IDH 2931-'Energy' [Fall 2001]:   Review and Sample Exam (with problem solutions)

Review for Exam 1 [RK  Ch 1, 2, 3;  R Ch.  2]

Reminder: Exam 1 is Monday 24 September --in class.  You are permitted one 8 1/2" x 11" sheet of notes.  Conversions and constants will be provided.

Here are what I consider the highlights of each chapter.  You of course should be prepared to do some calculations similar [but not identical!] to the assigned homework.
 

RK Ch 1--
Energy basics.  Potential & kinetic E.  E-types:  mechanical, electrical, chemical, thermal, mass, radiation.  E-units [calorie, Btu, Joule, kwh, etc].  Exponential growth & decay; doubling time [Appendix 1]. Patterns of US energy use.  Renewable/non-renewable resources.

RK Ch 2.--
Fossil-fuel E-resources.  Petroleum and natural gas:  Discovery, production, exhaustion.  Hubbert's prediction.  Oil & the energy crisis of 1973.  Enhanced oil recovery. Shale oil & tar-sands.  Coal.

RK Ch 3--
Heat engines [usually powered by fossil fuel].  Efficiency of engines, actual and Carnot [ideal].  Heat pumps.  Cogeneration.
 

R Ch2 --
The policy process or ‘cycle’ [be able to discuss any of the five phases]. Political 'processing'-- Constitutional framework [influences & constraints on policy-making]: Checks & balances,etc.  Federalism, interest groups.  Practical politics: Incrementalism, bargaining & compromise, terms-of-office, more ‘interest groups’; economic and other influences on public opinion.  Political ‘seasons’. The mechanics of government:  the White House, Congress, the courts.  Committees, bureaucracy (agencies).

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IDH 2931-Energy  Sample Exam 1

NOTE: This exam was used in a previous year when the textbook and the coverage may have differed; thus if a question appears out of context, ignore it.  For  practice purposes, use the constants and conversions in your textbook.

SPECIAL NOTE:  You will get more benefit from this sample exam if you try to work thorough it without looking at the solutions.

There are 10 questions—five may be answered by discussion (D) and five require calculations (P).  Answer any 8 questions, clearly indicating at the top of this page which ones you are omitting.  Each answer will be scored on a 10-point basis; thus the maximum possible score is 80 points.  If you answer more than 8 questions, the scoring basis will be reduced proportionately: 9 @ 9 points or 10 @ 8 points.  All work must be shown for problems:  write down equations before substituting numbers and make sure that your solution method is clear to the reader.  Problems will be graded primarily on correct reasoning and set-up with proper substitution of quantities/units and units of final answer.
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D1.  "Energy policy is environmental policy."—Rosenbaum (4th Ed.), p. 261.  Do you agree?  Give arguments/evidence supporting your answer.

D2.  Outline the policy cycle, briefly explaining each of the phases.  In which of the latter do you think the original goals of the policy proponents are most likely to be distorted or thwarted?  Why?

D3.  Describe Hubbert's prediction concerning petroleum resources.  Include in your discussion the facts and/or assumptions used by Hubbert, a concise statement summarizing the prediction, and your own view(s) on the likelihood of the prediction having been essentially correct.

D4.  Discuss the pros and cons of the long-term use of coal by the USA as a primary energy source.  What group(s) or persons are the major advocates of wide-spread coal use?

D5.  (a) Outline the political and practical reasons for the almost universal use of electricity as the primary energy delivery system in most of the world’s industrialized countries and  (b) Briefly indicate what the overall US policy (if any) has been regarding the electric utility industry.

P6.  An inventor claims to have developed a remarkable new engine that operates at a relatively non-polluting temperature of 160 degs.C and discharges heat at 22 degs.C.  Promotional literature advertises that 47% of the fuel energy is converted into useful work.  Would you invest money in this device?  Make calculations to support your answer.

P7.  The Four Corners Power Plant located near the border intersection of Arizona, New Mexico, Colorado, and Utah consumes 7200 tonnes of coal per day.  This coal has an average heat value of 20,000 Btu/kg.  If the overall thermal efficiency of the plant is 30% , (a)  what is the average electric power output of the plant in kW and (b)  how many kWh of heat energy are dumped into the atmosphere every day?

P8.  A jelly doughnut from one of the Reitz Union concessions contains approximately 330 ‘food-calories’ [1 food calorie = 1000 standard calories].  Suppose that after consuming two of these delicacies [yum!], a 70-kg person regrets the impulse and decides to work off the calories by jogging up and down the bleachers at Florida Field.  Assume that the stadium is 40m high, that no energy is expended on the downward trips and that all of the food energy is transformed into motion.  (a)  How many trips will (s)he have to make, and (b)  if 1 minute is required to reach the top row, what is the person’s power output level in watts?

P9.  The power output of a laborer amounts to about 50 watts during a continuous 8-hour working day.  a.  What quantity of gasoline contains this energy equivalent? [1 gal. gasoline = 36.6 kWh]
 b.  If only half of the body’s energy output is available to do work (the remainder is expended by the   metabolic processes) and the person’s daily food intake is 2500 kcal, what is the body’s efficiency   as a machine while the work is being done?

P10.  On a moderately cold day my house requires heat at a rate of approximately 30,000 Btu/hr.  I have two choices:  a heat pump having a Coefficient of Performance [COP] of 4 using electrical energy that costs 9 cents per kilowatt-hour, or a wood-burning stove that is 45% efficient [i. e., 45% of the heat of combustion goes into heating the house] using wood that costs $80 per cord [3.6 cubic m], each cord yielding 24 million Btu.  Compare the heating cost per 24-hr day for the two methods.

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Sample Exam 1 - Problem solutions

[Intermediate calculation results are underlined; final answer is in bold face.]

P 6.  T(hot) = 160 C= 433 K ; T(cold) = 22 C = 295 K

Carnot Efficiency = 1 - [295/433] = 0.3187 = 32%

But this is the absolute maximum efficiency, never possible with real engines!
The inventor is claiming over 40% efficiency---is this believable??  I wouldn’t invest....would you???

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P 7.  7200  Tn x 1000 kg/Tn x 20000 Btu/kg = 1.44 E11 Btu/day

On a daily basis, the electric power delivered is:

1.44 E11 Btu x 0.3 x 1 d/24h x 3600 s/h  x 1055 J/Btu = 5.28  E8 J/s = 528 E6 W = 528 MW

The daily heat loss is the remaining 70% of the energy input or 1.44 E11 Btu x 0.7 =1 E11 Btu

1 E11 Btu x 2.93 E-4 kWh/Btu = 2.95 E7 kWh

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P 8.  The work done per trip is the potential energy gained, W = mgh,

so W = 70 kg x 9.8 m/s2 x 40 m = 2.74 E4 Joules.

The energy input from the food is 2  x 330 E3 cal x 4.184 J/cal = 2.76 E6 J.  To 'burn' this amount of energy  will require

[2.76 E6 J/ 2.74 E4 J/trip] = 100 trips!!!!!

The power output is P = W/t = 2.74 E4 / 60 s  = 456 J/s = 456 W

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P 9.  50 W x 8 h = 400 Wh = 0.4 kWh

0.4 kWh / 36.6 kWh/gal =1.1 E-2 gal or 0.011 gallon!  [Can you estimate this volume in units that are more readily visualized?]

Efficiency = work delivered / energy input = [0.4 kWh x 0.5 ] / [2500  E3 cal x 1.19 E-6 kWh/cal]

 = 6.89 E-2 , or 7 %

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P 10. The daily energy requirement is 30000 Btu/h x 24 h/d = 7.2 E5 Btu

The heat pump’s energy consumption is  Eout / COP = 7.2 E5 Btu / 4 = 1.8 E5 Btu

 1.8 E5 Btu x 2.93 E-4 kWh/Btu = 52.7 kWh  which will cost $4.75

The wood stove will require, per day,  7.2 E5 Btu / [24 E6 Btu/cord  x 0.45]  = 6.67 E-2 cords,

 which will cost $5.33 .  So this heat pump actually costs less to operate than the wood stove.

[What costs have been ignored in this example?]

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