Tuesday, October 23rd….
Announcements….
• Homework 6 due Thursday
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 1
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 2
• Highlights that although natural gas is less bad for the environment than coal, it
is much more expensive. (Although perhaps the power companies were
overstating the price difference) In the absence of government regulations on CO2
emissions, it seems likely that many new coal plants will be built in the coming
years
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 3
• Highlights the influence of the recent Supreme Court
decision in Massachusetts v. Environmental
Protection Agency. Judges and regulators are
pointing to it to justify decisions limiting greenhouse
gas emissions. What was the Massachusetts v. EPA
case?
From Wikipedia - “Massachusetts v. Environmental Protection Agency is a U.S. Supreme Court case
decided 5-4 on April 2, 2007 in which twelve states and several cities of the United States brought suit against
the United States Environmental Protection Agency (EPA) to force that federal agency to regulate carbon
dioxide and other greenhouse gases as pollutants.”
“The Administrator of the Environmental Protection Agency determined in 2003, first, that the EPA lacked
authority under the Clean Air Act to regulate carbon dioxide and other greenhouse gases (GHGs), second, that
even if the EPA did have such authority the EPA declined to regulate carbon dioxide and other GHGs.”
“The petitioners asserted that the EPA does have authority over global warming and greenhouse gases
because of the broad wording of the statute, and that the EPA's decision not to regulate greenhouse gases
exceeded the scope of its discretion under the law.”
Majority opinion - “The petitioners were found to have standing, the Clean Air Act does give EPA the authority
to regulate tailpipe emissions of greenhouse gases, and the EPA is required to review its contention that it has
discretion in regulating carbon dioxide and other greenhouse gas emissions - specifically, its current rationale
for not http://en.wikipedia.org/wiki/Massachusetts_v._Environmental_Protection_Agency
regulating was found to be inadequate, and a scientific basis is now required. In addition, the majority
report commented
that "greenhouse gases fit well within the Clean Air Act!s capacious definition
of air
Physics 190E: Energy & Society
Lecture #13 - 4
pollutant.””
Fall 2007
Last time we started into the greenhouse effect. We want to understand what it is, how it
works and the role played by CO2 and other greenhouse gasses?
Why does a real greenhouse stay warm inside? The
glass lets in the sun’s rays, warming up the plants,
soil and air inside, but then blocks the warm air from
escaping.
The greenhouse effect for our planet makes the near
Earth atmosphere warmer than it would otherwise be
without the presence of heat trapping gasses.
The Royal Greenhouses of Laeken in Brussels.
The greenhouse effect is very well established
scientifically. Without it, as we’ll see, Earth’s
surface would be much colder, below the freezing
point of water & life as we know it would not have
evolved.
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 5
Before we try to understand how the greenhouse effect works, we’ll calculate what
Earth’s temperature would be without it…. This requires some physics!
Roughly speaking, Earth’s temperature is set by
an energy balance with the Sun. Every day the
Earth absorbs energy in the form of light from
the sun.
Every day the Earth must radiate away this
same amount of energy. If it doesn’t, it will
either heat up, or cool down. How much the
Earth radiates depends on its temperature. If its
temperature increases, it radiates more and viceversa.
This is a very important point. It is
what it means for Earth to be in
thermal equilibrium with the Sun.
Let’s look at all the pieces of this process, starting with the Sun. Where does the
Sun’s energy come from?
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 6
The Sun is made of hydrogen (74%) and helium (25%)
and is powered primarily by the nuclear fusion of
hydrogen into helium.
The key ingredient to understanding nuclear fusion is
Einstein’s famous equation
E = m c2
which says that mass is another form of energy.
How much energy does 1 kg of mass represent?
Let’s work this out as an inclass assignment
Physics 190E: Energy & Society
Fall 2007
“c” is the speed of light
c = 3 x 108 m/s
Lecture #13 - 7
The key ingredient to understanding nuclear fusion is
Einstein’s famous equation
E = m c2
which says that mass is another form of energy.
How much energy does 1 kg of mass represent?
E = (1 kg) x (3 x 108 m/s)2 = 9 x 1016 J
Physics 190E: Energy & Society
Fall 2007
“c” is the speed of light
c = 3 x 108 m/s
Lecture #13 - 8
Part 2 …..
The world used 447 Quads of energy in 2004. If all this energy
was in the form of mass, how many kilograms would this be?
Recall….
1 Quad = 1 quadrillion BTU = 1015 BTU
1 BTU = 1050 Joules
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 9
In class assignment…..
The world used 447 Quads of energy in 2004. If all this energy
was in the form of mass, how many kilograms would this be?
Recall….
1 Quad = 1 quadrillion BTU = 1015 BTU
1 BTU = 1050 Joules
First convert 447 Quads into Joules
E = 447 Quads = (447 x 1015 BTU)(1050 J/BTU) = 4.7 x 1020 J
Solving E = mc2 for m gives
m = E / c2 = (4.7 x 1020 J)/(3 x 108 m/s)2 = 5200 kg
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 10
Solving E = mc2 for m gives
m = E / c2 = (4.7 x 1020 J)/(3 x 108 m/s)2 = 5200 kg
This is an amazing result, that all the energy we
burn in a year is equivalent to about 10,000
pounds of mass energy!
This is why nuclear power is so attractive. But
neither fusion, nor fission convert all the mass
energy that one starts with into useful energy,
only a tiny bit.
Physics 190E: Energy & Society
Fall 2007
This is about 14 kg’s worth
of energy per day to supply
the world…
Lecture #13 - 11
Back to fusion energy & the Sun…..
In nuclear fusion, two light nuclei combine to produce a
heavier nuclei. However, the mass of the heavier nucleus is
slightly less than the sum of the masses of the original two
lighter nuclei. The difference in mass energy comes out of the
reaction in some other form, e.g. light.
The main fusion reaction in the Sun involves the merger of
two hydrogen nuclei into a helium nucleus. Although the
amount of energy released by each nuclear fusion reaction
is small, the Sun is huge…. Overall, some 4 billion
kilograms of matter are converted into energy every
second in the Sun.
The Sun is about 1.3 million
times Earth’s size. Its total
mass is 2 x 1030 kg.
The Earth absorbs some tiny fraction of this energy.
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 12
How much energy does the Earth receive from the Sun
each day?
As the light from the sun spreads out, it gets weaker. At the
radius of Earth’s orbit, the sunlight has power density of
1.35 kiloWatts/(meter)2
This is known as the solar constant, even though it is not
precisely constant. It varies by a few percent over the year,
as Earth’s slightly elliptical orbit moves our planet a little
closer, or farther from the Sun.
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 13
How much of the Sun’s power is the Earth absorbing on average?
From the Sun’s perspective, the Earth appears as a disk with
radius
Rearth= 6400 km
30% of the 1.35 kiloWatts/(meter)2 that
hits the Earth is reflected back into
space, by clouds, interactions with the
air and the Earth’s surface. This figure is
called Earth’s albedo.
The total solar power absorbed by Earth and the atmosphere is then…
2
Area = ! Rearth
Pabsorbed = (solar constant)(1-albedo)(area of Earth’s disk)
= (1.35 kW/m2)(1-0.30)(3.14)(6,400,000 m)2
= 1.2 x 1014 kilowatts = 120,000 Gigawatts
A truly huge number …..
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 14
In order for Earth’s temperature to remain constant on average, it must be
re-emitting this same amount of power back into space. How does this
work?
Note: this doesn’t
All hot objects radiate energy in a way that is characteristic of
mean we can’t make
their temperature….. We are familiar with this from thermal
use of the incoming
imaging. For warm blooded animals, such as humans, the
solar power!
energy radiated is in the infrared range, outside of the range of
our vision. Thermal imaging devices detect this and convert it
to images we can see. This has many applications, from
military ones to detecting heat leaks from buildings.
False color thermal image of a dog
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 15
It’s helpful to have an overview of the properties of light…..
Light is a type of wave built out of
electric and magnetic fields
We’ll talk more about these later on
when we talk about electricity…
• Light waves travel at the speed of light, c = 3 x 108 m/s.
• Like other kinds of waves, light waves have an amplitude (strength)
and a wavelength. The energy carried by the light depends both on the
Physics 190E: Energy & Society
strength
of the wave and its wavelength.
Fall 2007
Lecture #13 - 16
Visible light has a range of
wavelengths between 400700nm,
1 nm = 1 nanometer
= 10-9 meters
• At longer wavelengths,
there are infrared radiation,
microwaves and radio
waves.
• At shorter wavelengths,
there are ultraviolet rays,
X-rays and gamma rays.
Lightwaves come quantized in packets called photons. The energy of a photon is inversely
proportional to wavelength. So, a short wavelength photon has higher energy than a long
wavelength photon, gamma rays being the most energetic of all.
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 17
Sunlight is a mixture of different wavelengths of light.
A prism refracts (changes the angle of) light of different
wavelengths and separates the different colors.
A hot object radiates light with a mixture of
wavelengths characteristic of its temperature. For
a sort of perfect thermal emitter known as a
blackbody, the spectrum of emitted light can be
calculated and has a fairly simple form known as
the blackbody spectrum.
A blackbody is both a perfect emitter and a
perfect absorber - hence the name blackbody.
Physicists often make the approximation that
an object - like the Earth or the Sun - is a
blackbody, even if it is not a perfect absorber
at all wavelengths.
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 18
Blackbody spectrum graphs power emitted vs. wavelength
We see that the peak in the blackbody
spectrum moves to shorter wavelength higher energy - as the temperature is
increased.
This effect has a simple mathematical
description known as Wien’s displacement
law…
! peak
b
=
T
Wavelength
of peak
Temperature
Blackbody spectrum graphs power
emitted vs. wavelength
b = 2.9 x 10-3 m K
Wien’s displacement constant
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 19
! peak
b
=
T
b = 2.9 x 10-3 m K
What is the peak wavelength for human body temperature?
In Celsius, body temperature is 37C, which is (273 + 37)K = 310K.
! peak
2.9 " 10 #3 mK
=
= 9.3 " 10 #6 m = 9300nm
310K
Recall that visible light is in the range 400-700nm in wavelength. The peak
wavelength we’ve found is in the infrared range. Blackbodies below about
700K emit very little visible radiation and appear black. This is why we can’t
see each other at night with our eyes….
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 20
What about the Sun?
! peak
Tsun= 5780 K
This is the temperature at the Sun’s
surface. The temperature at the
Sun’s core is thousands of times
higher, Tcore =13,600,000 K.
2.9 " 10 #3 mK
=
= 5.0 " 10 #7 m = 500nm
5780K
Right in the middle of the visible
range. An object at this
temperature looks white to us.
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 21
When we look at the Sun through the atmosphere, it
appears yellow because the blue light has been
preferentially scattered out.
This effect is most pronounced at sunset, when the
sun looks red. At this time of day, sunlight is
passing through the greatest length of atmosphere to
reach us.
We see the blue light in the color of the sky.
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 22
To figure out what the temperature of the Earth would be without
the greenhouse effect, we need one more physics input… The
Stefan-Boltzmann law for the power emitted by a blackbody.
P = ! AT
4
P = power emitted, A = surface area, T= temperature
! = 5.7 " 10 #8
Watts
m2 K 4
Stefan-Boltzmann constant
We know that the Earth has to be emitting as much power as it absorbs
from the Sun
P = 1.2 x 1017 watts.
The surface area of the Earth is
A = 5.1 x 1017 m2
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 23
P = ! AT
4
P = power emitted, A = surface area, T= temperature
! = 5.7 " 10 #8
Watts
m2 K 4
We know that the Earth has to be emitting as much power as we receive
from the Sun, P = 1.2 x 1017 watts.
The surface area of the Earth is A = 5.1 x 1014 m2
P 1/ 4
1.2 " 1017 W
1/ 4
T =(
) =(
)
= 253K
#8
#2
#4
14
2
!A
(5.7 " 10 Wm K )(5.1 " 10 m )
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 24
P 1/ 4
1.2 " 1017 W
1/ 4
T =(
) =(
)
= 253K
#8
#2
#4
14
2
!A
(5.7 " 10 Wm K )(5.1 " 10 m )
This gives T = -4F, well below the freezing point of water. This is very
close to the temperature at the top of Earth’s atmosphere (255K).
The average temperature at Earth’s surface is 288K = 15C =
59F. The difference is due to the greenhouse effect - the heat
trapping properties of certain atmospheric gasses.
Physics 190E: Energy & Society
Fall 2007
Lecture #13 - 25