C Selected Answers

Numerical answers are given as ranges or other hints, meant to facilitate checking for gross departures from the right track, without revealing the precise answer so that shortcuts are discouraged. Questions for which the answer is already known (questions asking to verify an answer), easily validated in the text, or that are a matter of original thought or opinion may not be included here. The ranges sometimes may be annoyingly large, but think of them as guard rails to prevent a tragic miscalculation or to catch a fundamental misunderstanding of the underlying concepts. It can help catch errors like dividing the wrong things or swapping numerator and denominator, or multiplying when division is called for. In many cases, intuition, or guessing, might lead you already to similar answers or ranges. With practice, students may be able to anticipate what they think are reasonable ranges for answers. In fact, it is a great practice to think about expectations before working on the problem. This appendix, then, might be thought of as an “intuition implant” that simulates how problems are for experts. Real life does not provide “answers at the back of the book,” so experts rely on experience, intuition, and a sense for “reasonable” results to help them understand when they’ve taken a wrong turn. A successful use of this appendix would help train students to develop their own “common sense” guard rails. Chapter 1 20. A smidge higher then boiling 4. Between 250 and 300 years 5. Between 250 and 300 years 6. Between 1018 and 1020 7. Between 100 and 150 8. More than 1040 9. Between 5 and 500 10. Later than 23:50 11. Before 12:10 AM 12. Between 10 and 40 years 14. Between 75 and 100 years 15. Between 300 and 500 billion 16. It’s not 100 times longer 17. A few millennia 19. Between 50 and 100 W 21. Between 200 and 250 K 22. Between 150 and 250 K 23. Between 100 and 275 K Chapter 2

  1. Nearly $100 billion
  2. 4%: $1 trillion; 5%: more than $100 trillion
  3. On the low end of advanced countries
  4. Between 25 and 100 MJ/$
  5. Between 5% and 50%
  6. The text had trading art, singing lessons, therapy, and financial planning
  7. Between 100 and 1,000; Less than 10 to go
  8. Between 20 and 100 years
  9. May help to think of something once prevalent, now rare
  10. Especially fruitful might be biological dependencies
  11. It can’t all be free of material substance Chapter 3
  12. Less than a third
  13. Comparable to U.S. population today
  14. Comparable to world population 200 years ago
  15. Table 3.2 offers a rough check
  16. Over 16 billion; less than half the time we now experience
  17. Pretty close to Table 3.2 except for first two entries
  18. Answer must be less than 14 billion; whereas Problem 6 was in excess of 15 billion
  19. Two are negative; three are positive
  20. Between 1 and 5%
  21. Add almost a half million; more than half million born; less than half million died
  22. Answers should round to the table val- ues
  23. Only one country in the table creates more total demand, and only two have higher percitizen contributions
  24. Correct results are in the table
  25. See Figure 3.15
  26. This is why Africa gets attention, while North America is perhaps a greater concern.
  27. It nearly triples
  28. Area is key
  29. Lesotho is relevant Chapter 4 C Selected Answers 384
  30. Earth: smaller than peppercorn and basketball-court distant; Moon: sand grain a hand’s width away
  31. Comparable to the actual Earth radius
  32. 1 AU = 1 km; Earth 1/12,000 km
  33. A fast walk or slow jog
  34. Think about the subtended angle
  35. Multiply sets to get accumulated scale fac- tors
  36. A good deal farther than the moon, but still well short of the sun/Mars
  37. Ratio is more than a billion, and would take more than 4 lifetimes
  38. Think in terms of area as fraction of plot space
  39. Text has climbing Mt. Everest, supersonic commercial flight, squirrel obstacle course, and economic decoupling
  40. Will take 15-20 tanks of gas, and achieve a fuel economy a factor of 30 or so below typical cars
  41. Double the gasoline from previous problem; gasoline mass almost as much as the car itself

C Selected Answers 385 Chapter 5

  1. Several inches
  2. About the length of a typical room
  3. A few kJ total, most in sliding
  4. You’ve got this
  5. Nearly 1 GJ
  6. Two of the points in Example 5.2.1 offer guidance
  7. Figure 5.1 offers hints
  8. Roughly half human metabolic power
  9. Less than 5 seconds
  10. Between 50-100 kcal (200-400 kJ)
  11. Sensibly, a little less than 2 minutes
  12. Results should be roughly consistent with Figure 5.2
  13. A bit less than 10% of household electricity
  14. They’re actually close, within 10%
  15. More than two
  16. Several kWh; less than $1
  17. On the low end of the human metabolism range; the equivalent cost of 10-20 burritos
  18. A few hundred W
  19. Comparable to running a clothes dryer (Fig. 5.2)
  20. Several hundred MJ
  21. Over 100 kWh; 2-4 burritos-worth
  22. Several Therms; cost of fast-food lunch
  23. Several gallons; cost of fast-food lunch for two
  24. One is about twice the other
  25. A little in excess of 10 kW
  26. Less than a quarter of estimated
  27. Between 1 and 2 hours per day
  28. The largest number is near 108
  29. Six of the entries are inverses of six others
  30. A little over an Amp
  31. Nearly 10 kW; will cost over $1,000; don’t do this!
  32. Will last 2-3 hours
  33. In line with most chemical reactions, in the 50-200 kJ/mol range
  34. Between 3-5x\(10^{-19}\) J per photon; get more than 1018/sec
  35. In the neighborhood of 1 μm or 1 eV Chapter 6
  36. Approx. 200 kJ, depending on mass
  37. Several minutes
  38. Several minutes
  39. About 5 minutes
  40. A few hours
  41. Not below freezing
  42. Not quite up to “room” temperature
  43. Not quite half the time
  44. The cost of two burritos per day
  45. Instances of heat/flame causing move- ment
  46. See Table 6.2
  47. Roughly 30 kJ and 100 J/K
  48. Between 5-10%
  49. A couple dozen percent, roughly
  50. Pushing 100%, but not quite there
  51. Achieves about 1/3 of theoretical
  52. AT 50°C; environment not that cold
  53. Close to a dozen kJ

C Selected Answers 386 19. Twice, twice 20. Just short of 5 years Chapter 7

  1. a) between 30-40%; b) almost all; c) close to 2/3; d) roughly a quarter
  2. Coal is near 12 qBtu, for instance
  3. Nuclear is about 22%, for instance
  4. Residential is about 5 qBtu, for instance
  5. Industry is a little over 30%, for instance
  6. About 14% is renewable, for instance
  7. Less than 10%
  8. Between 5 and 10%
  9. It is one of the fossil fuels
  10. Well over 100 years
  11. Surprisingly soon: maybe before student loans paid off
  12. Nothing to see here
  13. Nothing to see here
  14. Pay attention to the dashed line
  15. Pay attention to the dashed line
  16. Roughly one-third
  17. 2 H per C plus 2 more
  18. In the neighborhood of 20 bbl/yr
  19. Should be appropriate fraction of 10,000 W total
  20. A little over 100 MJ and a few dozen kWh
  21. Sum to about 15 kg, which would fill a refrigerator shelf in the water-bottle equivalent.
  22. drinking glass
  23. A few dozen times more volume, and about 102 in mass

  24. 1,000x more expensive

  25. Will cost nearly $1,000
  26. Between \(10^{-15}\)%
  27. Approximately half-century
  28. Roughly a third
  29. If the rate of production increases…
  30. What have you wanted that was all gone?
  31. Shorter than R/P suggests
  32. Opposite of virtual
  33. Can’t have what’s not there Chapter 8
  34. All lines overlap the up-slope
  35. Likely vs. hopeful?
  36. Many features unchanged
  37. Won’t be zero into future
  38. What enabled, then disappeared?
  39. Opposite of ideal
  40. Did not behave like U.S.
  41. Based on energy density
  42. Reasons could fill a book

C Selected Answers 387 Chapter 9

  1. A single integer works okay for all three
  2. Nearly 100 kg
  3. Between \(10^{-15}\) kg
  4. Approaching 1 GJ, and human-mass scale
  5. Total is like small adult or large child
  6. More than a factor of two
  7. Get about 50 years; rate not constant
  8. The numbers basically match
  9. Between 1-2 ppm,, in agreement with Fig- ure 9.3
  10. What is it we know?
  11. Seems deserving of high marks
  12. Historical vs. current activity levels
  13. About 10°C cooler than actual
  14. Two pure cases and one partial
  15. Several degrees warmer
  16. Very good for us at the right level
  17. Numbers are not far from realistic
  18. Triple pre-industrial and almost 5°C
  19. End ~3°C high; almost linear, but not quite
  20. No need to balance: Nature doesn’t bother
  21. It’s no game-changer
  22. Student’s choice
  23. E.g., 390 152238 for a match
  24. Use 290.6 K; looks like continuation of panel progression
  25. A few millimeters
  26. A little over a century
  27. A year or two
  28. A couple of degrees
  29. Sum to about 700 years; almost all in ice and ocean
  30. A few hundred meters
  31. A finger’s breadth per year
  32. Keen to hear your thoughts
  33. Keen to hear your thoughts Chapter 10
  34. Mostly clean; not all, though
  35. Nothing is free
  36. What would unlimited mean?
  37. Table 10.2 has some help
  38. Can’t rely on any sun-driven energy
  39. Between 200-250 \(W/m^2\)
  40. Photosynthesis supports essentially all life
  41. Comparing numbers in TW
  42. More than half
  43. A little less than 1%
  44. Not far from 1,000 \(W/m^2\)
  45. Nearly 10 degrees
  46. Look for crazy-big input
  47. Between 0.5-1 gallon
  48. More than 4,000x

C Selected Answers 388 Chapter 11

  1. Roughly 20 kJ
  2. About 10 stories of a building
  3. Close to 0.1 kJ
  4. About 4 times higher than airliners travel
  5. About two-thirds Earth radius
  6. Try using half the mass and half the en- ergy
  7. Cube is roughly as big as height from ground
  8. About 6 times typical nuclear plant
  9. Nearly 200 m
  10. A little shy of 500 m3/s
  11. Between 50-75%
  12. Roughly 50%
  13. About a million homes
  14. Approaching 10,000 cubic meters per second
  15. You’ve got a little over an hour
  16. Less than 1 TW in the end
  17. Between 1-2 meters
  18. Runs approximately 10 kW to 1 MW
  19. Roughly two-thirds the original speed
  20. Close to 10 MW
  21. Closer to 10 m/s than to 15 m/s
  22. Almost double freeway speeds
  23. Between 5-10 m/s
  24. In the ballpark of 70 kW
  25. Recover 0.65%
  26. Unpack \(W/m^2\) to confirm kg/s3
  27. Outer box area corresponds to running at 100%, full time
  28. Definitely less than 50%
  29. Looks like a factor of 8
  30. Approaching (American) football field length
  31. Approximately 1 MW
  32. They may not have equivalent energy needs Chapter 12
  33. A few Joules
  34. Roughly 1°C
  35. Something like 10 m/s
  36. Mass shows up in both mgh and mv2
  37. In the neighborhood of 1,500 m/s
  38. About 5-10 humans-worth of mass!
  39. Comparable to the height of Mt. Everest
  40. Around about 8 times
  41. Follow the cube…

C Selected Answers 389 Chapter 13

  1. How big are the packages?
  2. Something times \(10^{21}\)
  3. Roughly \(10^{16}\)
  4. About 1,000
  5. About 4,000 times
  6. Use Eq. 13.3 to guide your reasoning
  7. Should match Figure 13.1
  8. One micron for each finger?
  9. Think about spill-over into UV and/or IR
  10. Peak around 2.5 x 108, about 1 μm wide; matches up well
  11. Think energetics and depth
  12. Is the answer transparent?
  13. Just comparing two energies
  14. Several hundred km/s
  15. Condense the saga to that of a winner
  16. Answer might involve physics, biology, rooftops
  17. Inversely: larger in one means smaller in the other
  18. Already extremely similar
  19. Think of current as a rate of electron flow in the circuit
  20. Get very close to 1,360 \(W/m^2\)
  21. Sweltering is not preferred
  22. Between 5-6 kWh/m2/day; between 200250 \(W/m^2\)
  23. Involves interpreting kWh/m2/day as full- sun-hours
  24. Not far from 200 \(W/m^2\)
  25. Range straddles 200 \(W/m^2\), varying about 10%
  26. Best at latitude; almost 15% better than flat
  27. Approaches 6 kWh/m2/day
  28. Large house (and just the PV for one person)
  29. Square is about as wide as Arizona or California east-to-west
  30. Cost, surely-but other challenges and mismatches as well
  31. A little over 200 W
  32. Roughly the size of a bedroom
  33. Will spend a little over $4,000
  34. A little over a decade
  35. Even lower than ~20% from insolation vs. overhead
  36. About $2-worth of sun
  37. Hint: study Figures 13.23 and 13.24
  38. In absolute terms… Chapter 14
  39. About a dozen tons of CO2
  40. Between 0.1-0.5%
  41. Almost 100 logs per person per year
  42. In the neighborhood of half-dozen logs per day
  43. Won’t be exactly 15 years, but close
  44. Almost 1.5 L of ethanol
  45. Roughly consistent with Table 14.1 for coal
  46. Net is one-third production
  47. Extra land is twice the yield-land
  48. A bit longer than a U.S. Presidential term
  49. Nothing to spare
  50. Corn now approximately 15% as much as this; still more than total arable land

C Selected Answers 390 13. Box barely fits north-south in U.S. 14. Personal preferences play a role Chapter 15

  1. A blueberry
  2. N = 8
  3. Use Z = 26 to get there
  4. Should match quite well
  5. Two diagonals have no gray squares
  6. One has a half-life longer than a million years
  7. Roughly twice as old as agriculture
  8. Between 1-2%
  9. One is about 3% of the other (both decay)
  10. Step right
  11. That last step might take a while
  12. Two decays do it
  13. Sand does the job
  14. Somewhere between a car and a bus?
  15. Close to 1 kg
  16. Around a couple-dozen micrograms
  17. Table should match
  18. Energy has a mass, via E = mc2
  19. Adds about 1% to the mass
  20. Not far from 1,500 MeV
  21. Not much
  22. Figure 15.14 is relevant
  23. It’s a strontium isotope
  24. A is twice a prime number
  25. Stick to 80 < A < 110 and 125 < A < 155 to respect distributions
  26. Mid-20s of MeV
  27. From steam onwards, it’s basically the same
  28. Between 3 and 5 cents per kWh
  29. A few per week!
  30. Around 20 tons per year (more in reality)
  31. Almost 2 million tons
  32. A few hundred tons
  33. Less than a decade
  34. Two stand out
  35. Centuries
  36. More often than once every two years
  37. A nearly exact match!
  38. Worked out in text: no calculation necessary just interpretation
  39. Energy jump size
  40. Like a milk jug Chapter 16
  41. Shortfall is more than a factor of 200
  42. A bit farther than the record
  43. About as thick as a six-story building is tall
  44. Ranges about 55-85%
  45. Geothermal is a bit less than 1% of alternative electricity
  46. A little shy of the 8 m design height, sensibly
  47. Works out
  48. Diameter like a small house’s footprint
  49. Comparable to human metabolism; 1% of American demand
  50. A little more than 6 times that in Example 16.4.1 C Selected Answers 391 Chapter 17
  51. Algae who?
  52. Two words almost say it all
  53. Fine if it is a little shy: transfer rates vary
  54. Think about what a house can access, and steam plants
  55. May be up there with solar (4 to 6, likely) Chapter 18
  56. 16 equal portions
  57. Predicts largest well; not too far on small- est
  58. Gaping disparities on opposite poles is no random fluke
  59. Brilliant future if you can figure out effective ways
  60. How else will change happen? (but elaborate…)
  61. Will contribute 2-3% of the annual total
  62. A bit over half the global energy budget!
  63. Two approaches: cynical or hopeful; make either pitch
  64. In the hundreds
  65. I was hoping you had some ideas Chapter 19
  66. Still could be a parasite, even if larger than a flea
  67. Easier to break than make
  68. What things are dependent on growth to operate normally?
  69. What limits?
  70. Does it bear on humanity in some way?
  71. Wait; who has my…
  72. Focus on what has mattered until now
  73. What’s the alternative?
  74. Please figure out how it can work!
  75. Is this the movie version, or the real-life one? Chapter 20
  76. What needs to happen to avert?
  77. Focus on demonstrable new conditions that likely push limits
  78. Obligations of reality?
  79. Some things are out of our control
  80. What type of activity tends to consume a lot of power?
  81. Duty cycle
  82. Proportional to AT
  83. Gasoline is about 4 times the other two
  84. Just a bit less than average in all categories
  85. Close to twice the gas is used in the form of electricity
  86. Both in the same neighborhood
  87. Big disparity; which is more likely?
  88. S.U.V. might not make the cut, but smaller cars will
  89. Surprisingly far: almost two-thirds of the way
  90. Is six-sevenths a coincidence?
  91. As if one day a week is all dairy/eggs
  92. Is it directed or emergent?
  93. Think frivolous or huge resource demand
  94. Do your best: might prevent the worst
  95. Can you even tell the needle isn’t at full?