The objective of this exercise is to predict what impact the (defunct) federal coal liquefaction program would have had on the fuel utilization pattern.
According to the first in, first out rule, the "free" variable, that is, the one that does not follow the market penetration rule, is the natural gas consumption fraction, fng. The questions are:
- In what year will fng peak?
- What is the maximum value of fng ?
Assume that fsyn (the fraction of the market supplied by synthetic fuel) is 0.01 in 1990 and 0.0625 in 2000. Please comment.
1.2 The annual growth rate of energy utilization in the world was 3.5% per year in the period between 1950 and 1973. How long would it take to consume all available resources if the consumption growth rate of 3.5% per year is maintained?
Assume that the global energy resources at the moment are sufficient to sustain, at the current utilization rate, a. 1000 years b. 10,000 years
1.3 A car moves on a flat horizontal road with a steady velocity of 80 km/h. It consumes gasoline at a rate of 0.1 liter per km. Friction of the tires on the road and bearing losses are proportional to the velocity and, at 80 km/h, introduce a drag of 222 N. Aerodynamic drag is proportional to the square of the velocity with a coefficient of proportionality of 0.99 when the force is measured in N and the velocity in m/s.
What is the efficiency of fuel utilization? Assuming that the efficiency is constant, what is the "kilometrage" (i.e., the number of kilometers per liter of fuel) if the car is driven at 50 km/h?
The density of gasoline is 800 kg per cubic meter, and its heat of combustion is 49 MJ per kg.
1.4 Venus is too hot in part because it is at only 0.7 AU from the sun. Consider moving it to about 0.95 AU. One AU is the distance between the Earth and sun and is equal to 150 million km.
To accomplish this feat, you have access to a rocket system that converts mass into energy with 100% efficiency. Assume that all the energy of the rocket goes into pushing Venus. What fraction of the mass of the planet would be used up in the project? Remember that you are changing both kinetic and potential energy of the planet.
1.5 Consider the following arrangement:
A bay with a narrow inlet is dammed up so as to separate it from the sea, forming a lake. Solar energy evaporates the water, causing the level inside the bay to be h meters lower than that of the sea.
A pipeline admits sea water in just the right amount to compensate for the evaporation, thus keeping h constant (on the average). The inflow water drives a turbine coupled to an electric generator. Turbine plus generator have an efficiency of 95%.
Assume that there is heat loss neither by conduction nor by radiation. The albedo of the lake is 20% (20% of the incident radiation is reflected, the rest is absorbed). The heat of vaporization of water (at STP) is 40.6 MJ per kilomole. Average solar radiation is 250 W/square meter.
If the area of the lake is 100 km2 , what is the mean electric power generated? What is the efficiency? Express these results in terms of h.
Is there a limit to the efficiency? Explain.
1.6 The thermonuclear (fusion) reaction,
151B + 1h ^ 3|He, is attractive because it produces essentially no radiation and uses only common isotopes.
How much energy does 1 kg of boron produce? Use the data of Problem 1.11.
1.7 The efficiency of the photosynthesis process is said to be below 1% (assume 1%). Assume also that, in terms of energy, 10% of the biomass produced is usable as food. Considering a population of 6 billion people, what percentage of the land area of this planet must be planted to feed these people.
1.8 Each fission of 235U yields, on average, 165 MeV and 2.5 neutrons. What is the mass of the fission products?
1.9 There are good reasons to believe that in early times, the Earth's atmosphere contained no free oxygen.
Assume that all the oxygen in the Earth's atmosphere is of pho-tosynthetic origin and that all oxygen produced by photosynthesis is in the atmosphere. How much fossil carbon must there be in the ground (provided no methane has evaporated)? Compare with the amount contained in the estimated reserves of fossil fuels. Discuss the results.
1.10 What is the total mass of carbon in the atmosphere?
CO2 concentration is currently 330 ppm but is growing rapidly!
If all the fossil fuel in the estimated reserves (see Section 1.8) is burned, what will be the concentration of CO2
1.11 Here are some pertinent data:
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