1.14 The California Air Resources Board (CARB) mandated, for 1995, an upper limit of 200 g/km for the emission of CO2 from a minivan.
This could be achieved by bubbling the exhaust through a Ca(OH)2 bath or through a similar CO2 sequestering substance. However, this solution does not seem economical. Assume that all the produced CO2 is released into the atmosphere.
What is the minimum mileage (miles/gallon) that a minivan had to have by 1995. Assume gasoline is pentane (C5H12) which has a density of 626 kg m~3. A gallon is 3.75 liters and a mile is 1609 meters. The atomic mass of H is 1, of C is 12, and of O is 16.
1.15 A geological survey revealed that the rocks in a region of northern California reach a temperature of 600 C at a certain depth. To exploit this geothermal source, a shaft was drilled to the necessary depth, and a spherical cave with 10-m diameter was excavated. Water at 30 C is injected into the cave where it reaches the temperature of 200 C (still in liquid form, owing to the pressure) before being withdrawn to run a steam turbine.
Assume that the flow of water keeps the cave walls at a uniform 200 C. Furthermore, assume that, at 100 m from the cave wall, the rocks are at their 600 C temperature. Knowing that the heat conductivity, A, of the rocks is 2W m-1K-1, what is the flow rate of the water?
The heat capacity of water is 4.2 MJ m-3K-1, and the heat power flux (W m-2) is equal to the product of the heat conductivity times the temperature gradient.
1.16 The following data are generally known to most people:
a. The solar constant, C (the solar power density), at Earth's orbit is 1360 W m-2.
b. The astronomical unit (AU, the average sun-Earth distance) is about 150 million km.
c. The angular diameter of the moon is 0.5°.
Assume that the sun radiates as a black body. From these data, estimate the sun's temperature.
1.17 Using the results from Problem 1.16, compare the sun's volumetric power density (the number of watts generated per m3) with that of a typical Homo sapiens.
1.18 Pollutant emission is becoming progressively the limiting consideration in the use of automobiles. When assessing the amount of pollution, it is important take into account not only the emissions from the vehicle but also those resulting from the fuel production processes. Gasoline is a particularly worrisome example. Hydrocarbon emission at the refinery is some 4.5 times larger than that from the car itself. Fuel cell cars (see Chapter 9) when fueled by pure hydrogen are strictly a zero emission vehicle. However, one must inquire how much pollution results from the production of the hydrogen. This depends on what production method is used (see Chapter 10). The cheapest hydrogen comes from reforming fossil fuels, and that generates a fair amount of pollution. A clean way of producing hydrogen is through the electrolysis of water; but, then, one must check how much pollution was created by the generation of the electricity. Again, this depends on how the electricity was obtained: if from a fossil fuel steam plant, the pollution is substantial; if from hydroelectric plants, the pollution is zero.
The technical means to build and operate a true zero emission vehicle are on hand. This could be done immediately but would, at the present stage of the technology result in unacceptably high costs.
Let us forget the economics and sketch out roughly one possible ZEV combination. Consider a fuel cell car using pure hydrogen
(stored, for instance, in the form of a hydride—Chapter 11). The hydrogen is produced by the electrolysis of water, and the energy required for this is obtained from solar cells (Chapter 14). Absolutely no pollution is produced. The system is to be dimensioned so that each individual household is independent. In other words, the solar cells are to be installed on the roof of each home.
Assume that the car is to be driven an average of 1°°° miles per month and that its gasoline-driven equivalent can drive 3° miles/gallon. The fuel cell version, being much more efficient, will drive three times farther using the same energy as the gasoline car. How many kilograms of hydrogen have to be produced per day? How large an area must the solar cell collector have? You must make reasonable assumptions about the solar cell efficiency, the efficiency of the electrolyzer, and the amount of insolation (Chapter 12). 1.19 From a fictitious newspaper story:
A solar power plant in the Mojave Desert uses 1000 photovoltaic panels, each "40 meters square." During the summer, when days are invariably clear, the monthly sale of electricity amounts to $22,000. The average price charged is 3 cents per kWh. The plant is able to sell all the electricity produced.
There is an unfortunate ambiguity in the story: "4° meters square" can be interpreted as a square with 4° meters to its side or as an area of 4° m2.
From the data in the story, you must decide which is the correct area.
1.2° Sport physiologists have a simple rule of thumb: Any healthy person uses about 1 kilocalorie per kilometer per kilogram of body weight when running.
It is interesting to note that this is true independently of how well trained the runner is. A trained athlete will cover 1 km in much less time than an occasional runner but will use about the same amount of energy. Of course, the trained athlete uses much more power.
The overall efficiency of the human body in transforming food intake into mechanical energy is a (surprisingly high) 25%!
A good athlete can run 1 (statute) mile in something like 4 minutes and run the Marathon (42.8 km) in a little over 2 hours.
1. Calculate the power developed in these races. Repeat for a poor performer who runs a mile in 8 minutes and the Marathon in 5 hours. Assume a body weight of 7° kg.
2. Evaporation of sweat is the dominant heat removal mechanism in a human body. Is this also true for a dog? for a horse?
3. Assuming that all the sweat evaporates (i.e., none of it drips off the body), how much water is lost by the runners in one hour. The latent heat of vaporization of water is 44.1 MJ/kmole.
1.21 One major ecological concern is the emission of hothouse gases, the main one being CO2.
A number of measures can be taken to alleviate the situation. For instance, the use of biomass-derived fuels does not increase the carbon dioxide content of the atmosphere.
Fossil fuels, on the other hand are a major culprit. Suppose you have the option of using natural gas or coal to fire a steam turbine to generate electricity. Natural gas is essentially methane, CH4, while coal can be taken (for the purposes of this problem only) as eicosane, C20H42. The higher heat of combustion of methane is 55.6 MJ/kg, and that of eicosane is 47.2 MJ/kg.
For equal amounts of generated heat, which of the two fuels is preferable from the CO2 emission point of view? What is the ratio of the two emission rates?
1.22 A planet has a density of 2500 kg/m3 and a radius of 4000 km. Its "air" consists of 30% ammonia, 50% carbon dioxide, and 20% nitrogen.
Note that the density, Searth, of Earth is 5519 kg/m3.
What is the acceleration of gravity on the surface of the planet?
1.23 At 100 million km from a star, the light power density is 2 kW/m2. How much is the total insolation on the planet of Problem 1.22 if it is 200 million km from the star. The total insolation on Earth is 173,000 TW.
1.24 3He can be used as fuel in "dream" fusion reactions—that is, in reactions that involve neither radioactive materials nor neutrons. Two possible reactions are
1. For each of the above reactions, calculate the energy (in kWh) released by 1 kg of 3He.
On Earth, 2He represents 0.00013% of the naturally occurring helium. The U.S. helium production amounts, at present, to 12, 000 tons per year.
2. If all this helium were processed to separate the helium-three, what would be the yearly production of this fuel?
There are reasons to believe that the moon has a substantial amount of 2He3. Let us do a preliminary analysis of the economics of setting up a mining operation on our satellite.
One advantage of using "dream" reactions is that only charged particles (protons and alphas) are produced. The energy associated with charged particles can be more efficiently transformed into electricity than when the energy is carried by neutrons, which must first produce heat that is then upgraded to mechanical and electric energy by inefficient heat engines. Thus, it is not necessarily optimistic to assign a 30% efficiency for the conversion of fusion energy into electricity.
3. How many kWh of electricity does 1 kg of 23He produce? Use the most economical of the two reactions mentioned.
Assume that the plant factor is 70% (the reactor delivers, on average, 70% of the energy it would deliver if running constantly at full power). Assume further that the cost of the fusion reactor is $2000/kW and that the cost of borrowing money is 10% per year. Finally, the cost of running the whole operation is $30 kW^year"1.
4. How much would the electricity cost (per kWh) if the fuel were free?
5. How much can we afford to pay for 1 kg of 3He and still break even when electricity is sold at 5 cents per kWh?
1.25 Between 1955 and 1995, the ocean temperature (Atlantic, Pacific, and Indian) increased by 0.06 C.
Estimate how much energy was added to the water.
What percentage of the solar energy incident on Earth during these 40 years was actually retained by the ocean?
1.26 It seems possible that climate changes will cause the polar ice caps to melt. The amount of ice in Antarctica is so large that if it were to melt, it would submerge all ports such as New York and Los Angeles.
Estimate by how much the sea level would rise if only the north pole ice is melted, leaving Greenland and Antarctica untouched.
1.27 Refueling a modern ICV with 50 liters of gasoline may take, say, 5 minutes. A certain amount of energy was transferred from the pump to the car in a given time. What is the power represented by this transfer? Assume that the overall efficiency of a gasoline car is 15% and that of an electric car is 60%. How much power is necessary to charge the batteries of the electric car in 5 minutes (as in the ICV case)? Assume that the final drive train energy is the same in both the ICV and the EV. Is it practical to recharge a car as fast as refueling one?
1.28 Some of the more attractive fuels happen to be gases. This is particularly true of hydrogen. Thus, storage of gases (Chapter 11) becomes an important topic in energy engineering. Lawrence Livermore Labs, for instance, has proposed glass micro-balloons, originally developed for housing minute amounts of tritium-deuterium alloy for laser fusion experiments. When heated, the glass becomes porous and hydrogen under pressure can fill the balloons. Cooled, the gas is trapped.
Clathrate is one of nature's ways of storing methane, even though no one is proposing it as a practical method for transporting the gas.
Methane clathrate frequently consists of cages of 46 H2O trapping 8 CH4 molecules.
1. What is the gravimetric concentration, GC, of methane in the clathrate? Gravimetric concentration is the ratio of the mass of the stored gas to the total mass of gas plus container.
Consider a hermetic container with 1 m3 internal volume filled completely with the clathrate described, which has a density of 900 kg/m3. Assume that by raising the temperature to 298 K, the material will melt and methane will evolve. Assume also (although this is not true) that methane is insoluble in water.
2. What is the pressure of the methane in the container?
1.29 A Radioisotope Thermal Generator (RTG) is to deliver 500 W of dc power to a load at 30 V. The generator efficiency (the ratio of the dc power out to the heat power in) is 12.6%. The thermoelectric generator takes heat in at 1200 K and rejects it at 450 K. The heat source is plutonium-241. This radioactive isotope has a half-life of 13.2 years and decays emitting a and ¡3- particles. These particles have an aggregate energy of 5.165 MeV.
Only 85% of the power generated by the plutonium finds its way to the thermoelectric generator. The rest is lost.
How many kilograms of plutonium are required? Note that radioactive substances decay at a rate proportional to the amount of undecayed substance and to a constant decay rate, A:
1.30 In the United States we burn (very roughly) an average of 150 GW of coal, 40 GW of oil, and 70 GW of natural gas.
Coal is (say) C20H44 and that it yields 40 MJ per kg.
Oil is (say) C10H22 and yields 45 MJ per kg.
How many kg of carbon are released daily by the combustion of coal alone? (Clearly, after you have handled coal, the other two fuels can be handled the same way. But, for the sake of time, don't do it.)
1.31 The photovoltaic plant at Serpa (southeast Portugal) has a peak output of 11 MW. Since the collectors track the sun, the power output is steady (at 11 MW) from 09:00 to 15:00, independently of the date. Assume the power output is zero outside this time interval. (Note that this is not actually true: the output ramps up in the morning before 09:00 and down in the evening, after 15:00.)
Serpa is notorious for its sunny climate. The average insolation for a surface facing the sun over the 09:00 to 15:00 period (and then averaged over the year) is 900 W/m2.
The lifetime of the system is 25 years. Yearly operating cost is US$1 million. Total capital investment is US$78 million. Cost of capital is 10% per year for the 25 years of the plant's life. The average efficiency of the collectors and distribution system is 15%. Of the generated electricity, 90% is delivered to the customers.
a. If the solar plant did not exist, the electric power would have to be generated by an oil-fired steam turbine with 30% efficiency. Oil has a heat of combustion of, say, 40 MJ/kg, and, for the purpose of this problem can be considered pure C-2H26. How many tons of CO2 would such a plant emit per year? Assume sunny days throughout the year.
b. What is the cost of the electricity generated by the photovoltaic plant ($/kWhr)? This includes the 10% of the electricity consumed in house, that is, not delivered to the customers. Compare with typical costs for nuclear and gas-fired turbines. What is the per kilowatt capital cost and the utilization factor of this photoelectric system? Compare with a thermal plant that costs around $1000/kW.
c. What is the capital cost of the square meter of solar collector? Include all the capital cost, not only that of the collectors.
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