmosphere absorbs about 50% of
(Ozone)
the incoming solar radiation before it
strikes the ground.
The Sankey diagram for incoming solar
radiation looks like this:
30% IR
(H2O, CO2)
30% arrives
at ground
Energy, Power, and Climate Change
8.9 The Greenhouse Effect
ATMOSPHERIC HEAT ABSORPTION
incoming
solar
radiation
20% UV and
X-rays
(Ozone)
30% IR
(H2O, CO2)
50% arrives
at ground
FYI: This
is in the IR region
of the and
spectrum.
Energy,
Power,
Climate
Change
FYI: Do not confuse
radiation
REFLECTED by
the ground with the
8.9 the
The
Greenhouse
Effect
radiation PRODUCED by the ground.
S
URFACE
Hthink
EAT ofABSORPTION
FYI:
You can
the ground as a frequency converter. It absorbs
Not all of the remaining 50% of the solar
radiation of ais
variety
of frequencies
andground.
converts it to infrared radiation.
radiation
absorbed
by the
incoming
Depending on the albedo of the ground, some of
solar
the radiation is reflected back to the
radiation
atmosphere.
The atmosphere WILL NOT absorb and of
the ground-reflected radiation. Why?
20% UV and
The remaining radiation is absorbed by
X-rays
the ground, increasing its temperature.
(Ozone)
The ground temperature will radiate
its own heat according to Wien's
displacement law:
30% IR
maxT = 2.9010-3 mK
(H2O, CO2)
max(288) = 2.9010-3
max = 1.0110-6 m = 10100 nm
Note that CO2 and H2O can both absorb IR
radiation.
50% arrives
at ground
Energy, Power, and Climate Change
8.9 The Greenhouse Effect
SURFACE HEAT ABSORPTION
Absorption by the ground is very complex.
Ice,
snow, water, sand, forest, crops, cities, etc.
incoming
all have different heat capacities.
solar
We can lump all of the specific heat
radiation
capacities into one overall surface heat
capacity Cs, which is defined to be the
amount of heat Q needed to raise the
temperature of 1 m2 of the ground by 1K.
20% UV and
For earth, Cs is estimated to be about
X-rays
8
2
410 J/K m .
(Ozone)
30% IR
(H2O, CO2)
50% arrives
at ground
Energy, Power, and Climate Change
8.9 The Greenhouse Effect
THE GREENHOUSE EFFECT
It is the absorption in the atmosphere of
the IR radiation produced by the warm earth
that we call the greenhouse effect.
Since H2O and CO2 are the gases in the
atmosphere that are able to absorb IR,
we call them greenhouse gases.
FYI: Water vapor and carbon dioxide are the
principal greenhouse gases.
FYI: If it wasn't for the greenhouse gases, all of the
heat radiated by the earth would pass through the
atmosphere and be lost to space.
FYI: The greenhouse gases account for much of
the difference between the earth's calculated
temperature of 254 K, and the earth's actual
temperature of 288 K.
incoming
solar
radiation
20% UV and
X-rays
(Ozone)
30% IR
(H2O, CO2)
30% arrives
at ground
FYI: By the way, since the greenhouse gases absorb IR (both incoming and
outgoing) they radiate IR just as the ground does, contributing to the overall
and
Climate
Change
temperatureEnergy,
of the earth. Power,
This makes for
a rather
involved Sankey
diagram!
8.9theThe
Effect
FYI: At each interface
energyGreenhouse
in equals the energy
out:
HE means
GREENHOUSE
EFFECT of the earth is constant.
FYI:TThis
that the temperature
30 77
235
30 77
radiated by earth
incoming
solar
radiation
342 W/m2
235
342
absorbed
by
greenhouse
gases
235
67
40
greenhouse
gases
the
atmosphere
radiated
by earth
168
390
the ground
WITHOUT GREENHOUSE
GASES
WITH GREENHOUSE
GASES
324