SUMMARY The goals of Chapter 11 have been to learn more about energy transformations and transfers. the laws of thermodynamics, and theoretical and practica l limitations on energy use.

GENERAL PRINCIPLES

Energy and Efficiency The Laws of Thermodynamics When energy is lransformed from one form into another, some may be ;'105t," usuall y to thermal energy, due to practical or theoret ical constraints. This limits the efficiency of processes . We defi ne efficiency as

The first law of thermodynamics is a statement of conservat ion of energy for systems in wh ich onl y thermal energy changes:

toE," ~ W + Q

what you get e

what YOLI had to pay

Entropy and Irreversibility

· , · · , : > · > , > . · · . . ,

> · > ,

, •

I ' " > , > • ; ~, . , , 'l. ~' •• ,. "

S YSlems move toward more probable states. T hese states have higher entropy- more di sorder. This change is irrevers ible. C hang ing other forms of energy to thermal energy is irrevers ible.

.I ncreas ing probability Increasing en tropy

IMPORTANT CONCEPTS

Thermal energy

For a gas, the thermal energy is the total kinetic energy of motion of the atoms.

Thermal energy is random kinetic energy and so has entropy.

Temperature

For a gas, temperature is proportional to the average kinetic energy of the motion of the atoms.

2 K avg T ~--

3 kB

Two systems are in thermal equilibrium if they are at the same temperature. No heat energy is transfen-ed at thermal equilibrium.

~ ~

APPLICATIONS

The second law of tbermodynamics spec ifies the way that iso­lated systems can evolve:

The entropy of an isolated system always increases.

This law has practical consequences:

Heat energy spontaneously nows only from ho t to cold.

A transfo rmation of energy into thermal energy is irreversible.

No heat e ngine can be 100% efficient.

Heat is ene rgy transferred between two objects at different temperatures. Energy wiLl be transfen-ed unti l thermal equilibrium is reached.

A heat engine converts thennal energy from a hot reservoir into useful work. Some heat is exhausted into a cold reservoir, limiting efficiency.

HOI reservoi r T,

Q, ~ Heal engi ne 19:v~

Q,

Cold reservoir T,

A heat pump uses an energy input to transfer heat from a cold side to a hot side. The coefficient of performance is analogous to effic iency. For cool ing, it is:

Tc COPma:c.= ---

71{ - Tc

Hot reservoir T,

~I Q"

Heat pump

Q,

Cold reservoir T,

Efficiencies

Energy in the body

Power plants Temperature scales

Cell s in the body metaboli ze chemical energy in food. Efficiency for most actions is about 25%.

Energy used by body at rate of 480 W

--Energy for forward propul sion at rate of 120W

A typical power plan t converts about 1/3 of the energy input into useful work . The rest is exhausted as waste heat.

Waste heat

Useful work out

-

Zero on the Kelvin temperature scale is the temperature at wh ich the kinetic energy of atoms is zero. This is absolute zero. The conversion from °C to K is

T(K) ~ T(' C) + 273

.... All temperatures in equations must be in kelv in . ..

350 CHAPTER 11 Using Energy

tMP)TM For homeWO~k assig~ed on MasteringPhysics, go to

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Problem difficulty is labeled as I (straightforward) to 11 111 (challenging) .

QUESTIONS

Conceptual Questions

1. Rub your hands together vigorously. What happens? Discuss the energy transfers and transformations that take place.

2. Write a few sente nces describi ng the e nergy tra nsformations that occur from the time moving waler enters a hydroelectri c plant until you see some water being pumped outaf a nozzle in a public fountain. Use the "Energy transformations" table on page 324 as an example.

3. Describe the energy transfers and transformations that OGcur BID from the time you sit down to breakfast unti l you ' ve completed

a fast bicycle ride. 4. According to Table 11 .4, cycl ing at 15 km/h requires less meta­

BID bolic energy than mnning at1 5 kmlh. Suggest reasons why thi s is the case.

S. You're stranded on a remote desert island with only a chicken, a bag of corn , and a shade tree. To survive as long as poss ible in hopes of be ing rescued, shou ld you eat the chicken at once and then the corn ? Or eat the corn , feeding enough to the chicken to keep it al ive. and then eat the chicken when the corn is gone? Or are yo ur surv iva l chances the same e ither way? Explain.

6. For most automobiles, the num ber of mi les per ga llon decreases as highway speed increases. Fuel economy drops as speeds increase from S5 to 65 mph, then decreases further as speeds increase to 75 mph. Expla in why thi s is the case.

7. When the space shuttle returns to earth , its surfaces get very hot as it passes th rough the atmosphere at high speed. a. Has the space shuttle been heated? If so, what was the

source of the heat? If not, why is it hot? b. Energy must be conserved. What happens to the space shut­

tle's ini tial ki netic energy?

8. One end of a short aluminum rod is G in a campfi re and the other end is in a :::::::::;: block of ice, as shown in Figlu'C Q 11 .8. If l Oa J of energy are transferred from the fire to the rod, and if the FtGURE 011 .8

temperatu re at every poin t in the rod has reached a steady value, how much energy goes from the rod in to the ice?

9. Two blocks of copper, one of mass I kg and the second of mass 3 kg, are at the same temperature. Which block has more ther­mal energy? If the blocks are placed in thermal contact, will the thermal energy of the blocks change? If so, how?

10. If the temperature Tof an ideal gas doubles, by what Factor does the average ki net ic energy of the atoms change?

II . A bottle of helium gas and a bott le of argon gas contain eq ual numbers of atoms at the same temperatu re. Which bottl e, if e ither, has the greater total thermal energy?

For Ques tions 12 th rough 17, give a spec ific example of a process that has the energy changes and transfers descri bed. (For example, if the question states " d E!h > 0, W = 0," you are to describe a process

Problems labeled INT integrate significant material from earlier

chapters; BID are of biological or medical interest.

that has an inc rease in thermal energy and no trans fer of energy by work. You could write "Heat ing a pan of water on the stove.")

12. ~ E,"<O, W ~O

13. ~ E," > 0, Q ~ 0

14. ~E,"< O, Q ~ O

15. ~ E'h > 0, W 'I' 0, Q 'I' 0

16. ~E,"<O, W 'I'O,Q'I'O

17. ~ E," ~ O, W 'I'O,Q'I'O

18. A fi re pi ston-an impress ive physics demonstration- ignites a fi re without matches. The oper­ation is shown in FigUJ'C Q 11.1 8. A wad of cotton is placed at the bottom of a sealed syringe with a tight-fi tt ing plunger. When the plunger is rapidly depressed. the air temperatul'C in the syringe ri ses enough to ign ite the cotton. Explain why the air temperature ri ses, and why the plunger must FIGURE 011 .18

be pushed in very quickl y. 19. In a gasoline engine, fue l vapors are ign ited by a spark. In a

diesel engine, a fuel- ai r mixture is drawn in, then rapid ly com­pressed to as little as 1120 the original vo lume, in the process inc reas ing the temperature enough to ign ite the fue l-air mix­ture. Explain why the temperature ri ses during the compression.

20. A drop of green ink falls into a beaker of clear water. First describe what happens. Then explaillthe outcome in tenns of entropy.

2 I. If you hold a rubber band loose ly between two fin gers and then stretch it, you can tell by touching it to the sens itive skin of your forehead that stretching the rubber band has increased its tem­perature. If you then let the rubber band rest aga insl your fore­head, it soon returns to il s original temperature. What are the signs of W and Q for the entire process?

22. In areas in which the air temperatu re drops very low in the win­ter, the exterior unit of a heal pump designed for heating is sometimes buried underground in order to use the earlh as a thermal rese rvoir. Why is it worth while to bury the heat exchanger, even if the underground unit costs more to purc hase and install than one above ground?

23 . Assuming improved materi als and belle r processes, can engi­neers ever des ign a heat engine that exceeds the max imum effi ­c iency indicated by Equation 11.1 4? Ifnol, why not?

24. Elect ri c vehicles increase speed by using an e lec tri c motor that draws energy from a battery. When the ve hicle slows, the motor runs as a generator, recharging the battery. Explain why thi s means that an electric vehicle can be more effic ient than a gasoli ne-fue led vehicle.

2S. When the sun's light hi ts the earth, the temperature ri ses. Is there an entropy change to accompany thi s transformat ion? Explain.

26. When you put an ice cube tray fi lled with liquid water in yo ur freezer, the water even tuall y becomes sol id ice. The solid is more ordered than the liquid- it has less entropy. Expla in how thi s transformat ion is poss ible without violat ing the second law of thermodynamics.

27. A company markets an electri c heater that is described as 100% efficient at converting electri c energy to the rmal energy. Does thi s violate the second law of thermodynamics?

Multiple-Choice Questions

28. III A person is walking on level ground at constant speed. What energy transformation is taking place? A. Chemical energy is being transformed to thermal energy. B. Chemical energy is being transformed to kinetic energy. C. Chemical energy is be ing transformed to kinet ic energy and

thermal energy. D. Chemical energy and thermal energy are being transformed

to ki netic energy. 29. 1 A person walks I km , turns around, and runs back to where

he started . Compare the energy used and the power du ring the two segments. A. The energy lIsed and the power are the same for both . B. The energy used while walking is greater. the power while

run ni ng is greater. C. The energy used while run ning is greater, the power while

runni ng is greater. D. The energy used is the same for both segments, the power

while runn ing is greater. 30. I The temperature of the ai r in a basketball increases as it is

pumped up. This means that A. The total ki netic energy of the a ir is increas ing and the ave r~

age kinet ic energy of the molecules is decreas ing. B. The total kineti c energy of the air is increas ing and the aver~

age kinetic energy of the molecules is increas ing. C. The total ki net ic energy of the air is decreasing and the

average ki net ic energy of the molecules is decreas ing. D. The total ki netic energy of the air is decreasing and the

average ki net ic energy of the molecules is increas ing.

PROBLEMS

Section 1l.1 Transforming Energy

I. II A 10% effi c ien t engine accelerates a 1500 kg car from rest to 15 m/s. How much energy is transferred to the engine by burn­ing gasol ine?

2. II A 60% effic ient dev ice uses chemical energy to generate 600 J of electri c energy. a. How much chemical energy is used? b. A second dev ice uses twice as much chemical energy to gen­

erate half as much electric energy. What is its effic iency? 3. A typical photovoltaic ce ll de li vers 4.0 X 10- 3 W of electric

energy when illumi nated with 1.2 X 10- 1 W of li ght energy. What is the effic iency of the ce ll?

4. II An ind ividual whi te LED (l ight-emitti ng diode) has an e ffi ­c iency of 20% and uses 1.0 W of e lectri c power. How many LEOs must be combined into one light source to give a total of 1.6 W of visible- light output (comparable to the light outpu t of a 40 W incandescent bul b)? What total power is necessary to n lll thi s LED light source?

Problems 351

3 1. I The thermal energy of a conta iner of hel ium gas is halved. What happens to the temperature, in kelvin? A. It dec reases to one-fourth its ini tial value. B. It decreases to one-hal f its initial value. C. It stays the same. D. It increases to twice its ini tial value.

32. I An inventor approaches you with a device that he cla ims will take 100 J of thermal energy input and produce 200 J of elec­tric ity. You decide not to invest you r money because this device would violate A. The first law ofthennodynamics. B. The second law of thermodynamics. C. Both the first and second laws of thermodynamics.

33. I Whi le keeping your food cold, your refri gerato r transfers energy from the inside to the surroundings. Thus thermal energy goes fro m a colder object to a warmer one. What can you say about thi s? A. It is a violation of the second law of thermodynam ics. B. It is not a violation of the second law of thermodynamics

because refrigerators can have effic iency of 100%. C. It is not a violation of the second law of thermodynamics

because the second law doesn't apply to re frigerators. D. The second law of thermodynamics applies in thi s situati on,

but it is not violated because the energy did not sponta­neously go from cold to hot.

34. An electric power plant uses energy from burning coal to gen-erate steam at 450°C. The plant is cooled by 20°C water fro m a neillby ri ver. If burn ing coal provides 100 MJ of heat, what is the theoret ical minimum amount of heat that must be transferred to the river during the convers ion of heat to electric energy? A. IOOMJ B.90MJ C. 60 MJ D. 40 MJ

35. II A re frigera tor's freezer compartment is set at _ 10°C; the ki tchen is 24°C. What is the theoret ical mi nimum amoun t of elec tri c energy necessary to pump 1.0 J of energy out of the freezer compartment? A. 0.89 J B. 0.87 J C. 0. 13 J D. O. ll J

Section 11.2 Energy in the Body: Energy Inputs

5. Il A fast-food hamburger (with cheese and bacon) contains BID 1000 Calories. What is the burger's energy in joules? 6. III In an average human, bas ic life processes require energy to

BID be suppl ied at a steady rate of 100 W. What daily energy in take, in Calories, is required to main tain these basic processes?

7. I An "energy bar" conta ins 6.0 g of fat. How much energy is BID thi s in joules? In calories? In Calories?

8. I An "energy bar" conta ins 22 g of cillbohydrates . How much BID energy is thi s in joules? .ln calories? In Calories?

Section 11.3 Energy in the Body: Energy Outputs

9. III An "energy bar" contains 22 g of carbohydrates. If the energy BID bar was his on ly fuel , how far could a 68 kg person walk at

5.0 km!h? 10. III Suppose your body was able to use the chemical energy in BID gasoli ne. How far could you pedal a bicycle at 15 km/h on the

energy in I gal of gas? ( I gal of gas has a mass of 3.2 kg.)

352 CHAPTER 11 Using Energy

11 . 11111 The label on a candy bar says 400 Calori es. Assuming a BID typica l effi ciency for energy use by the body, if a 60 kg person

were LO lise the energy in thi s candy bar to c limb stai rs, how high could she go?

12. III A we ightlifter curl s a 30 kg bar, rais ing it each time a BIO di stance of 0 .60 m . How many limes must he repeat thi s exe r­

c ise to burn off the energy in onc s lice o f pizza? 13. III Aweighll ifler works o Ul at the gym each day. Part o f her rou­BID tine is to lie on her back and lift a 40 kg barbell straight up from

chest height to full arm extension, a distance of 0.50 m. a. How much work does the we ightl iftcr do to li ft the barbell

one time? h. If the weightlirter does 20 repet itions a day, what lOlal

energy does she expend on lifting, ass uming a typ ica l effi ­ciency for e nergy use by the body.

c. How many 400 Calori e don uts can she eat a day to suppl y that energy?

Section 11.4 Thermal Energy and Temperature

14. I The planet Mercury's surface te mperature vari es from 700 K du ring the day to 90 K at night. What are these values in °C and OF?

IS. II An idea l gas is at 20°e. If we do ub le the ave rage ki neti c e nergy of the gas atoms, what is the new temperatu re in DC?

16. II An ideal gas is at 20°e. T he gas is cooled , reduc ing the ther­mal energy by 10%. What is the new temperature in DC?

17. II An ideal gas at ooe cons ists o f 1.0 X 1023 atoms. 10 J o f thermal energy are added to the gas. What is the new te mpera­ture in DC?

18. II An ideal gas at 20°C cons ists of 2.2 X 1022 atoms. 4.3 J of thermal energy are removed from the gas. What is the new tem­perature in DC?

Section U.S Heat and the First Law of Thermodynamics

19. II SOO J of work are done on a system in a process that dec reases the system 's thermal energy by 200 J . How much energy is transferred to or from the syste m as heat?

20. I 600 J of heat energy are transferred to a system that does 400 J of work. By how much does the system's thennal energy change?

2 1. I 300 J of e nergy are transferred to a system in the form of heat while the thermal energy increases by 150 J. How much work is done on or by the system?

22. I 10 J o f heat are removed fro m a gas sample while it is be ing compressed by a piston that does 20 J o f work. What is the change in the thermal energy of the gas? Does the temperature of the gas increase or decrease?

Section 11.6 Heat Engines

23. I A heat eng ine ex trac ts 55 kJ from the hot reservo ir and exhausts 40 kJ into the cold reservoir. What are (a) the work done and (b) the effic iency?

24. II A heat eng ine does 20 J o f work while exhausti ng 30 J o f waste heat. What is the eng ine's effic iency?

2S. II A heat e ng ine does 200 J o f work while ex hausti ng 600 J o f heat to the cold rese rvoir. What is the eng ine's effic iency?

26. I A heat eng ine with an effic ie ncy of 40% does 100 J of work. How muc h heat is (a) ex trac ted fro m the hot reservo ir and (b) exhausted into the cold reservoir?

27. II a. At what cold-reservoir temperature (in DC) would an engine operati ng at maximum theoretical e ffic ie ncy with a hot­reservo ir temperature of 427°C have an e fficiency of 60%?

b. If another eng ine, operat ing at max imum theoretical effi ­c iency with a hot-reservo ir temperature of 400°C, has the same effi ciency, what is its co ld-reservoir temperature?

28. III A heat eng ine operati ng between e nergy reservo irs at 20 0 e and 6000 e has 30% of the max imum possible effi c iency. How muc h energy does thi s engine ex trac t from the hot rese rvoir to do 1000 J of work?

29. I A newly proposed dev ice fo r generating electr ic ity from the sun is a heat eng ine in whi c h the hot reservoir is created by focusing sunlight on a small spot on one s ide of the eng ine. The cold reservoir is ambient air at 20°C. The des igner claims that the e ffi c ie ncy will be 60%. What minimum hot-rese rvoir te m­perature, in °e, would be req ui red to prod uce thi s effi ciency?

30. I Converting sunlight to elec· lricity with so lar cells has an effi ciency of = IS%. It 's possible to achieve a higher e ffi c iency (though curren tl y at higher cost) by using concentrated sunli ght as the hot reservoir of a heat engine. Each d ish in Figure P 11 .30 con­

~"' • . ~~- ,~~~~ ~.~." . D . ,,:,

, .. _ .. ,~-, ~ 1 ' ..., I, '

- . - '

centrates sunlight on one side of FIGURE P11 .30

a heat eng ine, produc ing a hot-reservoir te mperature of 6S00e. The cold reservo ir, ambient air, is approx imately 30°e. T he actual working effic iency of thi s device is =30%. What is the theoretical max imum effic iency?

Section 11.7 Heat Pumps

3 1. II A refri gerator takes in 20 J of work and exhausts 50 J o f heal. What is the refrigerator's coefficient of performance?

32. II Air conditioners are rated by their coeffic ient of perfomlance at 80°F inside temperature and 95°F outs ide temperature. An e ffi ­cient but realisti c air conditioner has a coefficient of performance of 3.2. What is the max imum poss ible coefficient of perfonnance?

33. II 50 J of work are done on a re frigerato r with a coeffi c ient of performance of 4 .0. How much heat is (a) ex tracted from the cold reservoir and (b) exhausted to the hot reservoir?

34. II F ind the max imum poss ible coeffic ie nt o f pe rform ance for a heat pump used to heat a house in a northerly climate in winter. The inside is kept at 200 e while the outside is - 20°e.

Section 11.8 Entropy and the Second Law of Thermodynamics

3S. I Which, if a ny, of the heat eng ines in Figure PIl.3S below vio late (a) the fi rst law of thermodynamics or (b) the second law of thermodynamics? Ex plain .

"'::.--' [~~:: engine

__ -JLOJ

(b) Ho< """0;' t FA ~ 600 K

Heat

-------, I t=---r, J - 4

4

J J

==--I·~ Cold reservoir Cold reservoir

FIGURE P11 .35 Cold reservoir Tc = 300 K

36. I Which, if any. of the refrigerators in Figure P I 1.36 below violate (a) the fi rst law of thermodynam ics or (b) the second law of thermodynamics? Expla in.

(3) Hot reservoir Til = 400 K (b) HOI rc:>cfVoir 7 II = 400 K

., Pi"" ~-"' Pi'" .~-. t 40J t 40 J F--Cold reservoir Tc = 300 K Cold reservoir

Cold reservoir

FIGURE P11 .36

37. II Draw all possible distinct arrangements in which three balls (labeled A, 8 , C) are placed into two different boxes (I and 2), as in Figure 11 .26. If all arrangements are equally likely, what is the probability that all three will be in box I?

General Problems

38. 11111 How many sli ces of pizza must you eat to walk for 1.0 h at a BID speed of 5.0 km/h? (Assume your mass is 68 kg.) 39. II A 60 kg hiker climbs to the top ofa 500-m-high hill. Ignoring

the energy needed for hori zontal motion and ass umi ng a typical efficiency for energy use by the body, how many frozen burritos would be needed to fuel thi s climb?

40. 11111 For how long would a 68 kg athlete have to swim at a fast BID crawl to use all the energy ava ilab le in a typical fast- food meal

of burger, fries, and a drink? 4 1. II a. How much metabolic energy is required for a 68 kg BID fu nner to run at a speed of 15 km/h for 20 min ?

b. How much metabo lic energy is required for this ru nner to walk at a speed of 5.0 kmlh for 60 min? Compare yo ur res ull to your answer to part a.

c. Compare your results of parts a and b to the res ult of Example I 1.4. Of these three modes of human mot ion, which is the most effic ient?

42. To a good approx imation, the only ex ternal fo rce that does BID work on a cycl ist moving on level ground is the fo rce of ai r

res istance. Suppose a cyclist is trave li ng at 15 kmlh on level ground. Assume he is using 480 W of metabo lic power. a. Est imate the amount of power he uses for forward moti on. b. How muc h force must he exert to overcome the fo rce of a ir

res istance? 43. I The winn ing time for the 2005 ann ual race up 86 floors of the BID Empire State Build ing was 10 min and 49 s. The winner's mass

was 60 kg. a. If each floor was 3.7 In high, what was the winner's change

in grav itat ional potential energy?

Problems 353

b. If the e ffic iency in climbing stairs is 25%, what total energy did the winne r expend during the race?

c. How many food Calories did the winner "burn" in the race? d. Of those Calories, how many were convened to thermal

energy? e. What was the winne r's metabolic power in walts duri ng the

race up the stairs? 44. III Championship swimmers take about 22 s and about 30 arm BID strokes to move ttll"ough the water in a 50 m freestyle race. INT a. From Table 11 .4, a swimmer's metabol ic power is 800 W. If

the effic iency for swimming is 25%, how muc h energy is expended moving through the water in a 50 m race?

b. IJ half the energy is used in arm motion and hal f in leg moti on, what is the energy expenditu re pe r arm stroke?

c. Model the swimmer's hand as a paddle . Dur ing one arm stroke, the padd le moves ha lfway around a 90-cm-rad ius c ircle. If all the swimmer 's fo rward propulsion duri ng an arm stroke comes from the hand pushi ng on the water and none from the arm (somewhat of an oversimplification), what is the average force of the hand on the water?

45. 1111 A 68 kg hiker walks at 5.0 km/h up a 7% slope. What is the BID necessary metabo lic power? Hint: You can mode l her power

needs as the sum of the power to wa lk on level ground plus the power needed to ra ise her body by the appropriate amount.

46. III A 70 kg student consumes 2500 Cal each day and stays the BID same weight. One day, he eats 3500 Cal and, want ing to keep INT from ga ining weight, dec ides to "work off' the excess by

jumping up and down. With each jump, he accele rates to a speed of 3.3 m/s before leav ing the ground. How many jumps must he make? Assume that the effic iency of the body in using energy is 25%

47. II To make your workouts more prod uct ive, you can get a gen­BID erator that you drive with the rear wheel of your bicycle when it

is mounted in a stand. a. Your laptop charger uses 75 W. What is your body 's meta­

bo lic power use whi le run ni ng the generator to power your laptop charger, given the typical e fficiency for such tasks? Assume 100% effic iency for the generator.

b. Your laptop takes 1 hour to recharge. If you run the genera­tor fo r I hour, how much energy does your body use? Express your resul t in joules and in Calor ies.

48. II The res istance of an exerc ise bike is often provided by a gen­BID erator; that is, the energy that you expend is used to generate

elec tri c energy, which is then diss ipated. Rather than diss ipate the energy, it could be used for prac ti cal purposes. a. A typ ical person can mainta in a steady energy expenditure

o r 400 W on a bicycle. Assuming a typica l e ffi c iency ror the body and a generator that is 80% effic ient, whal useful e lec tric power could yo u prod uce wilh a bicycle-powered generator?

b. How many people wo uld need to ride bicycle generators simultaneously 10 power a 400 W TV in the gym?

49. II Smaller mammals use proport ionate ly more energy than BID larger mammals; that is, it takes more energy per gram to power

a mouse than a human. A typical mouse has a mass of 20 g and, at res t, needs to consume 3.0 Cal each day for bas ic body processes. a. If a 68 kg human used the same energy per kg or body mass

as a mouse, how much energy would be needed each day? b. What resti ng power does thi s correspond to? How much

greater is thi s than the resting power noted in the chapter?

354 CHAPTER 11 Using Energy

50. II Larger animals use propor· BID tionately less energy than smalJ er

an imals; that is, it takes less energy per kg to power an ele­phan t than to power a human. A

5000 kg A frican elephanl requi res about 70,000 Cal fo r basic needs for one day. a. If a 68 kg hu man requi red

the same e nergy per kg of body mass as an elephant, how much energy would be required each day?

b. What rest ing power does thi s correspond to? How much less is thi s than the resting power noted in the chapter?

5 1. II A large horse can perfo rm work at a s tead y rate of about BIO I horsepower, as you might expect.

a. Ass uming a 25 % efficiency. how many Calori es would a horse need to consume to work at 1.0 hp for 1.0 h?

b. Dry hay cOnla ins about 10 MJ per kg. How many kilograms of hay would the horse need La eat to perform thi s work?

52. A co llege stude nt is work ing on her phys ics homework in her dorm room. Her room conta ins a total of 6.0 X 102b gas molecules . As she works, her body is converting che mical e nergy in La thermal energy at a rate o f 125 W. If her donn room were an isolated system (do rm rooms can cert ainly fee l li ke that) and if all of thi s thermal e nergy were transferred La the a ir in the room , by how muc h would the tem perature increase in

10 min? 53. 11 A conta ine r ho ld ing argon atoms changes te mperat ure by

20°C when 30 J o f heat are removed. How many atoms are in the container?

54. 11 A heat eng ine with a high-temperature reservo ir at 400 K has an efficie ncy of 0.20. What is the max imum poss ible te mpera­ture of the cold reservoir?

55. III An eng ine does 10 J of work and exhausts 15 J of waste heat. a. W hat is the engine 's e ffi ciency? b. If the cold-reservo ir temperature is 20°C, what is the m ini ­

mum possible temperature in °C of the hot reservoir? 56. I The heat exhausted to the cold reservoir of an eng ine operat­

ing at max imum theoreti cal e ffic ie ncy is two-thirds the heat extracted from the ho t reservo ir. What is the te mperature rati o

TclTH? 57. III An eng ine operati ng at max imum theoretical e ffi c iency

whose cold-rese rvoir te mperature is 7°C is 40% effic ient. By how much should the temperature of the hot reservoir be

increased to raise the efficiency to 60%? 58. 11 Some heat eng ines can run on very small temperature d iffer­

ences. One manufacturer claims to have a ve ry small heat eng ine that can ru n on the temperature d ifference between your hand and the air in the room. Estimate the theoret ical max imum effic iency of thi s heat engine.

59. III The coeffi cien t o f performance of a refri gerator is 5.0. a. If the compressor uses 10 J of energy, how muc h heat is

exhausted to the hot reservo ir? b. If the hot-reservoir temperature is 27°C, what is the lowest

poss ible temperature in °C of the cold rese rvo ir? 60. III An eng ineer claims to have meas ured the c haracteristics of a

hea t eng ine that takes in 100 J o f thermal energy and produces 50 J o f usefu l work. Is thi s e ng ine poss ible? IJ so, what is the smallest poss ible ratio of the temperatures (i n kelvin) of the hot and cold reservo irs?

61. III A 32% effic ient e lectri c power plant produces 900 MJ of electric energy per second and d ischarges waste heat into 200C ocean water. Sup pose the waste heat could be used to heat homes duri ng the winter instead of being d ischarged into the ocean. A typical American house requires an average 20 kW for heat ing. How many homes could be heated with the waste heat of thi s one power plan t?

62. 1111 A typical coal- fi red power plant burns 300 me lric to ns o f coal every hour to generalC 2 .7 X lOb MJ of e lec tric e nergy. 1 metri c ton = 1000 kg; 1 me tri c ton of coa l has a vol ume of 1.5 m]. The heat of combustion of coal is 28 MJ/kg. Assume that all heat is tra nsferred fro m the fue l to the bo ile r and that all the work done in spin ning the turbine is transformed into electric e nergy. a. Suppose the coa l is piled up in a 10 m X 10 m room. How

tall must the pi le be La operate the plant for one day? b. What is the power plant's effi ciency?

63. III Each second, a nuclear power plant generates 2000 MJ of thermal energy fro m nuclear reactions in the reaCLa r 's core . This ene rgy is used to bo il water and produce hi gh-pressure s team at 300°e. The steam spins a turb ine, which produces 700 MJ of elec tri c power, then the steam is condensed and the water is cooled to 300C before starting the cycle aga in. a. What is the max imum poss ible effic iency of the plant? b. What is the plant's actual effic iency?

64. III 250 students s il in an aud itorium li sten ing to a phys ics lec­ture. Because they are thi nking hard, each is using 125 W of metabo li c power, s li ghtl y more than they would use at rest. An air cond itioner with a COP of 5.0 is be ing used to keep the room at a constant te mperatu re. What mi nimum e lectri c power must be used to operate the air conditioner?

65 . II Driving on as phalt roads en ta il s very little ro Uing res istance, INT so most of the e ne rgy of the engine goes to overcomi ng air

res istance. But dri ving slowly in d ry sand is anothe r story. If a 1500 kg car is dri ven in sand at 5.0 mis, the coeffic ien t of rolli ng fri ction is 0.06. In thi s case, nearly all of the energy that the car uses to move goes to overcomi ng roll ing fricti on, so you can ignore air drag in thi s prob lem. a. What propu lsion force is needed to keep the car moving for­

ward at a constant speed? b. What power is req uired for propulsion at 5.0 m/s? c. If the car gets 15 mpg when d ri ving on sand, what is the

car's efficiency? 66. III Air cond itioners sold in the Un ited S tates are g iven a sea­

sonal energy-effic iency rat io (SEER) rat ing that consumers can use to compare d ifferent models. A SEER rati ng is the rat io of heat pumped to ene rgy inp ut, s imilar to a COP but us ing Eng­li sh uni ts, so a higher SEER rati ng means a more efficie nt mode l. Yo u can determ ine the COP of an air conditioner by d ivid ing the SEER rating by 3.4. For typical ins ide and outside te mpera­tures when you'd be using a ir cond ition ing, est imate the theo­ret ical max imum SEER rating of an a ir conditioner. (New air conditioners must have a SEER rati ng that exceeds 13, qui te a b it less than the theoreti cal max imum, but there are pract ica l issues that reduce effi ciency.)

67. II The surface waters of trop ical oceans are at a tempe rature o f 27 °C whi le wa ter at a depth of 1200 m is at 3°e. It has been suggested these warm and cold waters could be the e ne rgy rese rvo irs fo r a heat eng ine, allowing us to do work o r generate e lect ri c it y from the thermal e nergy of the ocean. What is the max imum effi c ie ncy poss ible of suc h a heat eng ine?

c 68. II The light energy that falls on a square meter of ground over

the course of a typical sunn y day is about 20 MJ . The average rate of electric energy consumption in one hOllse is 1.0 kW. a. On average, how much energy does one house use during

each 24 h day? b. If li ght energy to electric e nergy conversion using solar cell s

is 15% e ffi c ient, how many square miles of land must be covered with solar ce ll s to suppl y the e lectrical energy for 250,000 houses? Assume there is no cloud cover.

Passage Problems

Kangaroo Locomotion BIO

Kangaroos have very stout

tendons in their legs that' can be lIsed to store energy. When a kangaroo lands on its feet, the tendons stretch, transforming kinetic energy of motion to elas­tic potential energy. Much of this e nergy can be Lransformed back into kinet ic energy as the kangaroo takes another hop. The kangaroo's peculiar hopping gait is not very effi cient at low speeds but is quite efficient at high speeds.

Figure PII .69 shows the energy cost of human and kangaroo locomotion. The graph shows oxygen uptake (in mUs) per kg of body mass, allowing a direct comparison between the two spec ies.

Oxygen uptake (mL/ kg's)

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

Human, running

Red kangaroo, hopping

o +---~--~-~--~--~--~ Speed (mJs) o 2 4 6 10 12

FIGURE P11.69 Oxygen uptake (a measure of energy use per second) for a running human and a hopping kangaroo.

Stop to Think 11.1: C. In each case, what yo u get is the potential­e nergy change of the box. Crane 2 lifts a box with twice the mass the same distance as crane I, so you get twice as much energy with crane 2. How about what YOLI have to pay? Crane 2 uses 20 kJ , crane I only 10 kJ . Comparing crane I and crane 2, we find crane 2 has twice the energy out for twice the energy in , so the e ffici encies are the same.

Stop to Think 11.2: C. As the body uses chemical energy from food, approx imately 75% is trans formed into thermal energy. Also, kineti c energy of motion of the legs and feet is transformed into thermal energy with each stride. Most of the chemical energy is transformed into thermal energy.

Stop to Think 11.3: C. Samples 1 and 2 have the same thermal ene rgy, which is the total kineti c energy of all the atoms. Sample I has twice as many atoms, so the average energy per atom, and thus the temperature, must be less.

Problems 355

For humans, the e nergy used per second (i.e., power) is propor­tionalto the speed. That is, the human curve nearl y passes through the origin, so running twice as fast takes approximately twice as muc h power. For a hopping kangaroo, the graph of e nergy use has on ly a ve ry small s lope. In other words, the energy used per second changes very little with speed. Going faster requires very little addi ­tional power. Treadmill tests on kangaroos and observations in the wild have shown that they do not become winded at any speed at which they are able to hop. No matter how fast they hop, the neces­sary power is approximately the same. 69. I A person runs I km. How does hi s speed affect the totaJ

energy needed to cover thi s distance? A . A faster speed requires less total e nergy. B. A faster speed requires more total energy. C. The total energy is about the same for a fast speed and a

slow speed. 70. I A kangaroo hops I km. How does its speed affec t the total

energy needed to cover thi s di stance? A. A faster speed requires less total energy. B. A faster speed requires more total e nergy. C. The total energy is about the same for a fast speed and a

slow speed. 71. I At a speed of 4 mIs,

A . A running human is more e ffic ient than an equal-mass hop­ping kangaroo.

B. A running human is less effi cie nt than an equal-mass hop­ping kangaroo.

C. A running human and an equal -mass hopping kangaroo have about the same e ffi ciency.

72. I At approximately what speed would a human use half the power of an equal-mass kangaroo moving at the same speed? A. 3 mls B. 4 m/s C. 5 m/s D. 6 m/s

73. I At what speed does the hopping mot ion of the kangaroo become more effi cien t than the running gait of a human ? A. 3 m/s B. 5 m/s C. 7 m/s D. 9 m/s

Stop to Think t 1.4: C. The radiator is at a higher temperature than the sUlTounding air. Thermal energy is transferred out of the system to the e nvironment. so Q < O.

Stop to Think 11.5: A, D. The efficiency is fi xed by the ratio of Tc to TH. Decreasing this ratio increases effic iency; the heat engine will be more effi c ie nt with a hotter hot reservoir or a colder cold reservoir.

Stop to Think 11.6: A, D. The c loser the te mperatures of the hot and cold rese rvo irs, the more e ffi cie nt the heat pump can be. (It is also true that having the two temperatures be closer wil.l cause less thermal ene rgy to "leak" out.) Any change that makes the two tem­peratures closer will allow the refrigerator to use less energy to run.

Stop to Think 11.7: B. In this case, kinetic energy is transformed into potential energy; there is no e ntropy change. In the other cases, energy is Lransfonned into thermal e nergy, meaning elllropy increases.