H A&S 220c Energy and Environment: Life Under the Pale Sun
More review problems on the science core. (Refer to your class notes or the
lectures posted on the web.) (Next Tuesday’s quiz will have an essay question
relating to the Arctic, like the examples on the earlier review problem handout, and
some short questions from the science core and the Greenland/Arctic readings, such
as those below). You will be given some choice of problems to solve, from a larger
number.
The problems marked with an asterisk (*) are not ‘short’, and not quiz problems.
But they may help if you work on them. The rest are potential quiz problems.
• Mechanical energy. If a ball is dropped from a height of 100m, what will its
velocity of fall be at the ground, assuming its total mechanical energy is conserved? After
bouncing it will not go as high as 100m; what happens to the mechanical energy that
seems to be lost?
• Describe why the thermal energy of air is much greater than its mechanical
energy in a wind-storm, with winds of 10 meter/sec.
• We pay for electricity by the kilowatt-hour (kwh). How many Joules are
equivalent to 1 kwh?
(It is helpful to write the units and cancel them to get the answer…for example if
we are given a speed of 10 miles per second and want miles per hour, XX mile/hour =
10 mile/sec x 60 seconds/minute x 60 minutes/hour = 36000 mile/hour.)
• One practical result of the discussion of chemical bonding is the ‘richness’ or
‘intensity’ of chemical energy. Many fuels and foods have energy content in the range 10
to 50 million Joules per kg. (MJ/kg). This energy content is determined usually by
burning the fuel and measuring the heat produced. How does the kinetic energy of a
metric ton of water (1000 kg) moving at 1 meter per second (m sec-1) compare with the
chemical or ‘food’ energy in a candy bar ( say 0.1 kg)?
• *Suppose someone suggests heating your home by storing the summer’s heat in
swimming pool full of water, and then circulating the warm water through radiators in
winter. How big a swimming pool would you need?
• CO2 pollution of the atmosphere comes from burning of fossil fuels. Describe
the differing amounts of CO2 that result from gasoline (octane) and methane (natural
gas), by comparing the ratio of carbon to hydrogen atoms in each substance. Generally,
what is the approximate ratio of C to H atoms in long hydrocarbon molecules? (Further
work: compare also with coal and wood combustion.)
• Why does ice float, in terms of its molecular structure, whereas most substances
are more dense in the solid phase than the liquid phase?
• What force is the origin of chemical bonds, which hold atoms together to form
molecules? What are the main factors that decide whether a bond is strong or weak?
• If you pass an electric current through a beaker of water, bubbles of gas appear.
What chemical bonds are being broken to make this happen, and how what is the makeup
of that gas?
• Jupiter is 484 million miles..779 million km.. from the sun or 5.2 times the
Earth’s distance from the sun. What is the ratio of the energy flow (power) of solar
radiation arriving at Jupiter, compared with the Earth?
• What is the Arctic Circle?
• Solar energy reaching the Earth varies in intensity (power) due to several
astronomical effects (the simplest being the rotation of the Earth). Describe some other of
these effects.
• *[Done in class] We would like to find a quick way to estimate the efficiency of
an automobile engine. [The efficiency of a heat engine like the Stirling engine is defined
as the ratio of useful work it does to the rate of heat flow that drives it. Since total energy
is conserved, the incoming heat is divided into work plus outgoing (‘exhaust’) heat flow.
We are told that automobiles are something like 20% efficient in converting the heat of
burning gasoline into kinetic energy of the car]
You could measure this by the following simple test: drive on a level road at 50 mph
(22 meters/sec); take your foot off the throttle and coast to a stop. The ratio of the
kinetic energy of the car at speed, to the time it takes to slow to a stop, is a power, that is
energy divided by time. When the car is moving steadily, the engine power goes into
fighting the air drag and the friction forces within the car’s drive train. When you take
your foot off, those forces are unopposed and bring the car to a stop. So, measuring the
time it takes to stop gives us an estimate of those forces.
Suppose you do this. The car weighs 2000 kg, and it takes 30 sec to slow to 25
mph, ½ its initial speed. What is the force implied by this deceleration? What is the
change in energy divided by the change in time? If this force is close to the force
required to keep the car going at 50 mph, this gives an estimate of the power in watts
(and hence estimate as the power required to drive steadily at 50 mph. What would this
be in horsepower (1 h.p. = 747 watts)? If we get 20 miles per gallon, what is the
efficiency of the car?
•* Steady-state box models. Tetrachloroethylene is an organic solvent used in
dry cleaning. It gets into ground water which people drink. Government standards
suggest that anything greater than about 1 part per million is dangerous. Suppose a dry
cleaning company dumps 100 kg per year into the ground. A ground water stream is
flowing by at a speed V of 10 meters per day, and it has a cross-sectional area A of 100
square meters. What will the concentration of the pollutant be on average? [assume the
solvent is uniformly mixed across the underground stream and flows with it…is this
likely a good assumption?] . Note that the rate of flow of water is ρVA kg/sec where ρ =
103 kg m-3 is the density of water. [A useful number here is the number of seconds in a
year which is π x 107, to within one percent].
• *If the Greenland ice cap melted, how much would sea level rise around the
world, on average (Greenland is about 2000 km x 500 km in area and the ice cap is 3 km
high at its peak)
How much heat would it take to melt this much ice (in Joules)?
If the melting occurred over 1000 years, how much heat flow would this represent
(in Watts)? Compare this number with the average heat flow in the ocean-atmosphere
system which is 5 x 1015 watts … 5 petawatts.
• Why does a mist of very fine droplets (at room temperature) feel cool when it
lands on your forehead?
• Describe the shape of the water molecule, and some the effects of that shape on
the properties of water.
• * From the website: The point here is to begin to work with the large numbers
of energy consumption round the world.
Election day: what does it mean to energy and environment? There are strong
opinions from all sides. And abrupt change is everywhere ($50-55 per barrel of oil today,
as little as $12 per barrel in 1998, $28 per barrel one year ago) Energy independence?
The USA uses about 1/4 of the world's energy resources. Oil is the largest part of our
energy profile, currently 20 million barrels per day, half of that imported.
In studying the Arctic environment this pall of global fuel consumption hangs over us: we
will see how ocean and atmosphere react to human energetics during the remainder of the
term. The Arctic is melting, ecosystems shifting, but its behavior is not simple. With US
oil production declining, how do we manage the near future? In the end we will see that
climate change and the dynamics of human activity are tightly linked. Our response to the
problem will have implications to every aspect of life, and especially to our relations with
the rest of the world.
[let's do the numbers: one barrel of oil is 42 gallons, that is 159 liters. It has 6 x 10^9 Joules (6 billion J) of
chemical energy. Dividing by 42, one gallon of oil has 1.4 x 10^8 Joules...like 140 candy bars. The more
common unit is Joules per kg.of fuel, which for crude oil is about 4.5 x 10^7 Joules/kg; quite similar to
many other fuels, except hydrogen which is the clear winner (see figure below). Gauge this against your
daily activity: 20 million barrels per day divided by 295M US citizens is .067 barrels per person each day,
or 2.8 gallons of oil per person per day. And..only 19.5 gallons of gasoline can be refined from the 42
gallons of oil in a barrel. How do you imagine the energy use per person compares with other countries,
and with Greenland? ]