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Chapter 10:
Global Warming
Is Global Warming real? How sure are we?
Who/what is causing it? How sure are we?
What are the consequences likely to be?
What is the Greenhouse Effect?
Who is responsible for Greenhouse Gas Emissions—the
developed world or the developing world?
What would we have to do to stop Global Warming?
Are we running out of fossil fuels?
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
1
Scientific Consensus
The Intergovernmental Panel on Climate Change (IPCC)
periodically reports a Consensus opinion that (almost) all of the
scientific community agrees with
The IPCC Consensus is not the whole story, but it represents the
best, most factual summary available of human knowledge
about Climate Change and Global Warming
https://upload.wikimedia.org/wikipedia/en/2/28/Intergovernmen
tal_Panel_on_Climate_Change_Logo.jpeg
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
2
Scientific Consensus
To emphasize quotes from the IPCC Synthesis Report (2014), I
will use this font:
“Human influence on the climate system is clear”
Also, please note that I’m using the 2014 IPCC report as a
source for most of this information. The book uses a somewhat
out-of-date report, so I will update the book’s information when
possible.
The summary report can be found online here:
https://www.ipcc.ch/pdf/assessment-
report/ar5/syr/AR5_SYR_FINAL_SPM.pdf
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Scientific Consensus
As it happens, our textbook author, Richard Muller, is a famous
climate change skeptic
He started his own project called Berkeley Earth to check many
of the IPCC claims for himself
I will highlight quotes from Muller and Berkeley Earth like this:
“The good match between the new temperature record and
historical carbon dioxide records suggests that the most
straightforward explanation for this warming is human
greenhouse gas emissions”
http://berkeleyearth.org/
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Chapter 10A:
The Facts
Global Warming is real—We can measure it directly
Global Temperature has gone up
Sea level has risen
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Global Warming is Definitely Real
“Warming of the climate system is unequivocal”
“The atmosphere and ocean have warmed, the amounts of snow
and ice have diminished, and sea level has risen.”
“Global Land temperatures have increased by 1.5°C over the
past 250 years”
There is no debate about whether Warming is occurring.
We can check this very easily by simply looking at (direct and
indirect) temperature records.
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Global Warming is Definitely Real
Globally, temperatures are up around 1-2⁰C (2-4⁰F) since 1850
http://berkeleyearth.org/berkeley-earth-temperature-update/
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Global Warming is Definitely Real
Here is the temperature since 1750
http://berkeleyearth.org/summary-of-findings/
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Black line represents our best guess
Gray shading represents uncertainty
Global Warming is Definitely Real
The sea level has risen about 20cm (8 inches) since 1900
From IPCC report (2014)
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Prof. Michael Opferman | Phys 0847 | Temple University
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Chapter 10B:
The Reason Why
We have an explanation for Global Warming that explains what
we see:
Global Warming is mostly caused by humans.
The main reason for Global Warming is the Greenhouse Effect.
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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What Determines Earth’s Temperature?
The Earth gains Energy (and heats up) by absorbing sunlight
The Earth loses Energy (and cools down) by emitting Infrared
Light (Recall: Ch. 9)
If these two effects are balanced, the Earth’s Temperature will
remain about the same
If they are out of balance, the Earth’s Temperature will go up or
down
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Prof. Michael Opferman | Phys 0847 | Temple University
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Greenhouse Effect
Greenhouse Gases allows sunlight to come in, but block
Infrared Light as it tries to get out
Greenhouse Gases are like a blanket that hold in the Heat to
keep the Earth warm
http://science.howstuffworks.com/environmental/green-
science/question7462.htm
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Greenhouse Effect
If the Greenhouse Gas concentration is too high, then not
enough Energy escapes, and the Earth warms up
If the Greenhouse Gas concentration is too low, then too much
Energy escapes, and the Earth cools down
http://science.howstuffworks.com/environmental/green-
science/question7462.htm
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Carbon Dioxide
The most important Greenhouse Gas is Carbon Dioxide (CO2)
It makes up only a very small percentage of the air (less than
0.1%) but has a big effect
Plants remove Carbon Dioxide from the air and emit Oxygen
Animals remove Oxygen from the air and emit Carbon Dioxide
Normally, there is a balance between plants and animals and the
levels of CO2 remain roughly constant
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Carbon Dioxide
CO2 is also emitted whenever Carbon compounds (like fossil
fuels) are burned in the presence of Oxygen
Once emitted, the CO2 stays in the air for hundreds of years
The CO2 concentration in the air has been slowly building up
since we began using fossil fuels
This makes perfect sense since there is no effective mechanism
for removing this CO2 from the air as we release it
But is the amount of CO2 emitted due to fossil fuels really
significant?
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Source of Carbon Dioxide
From IPCC report (2014)
“Emissions of CO2 from fossil fuel combustion and industrial
processes contributed about 78% of the total greenhouse gas
emissions increase from 1970 to 2010.”
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Source of Carbon Dioxide
From IPCC report (2014)
“About half of anthropogenic CO2 emissions between 1750 and
2011 have occurred in the last 40 years.”
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Summary So Far
We are releasing lots of CO2 into the air
Mainly due to fossil fuel use
Once it is there, we would expect it to stay there
So, have we actually seen CO2 levels in the air going up?
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Greenhouse Gas Concentrations in the Air
Carbon Dioxide (CO2) levels are up 40% since 1850
Methane (CH4) levels are up 125%
Nitrous Oxide (N2O) levels are up 20%
From IPCC report (2014)
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Greenhouse Gas Concentrations in the Air
“Atmospheric concentrations of carbon dioxide, methane and
nitrous oxide [are at levels] unprecedented in at least the last
800,000 years.”
From IPCC report (2014)
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
20
Summary So Far
We are releasing lots of CO2 into the air
Mainly due to fossil fuel use
Once it is there, we would expect it to stay there
CO2 levels in the air are the highest they’ve been in about a
million years
Based on the Greenhouse Effect, we would expect this to affect
the Temperature. Is this what we see?
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Carbon Dioxide and Temperature
temperature seems to track CO2 levels in the air almost exactly
Based on what has happened in the past, global
From Physics and Technology for Future Presidents
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
22
Carbon Dioxide and Temperature
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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This, by itself, does not necessarily prove anything, but our
textbook author (skeptical that CO2 levels were so important)
took the argument one step further by calculating how much the
temperature would be expected to go up due to many different
known reasons (CO2 as well as other ones you may have heard
about from Global Warming skeptics)
He found (much to his surprise) that the only things that make a
noticeable difference are CO2 levels and major volcanic
eruptions
Carbon Dioxide and Temperature
Black: Actual measurements
Red: Calculation that assumes only CO2 and volcanoes are
important
http://berkeleyearth.org/summary-of-findings/
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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With just these two factors, you can explain why the
temperature has gone up the way it has
Summary So Far
We are releasing lots of CO2 into the air
Mainly due to fossil fuel use
Once it is there, we would expect it to stay there
CO2 levels in the air are the highest they’ve been in about a
million years
Global Temperature is going up
Global Temperature seems to always go up when CO2 levels go
up
This makes sense because of the Greenhouse Effect
Calculations show that CO2 levels are, by far, the most
important factor in determining global temperature
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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“Atmospheric concentrations of carbon dioxide, methane and
nitrous oxide [are at levels] unprecedented in at least the last
800,000 years. Their effects, together with those of other
anthropogenic drivers […] are extremely likely to have been the
dominant cause of the observed warming since the mid-20th
century.”
The IPCC define “Extremely Likely” as at least 95% likely.
“Anthropogenic” = Caused by humans
So, the IPCC estimates that it is at least 95% likely that humans
are the main cause of Global Warming
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Conclusion: Recent Global Warming is almost certainly caused
by humans
“The exquisite agreement between the warming and CO2
suggests that most—maybe all—of the warming of the past 250
years was caused by humans. That’s a remarkable conclusion
for someone (me) who had been stigmatized as a skeptic by the
media.”
–Richard Muller in Energy for Future Presidents
“I was not expecting this, but as a scientist, I feel it is my duty
to let the evidence change my mind.”
-Richard Muller on berkeleyearth.org
Conclusion: Recent Global Warming is almost certainly caused
by humans
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Chapter 10C:
So What?
Is Warming likely to continue?
What effects is Warming likely to have? Is it that big of a deal?
What would we have to do to stop it?
What is the worst case scenario?
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Effect of Global Warming
Recall: The effect we are talking about is only about 1-2
degrees Celsius (about 2-4 degrees Fahrenheit)
You may wonder what the big deal is about an increase of just a
couple of degrees
The bottom line: It is not the increase so far that concerns us,
but the fact that (until we stop using fossil fuels completely)
this effect will keep getting worse as we release more and more
CO2 into the air
And we will have to live with the world we’ve created for
hundreds of years to come
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Effect of Global Warming
If things continue along the present path, the temperature will
go up about 1°F every 15 years
“Just a few degrees can change fertile regions into deserts or
melt ice caps.”
For comparison: A 10°F change would be as severe as a major
ice age!
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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“Continued emission of greenhouse gases will cause further
warming and long-lasting changes in all components of the
climate system, increasing the likelihood of severe, pervasive
and irreversible impacts for people and ecosystems. Limiting
climate change would require substantial, sustained reductions
in greenhouse gas emissions”
Effect of Global Warming
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Consequences
“Surface temperature is projected to rise over the 21st century
under all assessed emission scenarios. It is very likely that heat
waves will occur more often and last longer, and that extreme
precipitation events will become more intense and frequent in
many regions. The ocean will continue to warm and acidify, and
global mean sea level to rise.”
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Consequences
“In most scenarios without additional mitigation efforts, [there
will be] substantial species extinction, global and regional food
insecurity, consequential constraints on human activities and
limited potential for adaptation”
Mitigation Efforts = Reducing Greenhouse Gas emissions
Adaptation = Our ability to deal with the warming that we get
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Consequences:
Extinction
“A large fraction of species faces increased extinction risk due
to climate change.”
“Most plant species cannot naturally shift their geographical
ranges sufficiently fast to keep up with current and high
projected rates of climate change in most landscapes”
Most plants and some animals simply will not be able to migrate
to new habitats as fast as they are changing, and are likely to go
extinct as a result.
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
34
Scenario 1: If warming is 2⁰C (4⁰F) above late 20th century
levels, it will negatively impact food production
Scenario 2: If warming is 4⁰C (7⁰F) above late 20th century
levels, it “ would pose large risks to food security globally”
“Just a few degrees can change fertile regions into deserts”
Consequences:
Food
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
35
Urban Areas: “ heat stress, storms and extreme precipitation,
inland and coastal flooding, landslides, air pollution, drought,
water scarcity, sea level rise and storm surges”
Rural Areas: “ water availability and supply, food security,
infrastructure and agricultural incomes, including shifts in the
production areas of food and non-food crops around the world”
Consequences:
In Populated Areas
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
36
Tipping Points
Even worse, it is possible (though not necessarily likely) that at
some point we may cross a “tipping point” where a cataclysmic
event is triggered
Example: If the Antarctic Ice Sheet falls into the sea—sea level
goes up by over 100 feet
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
37
Tipping Points
Example: The Arctic Ocean warms, causing it to release
Methane. Since Methane is a Greenhouse Gas, the Methane
causes more Warming, which releases more Methane. The
temperature rises out of control due to a vicious cycle
“Runaway greenhouse warming is responsible for the hot
surface conditions of Venus—900°F—on a planet that is
otherwise very similar to earth”
It’s very unlikely that we could see anything close to this
dramatic, but it’s important to understand that the impact of
Greenhouse Gases on temperature can be huge
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
38
Chapter 10D:
What Can We Do?
What would we have to do to halt Global Warming?
What would we have to do to reverse Global Warming?
Which countries are causing the problems?
Developed countries like the US or developing countries like
China?
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
39
Cumulative Carbon Dioxide Production
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Problem #1: It is not our present levels of CO2 emissions that
matter, but the cumulative total of all CO2 emissions in history
Cumulative Carbon Dioxide Production
“Cumulative emissions of CO2 largely determine global mean
surface warming”
“Multiple lines of evidence indicate a strong, consistent, almost
linear relationship between cumulative CO2 emissions and
projected global temperature change to the year 2100”
Note: This means that even if we stabilize our yearly CO2
output, Global Warming will keep getting worse because it
depends on the sum total of all emissions in history. We have to
stop putting CO2 into the atmosphere all together just to halt
warming and stabilize the temperature.
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
41
Cumulative Carbon Dioxide Production
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Problem #1: It is not our present levels of CO2 emissions that
matter, but the cumulative total of all CO2 emissions in history
Problem #2: Even after we’ve totally stopped emitting CO2, the
Temperature won’t start going down. It will only stop going up.
“Many aspects of climate change and associated impacts will
continue for centuries, even if anthropogenic emissions of
greenhouse gases are stopped.”
“temperatures will remain approximately constant at elevated
levels for many centuries after a complete cessation of net
anthropogenic CO2 emissions”
Cumulative Carbon Dioxide Production
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
43
Cumulative Carbon Dioxide Production
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Problem #1: It is not our present levels of CO2 emissions that
matter, but the cumulative total of all CO2 emissions in history
Problem #2: Even after we’ve totally stopped emitting CO2, the
Temperature won’t start going down. It will only stop going up.
Problem #3: The temperature won’t start going down until CO2
levels go down. This takes hundreds of years to happen
naturally, and we’re not very good at removing CO2 from the
air ourselves.
Can we remove the CO2 that is already in the air?
Short Answer: We don’t presently have any effective ways to do
this, but there are some ideas floating around.
One of the most effective methods currently is to
Plant trees. Let them absorb CO2 from the air.
Ensure (somehow) that the carbon removed from the air does
not go back into the air again later—e.g. when the trees burn or
decompose
One idea: Cut down the trees and burn the wood, but carefully
capture all the CO2 emitted during the burning. Then
(somehow) store it permanently underground
Bonus: You can use the burning wood as an Energy source
(using Engines—Recall Ch. 2)
What Can We Do?
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
45
More realistically, the answers to Climate Change are usually
categorized as Mitigation and Adaptation
Mitigation: Take steps to reduce the severity of Climate Change
Maybe we can’t stop it, but at least we can reduce its magnitude
The main way to mitigate the disaster is to stop CO2
emissions—i.e. stop using fossil fuels
Adaptation: Takes steps to limit our vulnerability to what
happens
Find ways of dealing with the problems that Climate Change
creates
What Can We Do?
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
46
“Without additional mitigation efforts beyond those in place
today, and even with adaptation, warming by the end of the 21st
century will lead to very high risk of severe, widespread and
irreversible impacts globally.”
“There are multiple mitigation pathways that are likely to limit
warming below 2⁰C relative to pre-industrial levels. These
pathways would require substantial emissions reductions over
the next few decades and near zero emissions of CO2 and other
long-lived greenhouse gases by the end of the century.”
What Can We Do?
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
47
“Effective mitigation will not be achieved if individual agents
advance their own interests independently. Cooperative
responses, including international cooperation, are therefore
required to effectively mitigate greenhouse gas emissions and
address other climate change issues.”
“Delaying additional mitigation to 2030 will substantially
increase the challenges associated with limiting warming over
the 21st century”
What Can We Do?
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
48
Human Energy Use
Observations show that the richest countries in the world use
the most Energy per person
Richer = more to the right
More Energy use per person = closer to top
From Physics and Technology for Future Presidents
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
49
Global Emissions
But developing countries account for more than half of present
CO2 emissions from the burning of fossil fuels, because there
are more people in developing countries.
China’s emission are about double the US, but their population
is about 4 times as large
http://www.epa.gov/climatechange/ghgemissions/global.html
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
50
Global Emissions
Emissions from the developing world are rising very rapidly,
while those from the developed world are stable (but already
high, per person)
“To favor dropping carbon dioxide [levels in the air], while
arguing for no restraints on the developing world is inconsistent
[…] Just to stabilize greenhouse emissions, the emerging
economies must cut emission intensity by 8%-10% per year.
That will be hard—probably impossible.”
And remember: our goal is not to stabilize emissions, but to
reduce them to zero
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
51
Global Emissions
Although China has offered to start reducing their emissions per
unit of GDP, their economy is growing so fast that their
emissions are still expected to rise for at least anther 10 years
Recall again: Our goal is not to stabilize emissions—it’s to get
them down to zero
Although the US has offered to decrease emissions by about
25% over the next 10 years, recall again that we are trying to
get to zero. Even 25% is only a small step.
Bottom line: Although it’s nice that people are starting to talk
about cutting emissions, the progress has been very slow
compared to IPCC goals
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
52
Greenhouse Gas Sources
This chart shows where our Greenhouse Gas emissions are
coming from.
From this, we can deduce what some of the most pressing
concerns are
http://www.epa.gov/climatechange/ghgemissions/global.html
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
53
Greenhouse Gas Sources
http://www.epa.gov/climatechange/ghgemissions/global.html
Switch to Clean Energy
Better insulation and efficiency
Use less Energy
Esp. Heat/AC
Switch to Clean Vehicles
Long-term: Electric/Hydrogen powered by solar/wind/nuclear
Short-term: Hybrids/better mpg, Natural Gas cars, Drive less
Stricter environmental regulations
Less consumption of animal products
Stop deforestation
Stricter regulations
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
54
Chapter 10E:
Energy Security and
Fossil Fuel Supply
Are we running out of fossil fuels?
Will the Global Warming problem solve itself because we have
no fuels left to burn?
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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Fossil Fuels
One of the key sources of CO2 is the burning of fossil fuels
Let us explore some of the questions surrounding the
availability and use of fossil fuels
Will this problem solve itself when we run out of fossil fuels?
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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https://s-media-cache-
ak0.pinimg.com/736x/19/27/12/192712e882c33b41833ec427bf6
5724c.jpg
Fossil Fuels
Are we running out of Fossil Fuels?
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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No, definitely not.
We are running out of cheap, easily extracted oil, but if the
price of oil goes up it will become economical to extract and
use the many vast supplies of other resources
We still have vast supplies of
Alternative sources of oil (underwater, oil shale, etc.)
Coal (which can be turned into diesel fuel)
Natural Gas (including under the ocean)
Many other sources that we haven’t bothered with because they
are expensive to produce
Oil Supply
We have only extracted a small fraction of the world’s oil, but
(aside from OPEC’s supply), most of the remainder is difficult
to extract
From Physics and Technology for Future Presidents
Oil we’ve used so far
Oil we have left
And that’s only oil!
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
58
Oil Price
The high price of oil not long ago made a number of
oil extraction techniques economically viable, even though they
would never have been used in the 1990’s
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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http://inflationdata.com/articles/charts/inflation-adjusted-oil-
prices-chart/
Oil Price
When the oil price goes up, other sources of Energy become
viable, but (not coincidentally) OPEC ensures that the price of
oil never exceeds these levels for long
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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http://inflationdata.com/articles/charts/inflation-adjusted-oil-
prices-chart/
Fossil Fuel Comparison
There are also other sources of Fossil Fuels besides oil
Including coal and natural gas
These also become more attractive when the price of oil goes up
From Physics and Technology for Future Presidents
Compare
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
61
Fossil Fuels
The good news is that the fossil fuel supply is not such a big
issue as some people make it. There are plenty of fossil fuel
sources left in the US and around the world. They will just cost
a bit more to use.
The bad news is that, even though these fossil fuels are
available, we shouldn’t use them. Burning these fuels releases
CO2, and we need to stop emitting CO2 immediately or the
problem of Global Warming is only going to get worse
Possible exception: Maybe as a short-term solution we should
wean ourselves off of fossil fuels by switching to fuels that emit
less CO2, such as Natural Gas
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
62
Fossil Fuels
For a more in-depth discussion of many of the various Energy
sources available, an excellent source is our textbook author’s
other book, Energy for Future Presidents
11/8/2016
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63
Chapter 10 Summary
Evidence of Global Warming is clear and obvious.
It is almost certain that Global Warming has been caused
completely or mostly by humans. This is most obvious because
of the clear relationship between global temperature and CO2
concentration in the air
CO2 increases the temperature because it prevents Heat Energy
from escaping into outer space. This is called the Greenhouse
Effect
CO2 concentrations are at their highest levels in hundreds of
thousands (perhaps millions) of years
CO2 is released when fossil fuels are burned
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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64
Chapter 10 Summary
The temperature is determined by cumulative CO2 emissions, so
stopping Global Warming means stopping the use of fossil fuels
completely
Most Greenhouse Gas emissions come from the developing
world (such as China), but the most Greenhouse Gas emissions
per person come from the richest countries (such as the US)
The world is not running out of fossil fuels. We are only
running out of the cheap oil we have been using for the past few
decades.
11/8/2016
Prof. Michael Opferman | Phys 0847 | Temple University
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  • 1. Chapter 10: Global Warming Is Global Warming real? How sure are we? Who/what is causing it? How sure are we? What are the consequences likely to be? What is the Greenhouse Effect? Who is responsible for Greenhouse Gas Emissions—the developed world or the developing world? What would we have to do to stop Global Warming? Are we running out of fossil fuels? 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 1 Scientific Consensus The Intergovernmental Panel on Climate Change (IPCC) periodically reports a Consensus opinion that (almost) all of the scientific community agrees with The IPCC Consensus is not the whole story, but it represents the best, most factual summary available of human knowledge about Climate Change and Global Warming https://upload.wikimedia.org/wikipedia/en/2/28/Intergovernmen tal_Panel_on_Climate_Change_Logo.jpeg 11/8/2016
  • 2. Prof. Michael Opferman | Phys 0847 | Temple University 2 Scientific Consensus To emphasize quotes from the IPCC Synthesis Report (2014), I will use this font: “Human influence on the climate system is clear” Also, please note that I’m using the 2014 IPCC report as a source for most of this information. The book uses a somewhat out-of-date report, so I will update the book’s information when possible. The summary report can be found online here: https://www.ipcc.ch/pdf/assessment- report/ar5/syr/AR5_SYR_FINAL_SPM.pdf 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 3 Scientific Consensus As it happens, our textbook author, Richard Muller, is a famous climate change skeptic He started his own project called Berkeley Earth to check many of the IPCC claims for himself I will highlight quotes from Muller and Berkeley Earth like this:
  • 3. “The good match between the new temperature record and historical carbon dioxide records suggests that the most straightforward explanation for this warming is human greenhouse gas emissions” http://berkeleyearth.org/ 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 4 Chapter 10A: The Facts Global Warming is real—We can measure it directly Global Temperature has gone up Sea level has risen 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 5 Global Warming is Definitely Real “Warming of the climate system is unequivocal” “The atmosphere and ocean have warmed, the amounts of snow and ice have diminished, and sea level has risen.” “Global Land temperatures have increased by 1.5°C over the
  • 4. past 250 years” There is no debate about whether Warming is occurring. We can check this very easily by simply looking at (direct and indirect) temperature records. 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 6 Global Warming is Definitely Real Globally, temperatures are up around 1-2⁰C (2-4⁰F) since 1850 http://berkeleyearth.org/berkeley-earth-temperature-update/ 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 7 Global Warming is Definitely Real Here is the temperature since 1750 http://berkeleyearth.org/summary-of-findings/ 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 8 Black line represents our best guess Gray shading represents uncertainty
  • 5. Global Warming is Definitely Real The sea level has risen about 20cm (8 inches) since 1900 From IPCC report (2014) 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 9 Chapter 10B: The Reason Why We have an explanation for Global Warming that explains what we see: Global Warming is mostly caused by humans. The main reason for Global Warming is the Greenhouse Effect. 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 10 What Determines Earth’s Temperature? The Earth gains Energy (and heats up) by absorbing sunlight
  • 6. The Earth loses Energy (and cools down) by emitting Infrared Light (Recall: Ch. 9) If these two effects are balanced, the Earth’s Temperature will remain about the same If they are out of balance, the Earth’s Temperature will go up or down 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 11 Greenhouse Effect Greenhouse Gases allows sunlight to come in, but block Infrared Light as it tries to get out Greenhouse Gases are like a blanket that hold in the Heat to keep the Earth warm http://science.howstuffworks.com/environmental/green- science/question7462.htm 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 12 Greenhouse Effect If the Greenhouse Gas concentration is too high, then not enough Energy escapes, and the Earth warms up
  • 7. If the Greenhouse Gas concentration is too low, then too much Energy escapes, and the Earth cools down http://science.howstuffworks.com/environmental/green- science/question7462.htm 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 13 Carbon Dioxide The most important Greenhouse Gas is Carbon Dioxide (CO2) It makes up only a very small percentage of the air (less than 0.1%) but has a big effect Plants remove Carbon Dioxide from the air and emit Oxygen Animals remove Oxygen from the air and emit Carbon Dioxide Normally, there is a balance between plants and animals and the levels of CO2 remain roughly constant 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 14 Carbon Dioxide CO2 is also emitted whenever Carbon compounds (like fossil fuels) are burned in the presence of Oxygen Once emitted, the CO2 stays in the air for hundreds of years The CO2 concentration in the air has been slowly building up since we began using fossil fuels
  • 8. This makes perfect sense since there is no effective mechanism for removing this CO2 from the air as we release it But is the amount of CO2 emitted due to fossil fuels really significant? 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 15 Source of Carbon Dioxide From IPCC report (2014) “Emissions of CO2 from fossil fuel combustion and industrial processes contributed about 78% of the total greenhouse gas emissions increase from 1970 to 2010.” 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 16 Source of Carbon Dioxide From IPCC report (2014) “About half of anthropogenic CO2 emissions between 1750 and 2011 have occurred in the last 40 years.” 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 17
  • 9. Summary So Far We are releasing lots of CO2 into the air Mainly due to fossil fuel use Once it is there, we would expect it to stay there So, have we actually seen CO2 levels in the air going up? 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 18 Greenhouse Gas Concentrations in the Air Carbon Dioxide (CO2) levels are up 40% since 1850 Methane (CH4) levels are up 125% Nitrous Oxide (N2O) levels are up 20% From IPCC report (2014) 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 19
  • 10. Greenhouse Gas Concentrations in the Air “Atmospheric concentrations of carbon dioxide, methane and nitrous oxide [are at levels] unprecedented in at least the last 800,000 years.” From IPCC report (2014) 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 20 Summary So Far We are releasing lots of CO2 into the air Mainly due to fossil fuel use Once it is there, we would expect it to stay there CO2 levels in the air are the highest they’ve been in about a million years Based on the Greenhouse Effect, we would expect this to affect the Temperature. Is this what we see? 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 21 Carbon Dioxide and Temperature temperature seems to track CO2 levels in the air almost exactly
  • 11. Based on what has happened in the past, global From Physics and Technology for Future Presidents 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 22 Carbon Dioxide and Temperature 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 23 This, by itself, does not necessarily prove anything, but our textbook author (skeptical that CO2 levels were so important) took the argument one step further by calculating how much the temperature would be expected to go up due to many different known reasons (CO2 as well as other ones you may have heard about from Global Warming skeptics) He found (much to his surprise) that the only things that make a noticeable difference are CO2 levels and major volcanic eruptions Carbon Dioxide and Temperature Black: Actual measurements
  • 12. Red: Calculation that assumes only CO2 and volcanoes are important http://berkeleyearth.org/summary-of-findings/ 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 24 With just these two factors, you can explain why the temperature has gone up the way it has Summary So Far We are releasing lots of CO2 into the air Mainly due to fossil fuel use Once it is there, we would expect it to stay there CO2 levels in the air are the highest they’ve been in about a million years Global Temperature is going up Global Temperature seems to always go up when CO2 levels go up This makes sense because of the Greenhouse Effect Calculations show that CO2 levels are, by far, the most important factor in determining global temperature 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 25
  • 13. “Atmospheric concentrations of carbon dioxide, methane and nitrous oxide [are at levels] unprecedented in at least the last 800,000 years. Their effects, together with those of other anthropogenic drivers […] are extremely likely to have been the dominant cause of the observed warming since the mid-20th century.” The IPCC define “Extremely Likely” as at least 95% likely. “Anthropogenic” = Caused by humans So, the IPCC estimates that it is at least 95% likely that humans are the main cause of Global Warming 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 26 Conclusion: Recent Global Warming is almost certainly caused by humans “The exquisite agreement between the warming and CO2 suggests that most—maybe all—of the warming of the past 250 years was caused by humans. That’s a remarkable conclusion for someone (me) who had been stigmatized as a skeptic by the media.” –Richard Muller in Energy for Future Presidents “I was not expecting this, but as a scientist, I feel it is my duty to let the evidence change my mind.” -Richard Muller on berkeleyearth.org Conclusion: Recent Global Warming is almost certainly caused by humans 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 27
  • 14. Chapter 10C: So What? Is Warming likely to continue? What effects is Warming likely to have? Is it that big of a deal? What would we have to do to stop it? What is the worst case scenario? 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 28 Effect of Global Warming Recall: The effect we are talking about is only about 1-2 degrees Celsius (about 2-4 degrees Fahrenheit) You may wonder what the big deal is about an increase of just a couple of degrees The bottom line: It is not the increase so far that concerns us, but the fact that (until we stop using fossil fuels completely) this effect will keep getting worse as we release more and more CO2 into the air And we will have to live with the world we’ve created for hundreds of years to come 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 29
  • 15. Effect of Global Warming If things continue along the present path, the temperature will go up about 1°F every 15 years “Just a few degrees can change fertile regions into deserts or melt ice caps.” For comparison: A 10°F change would be as severe as a major ice age! 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 30 “Continued emission of greenhouse gases will cause further warming and long-lasting changes in all components of the climate system, increasing the likelihood of severe, pervasive and irreversible impacts for people and ecosystems. Limiting climate change would require substantial, sustained reductions in greenhouse gas emissions” Effect of Global Warming 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 31
  • 16. Consequences “Surface temperature is projected to rise over the 21st century under all assessed emission scenarios. It is very likely that heat waves will occur more often and last longer, and that extreme precipitation events will become more intense and frequent in many regions. The ocean will continue to warm and acidify, and global mean sea level to rise.” 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 32 Consequences “In most scenarios without additional mitigation efforts, [there will be] substantial species extinction, global and regional food insecurity, consequential constraints on human activities and limited potential for adaptation” Mitigation Efforts = Reducing Greenhouse Gas emissions Adaptation = Our ability to deal with the warming that we get 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 33 Consequences: Extinction
  • 17. “A large fraction of species faces increased extinction risk due to climate change.” “Most plant species cannot naturally shift their geographical ranges sufficiently fast to keep up with current and high projected rates of climate change in most landscapes” Most plants and some animals simply will not be able to migrate to new habitats as fast as they are changing, and are likely to go extinct as a result. 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 34 Scenario 1: If warming is 2⁰C (4⁰F) above late 20th century levels, it will negatively impact food production Scenario 2: If warming is 4⁰C (7⁰F) above late 20th century levels, it “ would pose large risks to food security globally” “Just a few degrees can change fertile regions into deserts” Consequences: Food 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 35 Urban Areas: “ heat stress, storms and extreme precipitation, inland and coastal flooding, landslides, air pollution, drought, water scarcity, sea level rise and storm surges”
  • 18. Rural Areas: “ water availability and supply, food security, infrastructure and agricultural incomes, including shifts in the production areas of food and non-food crops around the world” Consequences: In Populated Areas 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 36 Tipping Points Even worse, it is possible (though not necessarily likely) that at some point we may cross a “tipping point” where a cataclysmic event is triggered Example: If the Antarctic Ice Sheet falls into the sea—sea level goes up by over 100 feet 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 37 Tipping Points Example: The Arctic Ocean warms, causing it to release Methane. Since Methane is a Greenhouse Gas, the Methane causes more Warming, which releases more Methane. The temperature rises out of control due to a vicious cycle “Runaway greenhouse warming is responsible for the hot
  • 19. surface conditions of Venus—900°F—on a planet that is otherwise very similar to earth” It’s very unlikely that we could see anything close to this dramatic, but it’s important to understand that the impact of Greenhouse Gases on temperature can be huge 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 38 Chapter 10D: What Can We Do? What would we have to do to halt Global Warming? What would we have to do to reverse Global Warming? Which countries are causing the problems? Developed countries like the US or developing countries like China? 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 39 Cumulative Carbon Dioxide Production 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 40
  • 20. Problem #1: It is not our present levels of CO2 emissions that matter, but the cumulative total of all CO2 emissions in history Cumulative Carbon Dioxide Production “Cumulative emissions of CO2 largely determine global mean surface warming” “Multiple lines of evidence indicate a strong, consistent, almost linear relationship between cumulative CO2 emissions and projected global temperature change to the year 2100” Note: This means that even if we stabilize our yearly CO2 output, Global Warming will keep getting worse because it depends on the sum total of all emissions in history. We have to stop putting CO2 into the atmosphere all together just to halt warming and stabilize the temperature. 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 41 Cumulative Carbon Dioxide Production 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 42 Problem #1: It is not our present levels of CO2 emissions that matter, but the cumulative total of all CO2 emissions in history Problem #2: Even after we’ve totally stopped emitting CO2, the Temperature won’t start going down. It will only stop going up.
  • 21. “Many aspects of climate change and associated impacts will continue for centuries, even if anthropogenic emissions of greenhouse gases are stopped.” “temperatures will remain approximately constant at elevated levels for many centuries after a complete cessation of net anthropogenic CO2 emissions” Cumulative Carbon Dioxide Production 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 43 Cumulative Carbon Dioxide Production 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 44 Problem #1: It is not our present levels of CO2 emissions that matter, but the cumulative total of all CO2 emissions in history Problem #2: Even after we’ve totally stopped emitting CO2, the Temperature won’t start going down. It will only stop going up. Problem #3: The temperature won’t start going down until CO2 levels go down. This takes hundreds of years to happen naturally, and we’re not very good at removing CO2 from the air ourselves.
  • 22. Can we remove the CO2 that is already in the air? Short Answer: We don’t presently have any effective ways to do this, but there are some ideas floating around. One of the most effective methods currently is to Plant trees. Let them absorb CO2 from the air. Ensure (somehow) that the carbon removed from the air does not go back into the air again later—e.g. when the trees burn or decompose One idea: Cut down the trees and burn the wood, but carefully capture all the CO2 emitted during the burning. Then (somehow) store it permanently underground Bonus: You can use the burning wood as an Energy source (using Engines—Recall Ch. 2) What Can We Do? 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 45 More realistically, the answers to Climate Change are usually categorized as Mitigation and Adaptation Mitigation: Take steps to reduce the severity of Climate Change Maybe we can’t stop it, but at least we can reduce its magnitude The main way to mitigate the disaster is to stop CO2 emissions—i.e. stop using fossil fuels
  • 23. Adaptation: Takes steps to limit our vulnerability to what happens Find ways of dealing with the problems that Climate Change creates What Can We Do? 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 46 “Without additional mitigation efforts beyond those in place today, and even with adaptation, warming by the end of the 21st century will lead to very high risk of severe, widespread and irreversible impacts globally.” “There are multiple mitigation pathways that are likely to limit warming below 2⁰C relative to pre-industrial levels. These pathways would require substantial emissions reductions over the next few decades and near zero emissions of CO2 and other long-lived greenhouse gases by the end of the century.” What Can We Do? 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 47
  • 24. “Effective mitigation will not be achieved if individual agents advance their own interests independently. Cooperative responses, including international cooperation, are therefore required to effectively mitigate greenhouse gas emissions and address other climate change issues.” “Delaying additional mitigation to 2030 will substantially increase the challenges associated with limiting warming over the 21st century” What Can We Do? 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 48 Human Energy Use Observations show that the richest countries in the world use the most Energy per person Richer = more to the right More Energy use per person = closer to top From Physics and Technology for Future Presidents 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 49 Global Emissions But developing countries account for more than half of present
  • 25. CO2 emissions from the burning of fossil fuels, because there are more people in developing countries. China’s emission are about double the US, but their population is about 4 times as large http://www.epa.gov/climatechange/ghgemissions/global.html 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 50 Global Emissions Emissions from the developing world are rising very rapidly, while those from the developed world are stable (but already high, per person) “To favor dropping carbon dioxide [levels in the air], while arguing for no restraints on the developing world is inconsistent […] Just to stabilize greenhouse emissions, the emerging economies must cut emission intensity by 8%-10% per year. That will be hard—probably impossible.” And remember: our goal is not to stabilize emissions, but to reduce them to zero 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 51 Global Emissions
  • 26. Although China has offered to start reducing their emissions per unit of GDP, their economy is growing so fast that their emissions are still expected to rise for at least anther 10 years Recall again: Our goal is not to stabilize emissions—it’s to get them down to zero Although the US has offered to decrease emissions by about 25% over the next 10 years, recall again that we are trying to get to zero. Even 25% is only a small step. Bottom line: Although it’s nice that people are starting to talk about cutting emissions, the progress has been very slow compared to IPCC goals 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 52 Greenhouse Gas Sources This chart shows where our Greenhouse Gas emissions are coming from. From this, we can deduce what some of the most pressing concerns are http://www.epa.gov/climatechange/ghgemissions/global.html 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 53
  • 27. Greenhouse Gas Sources http://www.epa.gov/climatechange/ghgemissions/global.html Switch to Clean Energy Better insulation and efficiency Use less Energy Esp. Heat/AC Switch to Clean Vehicles Long-term: Electric/Hydrogen powered by solar/wind/nuclear Short-term: Hybrids/better mpg, Natural Gas cars, Drive less Stricter environmental regulations Less consumption of animal products Stop deforestation Stricter regulations 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 54 Chapter 10E: Energy Security and Fossil Fuel Supply Are we running out of fossil fuels? Will the Global Warming problem solve itself because we have no fuels left to burn? 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 55
  • 28. Fossil Fuels One of the key sources of CO2 is the burning of fossil fuels Let us explore some of the questions surrounding the availability and use of fossil fuels Will this problem solve itself when we run out of fossil fuels? 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 56 https://s-media-cache- ak0.pinimg.com/736x/19/27/12/192712e882c33b41833ec427bf6 5724c.jpg Fossil Fuels Are we running out of Fossil Fuels? 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 57 No, definitely not. We are running out of cheap, easily extracted oil, but if the price of oil goes up it will become economical to extract and use the many vast supplies of other resources We still have vast supplies of Alternative sources of oil (underwater, oil shale, etc.) Coal (which can be turned into diesel fuel) Natural Gas (including under the ocean) Many other sources that we haven’t bothered with because they are expensive to produce
  • 29. Oil Supply We have only extracted a small fraction of the world’s oil, but (aside from OPEC’s supply), most of the remainder is difficult to extract From Physics and Technology for Future Presidents Oil we’ve used so far Oil we have left And that’s only oil! 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 58 Oil Price The high price of oil not long ago made a number of oil extraction techniques economically viable, even though they would never have been used in the 1990’s 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 59 http://inflationdata.com/articles/charts/inflation-adjusted-oil- prices-chart/
  • 30. Oil Price When the oil price goes up, other sources of Energy become viable, but (not coincidentally) OPEC ensures that the price of oil never exceeds these levels for long 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 60 http://inflationdata.com/articles/charts/inflation-adjusted-oil- prices-chart/ Fossil Fuel Comparison There are also other sources of Fossil Fuels besides oil Including coal and natural gas These also become more attractive when the price of oil goes up From Physics and Technology for Future Presidents Compare 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 61
  • 31. Fossil Fuels The good news is that the fossil fuel supply is not such a big issue as some people make it. There are plenty of fossil fuel sources left in the US and around the world. They will just cost a bit more to use. The bad news is that, even though these fossil fuels are available, we shouldn’t use them. Burning these fuels releases CO2, and we need to stop emitting CO2 immediately or the problem of Global Warming is only going to get worse Possible exception: Maybe as a short-term solution we should wean ourselves off of fossil fuels by switching to fuels that emit less CO2, such as Natural Gas 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 62 Fossil Fuels For a more in-depth discussion of many of the various Energy sources available, an excellent source is our textbook author’s other book, Energy for Future Presidents 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 63
  • 32. 63 Chapter 10 Summary Evidence of Global Warming is clear and obvious. It is almost certain that Global Warming has been caused completely or mostly by humans. This is most obvious because of the clear relationship between global temperature and CO2 concentration in the air CO2 increases the temperature because it prevents Heat Energy from escaping into outer space. This is called the Greenhouse Effect CO2 concentrations are at their highest levels in hundreds of thousands (perhaps millions) of years CO2 is released when fossil fuels are burned 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 64 64 Chapter 10 Summary The temperature is determined by cumulative CO2 emissions, so stopping Global Warming means stopping the use of fossil fuels completely
  • 33. Most Greenhouse Gas emissions come from the developing world (such as China), but the most Greenhouse Gas emissions per person come from the richest countries (such as the US) The world is not running out of fossil fuels. We are only running out of the cheap oil we have been using for the past few decades. 11/8/2016 Prof. Michael Opferman | Phys 0847 | Temple University 65 65