The Language of Physics

TemperatureThe simplest definition of temperature isthat temperature is a measure of thehotness or coldness of a body. A betterdefinition is that temperature is a measureof the mean kinetic energy of the moleculesof the body (p. 403).ThermometerA device for measuring the temperature ofa body (p. 404).Celsius temperature scaleA temperature scale that uses 0° for themelting point of ice and 100° for theboiling point of water (p. 404).Fahrenheit temperature scaleA temperature scale that uses 32° for themelting point of ice and 212° for theboiling point of water (p. 405).Kelvin temperature scaleThe absolute temperature scale. The lowesttemperature attainable is absolute zero, the0 K of this scale. The temperature for themelting point of ice is 273 K and 373 K forthe boiling point of water (p. 405).Internal energyThe sum of the potential and kinetic energyof all the molecules of a body (p. 408).HeatThe flow of thermal energy from a body ata higher temperature to a body at a lower ,

temperature. When a body cools, itsinternal energy is decreased; when it isheated, its internal energy is increased(p. 408).Thermal equilibriumWhenever two bodies at differenttemperatures are touched together, thermalenergy always flows from the hotter body tothe cooler body until they are both at thesame temperature. When this occurs thetwo bodies are said to be in thermalequilibrium (p. 408).KilocalorieA unit of heat. It is defined as the amountof thermal energy required to raise thetemperature of 1 kg of water 1 °C (p. 408).British thermal unit (Btu)The amount of thermal energy required toraise the temperature of 1 lb of water 1 °F(p. 408).Mechanical equivalent of heatThe equivalence between mechanicalenergy and thermal energy. One kcal isequal to 4186 J (p. 408).Specific heatA characteristic of a material. It is definedas the number of kilocalories required toraise the temperature of 1 kg of thematerial 1 °C (p. 409).

CalorimetryThe measurement of heat (p. 411).CalorimeterAn instrument that is used to makemeasurements of heat. The basic principleunderlying the calorimeter is theconservation of energy. The thermal energylost by those bodies that lose thermalenergy is equal to the thermal energygained by those bodies that gain thermalenergy (p. 411).Phases of matterMatter exists in three phases, the solidphase, the liquid phase, and the gaseousphase (p. 413).Change of phaseThe change in a body from one phase ofmatter to another. As an example, meltingis a change from the solid state of a body tothe liquid state. Boiling is a change in statefrom the liquid state to the gaseous state(p. 413).Latent heat of fusionThe amount of heat necessary to convert 1kg of the solid to 1 kg of the liquid(p. 414).Latent heat of vaporizationThe amount of heat necessary to convert 1kg of the liquid to 1 kg of the gas (p. 414).

Summary o f Impor tant Equat ions

Convert Fahrenheit temperatureto Celsius?°C = i(t°F - 32°)

Convert Celsius temperatureto Fahrenheitt " F k °C + 32°

(14.1)

(14.2)

Convert Celsius temperature to KelvinT K = r ° C + 2 7 3 ( 1 4 . 4 )Thermal energy absorbedor liberatedQ = m c A t ( 1 4 . 6 )Principle of calorimetryThermal = Thermalenergy lost energy gained (14.7)

FusionQx = m,LiVaporizationQy = m„Ly

(14.15)

(14.16)

Quest ions for Chapter 14

1. What is the difference betweentemperature and heat?

2. Explain how a bathtub of water at5 °C can contain more thermalenergy than a cup of coffee at 95 °C.

3. Discuss how the human body usesthe latent heat of vaporization to coolitself through the process ofevaporation.

+4. Relative humidity is defined as thepercentage of the amount of watervapor in the air to the maximum

amount of water vapor that the aircan hold at that temperature. Discusshow the relative humidity affects theprocess of evaporation in general andhow it affects the human body inparticular.

+5. It is possible for a gas to go directlyto the solid state without goingthrough the liquid state, and viceversa. The process is called

x sublimation. An example of such aprocess is the formation of frost.

Discuss the entire process ofsublimation, the latent heat involved,and give some more examples of theprocess.

+6. Why does ice melt when an object isplaced upon it? Describe the processof ice skating from the pressure ofthe skate on the ice.

7. Why are the numerical values of thespecific heat the same in SI units andBritish engineering units?

420 Thermodynamics

Problems for Chapter 14

14.1 Tempera tu re1. Convert the following normal body

temperatures to degrees Celsius:(a) oral temperature of 98.6 °F,(b) rectal temperature of 99.6 °F,and (c) axial (armpit) temperature of97.6 °F.

2. Find the value of absolute zero on theFahrenheit scale.

3. For what value is the Fahrenheittemperature equal to the Celsiustemperature?

'« 4. Convert the following temperaturesto Fahrenheit: (a) 38.0 °C,(b) 68.0 °C, (c) 250 °C,(d) -10.0 °C, and (e) -20.0 °C.

^ 5. Convert the following Fahrenheittemperatures to Celsius:(a) -23.0 °F, (b) 12.5 °F,(c)55.0 °F, (d) 90.0 °F, and(e) 180 °F.

6. A temperature change of 5 °Fcorresponds to what temperaturechange in Celsius degrees?

+7. Derive an equation to convert thetemperature in Fahrenheit degrees toits corresponding Kelvin temperature.

+8. Derive an equation to convert thechange in temperature in Celsiusdegrees to a change in temperaturein Fahrenheit degrees.

74.3 Specific HeatX 9. A 450-g ball of copper at 20.0 °C is

placed in a pot of boiling water untilequilibrium is reached. How muchthermal energy is absorbed by theball?

10. A 250-g glass marble is taken from afreezer at —23.0 °C and placed intoa beaker of boiling water. How muchthermal energy is absorbed by themarble?

11. How much thermal energy must besupplied by an electric immersionheater if you wish to raise thetemperature of 5.00 kg of water from20.0 °C to 100 °C?

12. A 2.00-kg mass of copper falls froma height of 3.00 m to an insulatedfloor. What is the maximum possibletemperature increase of the copper?

13. An iron block slides down an ironinclined plane at a constant speed.The plane is 10.0 m long and isinclined at an angle of 35.0° with thehorizontal. Assuming that half theenergy lost to friction goes into theblock, what is the difference intemperature of the block from thetop of the plane to the bottom of theplane?

14. A 2000-kg car is traveling at 96.6km/hr when it is braked to a stop.What is the maximum possiblethermal energy generated in thebrakes?

15. How much thermal energy isabsorbed by an aluminum ball 20.0cm in diameter, initially at atemperature of 20.0 °C, if it isplaced in boiling water?

74.4 Calorimetry16. If 30.0 g of water at 5.00 °C are

mixed with 50.0 g of water at70.0 °C and 25.0 g of water at100 °C, find the resultanttemperature of the mixture.

17. If 80.0 g of lead shot at 100 °C isplaced into 100 g of water at 20.0 °Cin an aluminum calorimeter of 60.0-gmass, what is the final temperature?

18. A 100-g mass of an unknownmaterial at 100 °C is placed in analuminum calorimeter of 60.0 g thatcontains 150 g of water at an initialtemperature of 20.0 °C. The finaltemperature is observed to be21.5 °C. What is the specific heat ofthe substance and what substance doyou think it is?

19. A 100-g mass of an unknownmaterial at 100 °C, is placed in analuminum calorimeter of 60.0-g massthat contains 150 g of water at aninitial temperature of 15.0 °C. Atequilibrium the final temperature is19.5 °C. What is the specific heat ofthe material and what material is it?

20. How much water at 50.0 °C must beadded to 60.0 kg of water at 10.0 °Cto bring the final mixture to20.0 °C?

+21. A 100-g aluminum calorimetercontains 200 g of water at 15.0 °C.If 100.0 g of lead at 50.0 °C and60.0 g of copper at 60.0 °C areplaced in the calorimeter, what is thefinal temperature in the calorimeter?

^ 22. A 200-g piece of platinum is placedinside a furnace until it is in thermalequilibrium. The platinum is thenplaced in a 100-g aluminumcalorimeter containing 400 g of waterat 5.00 °C. If the final equilibriumtemperature of the water is 10.0 °C,find the temperature of the furnace.

74.5 Change of PhaseJ 23. How many calories are needed to

change 50.0 g of ice at - 10.0 °C towater at 20.0 °C?

24. If 50.0 g of ice at 0.0 °C are mixedwith 50.0 g of water at 80.0 °C whatis the final temperature of themixture?

y 25. How much ice at 0 °C must bemixed with 50.0 g of water at75.0 °C to give a final watertemperature of 20 °C?

26. If 50.0 g of ice at 0.0 °C are mixedwith 50.0 g of water at 20.0 °C,what is the final temperature of themixture? How much ice is left in themixture?

27. How much heat is required toconvert 10.0 g of ice at - 15.0 °C tosteam at 105 °C?

28. In the laboratory, 31.0 g of ice at0 °C is placed into an 85.0-g coppercalorimeter cup that contains 155 g

Chapter 14 Temperature and Heat 421

Nu

29.

of water at an initial temperature of23.0 °C. After the ice melts, the finaltemperature of the water is found tobe 6.25 "C. From this laboratorydata, find the heat of fusion of waterand the percentage error between thestandard value and this experimentalvalue.A 100-g iron ball is heated to 100 °Cand then placed in a hole in a cake ofice at 0.00 °C. How much ice willmelt?

30. How much steam at 100 °C must bemixed with 300 g of water at20.0 °C to obtain a final watertemperature of 80.0 °C?

31. How much steam at 100 °C must bemixed with 1 kg of ice at 0.00 °C toproduce water at 20.0 °C?

32. In the laboratory, 6.00 g of steam at100 °C is placed into an 85.0-gcopper calorimeter cup that contains155 g of water at an initialtemperature of 18.5 °C. After thesteam condenses, the finaltemperature of the water is found tobe 41.0 °C. From this laboratorydata, find the heat of vaporization ofwater and the percentage errorbetween the standard value and thisexperimental value.

+33. An electric stove is rated at 1 kW ofpower. If a pan containing 1.00 kg ofwater at 20.0 CC is placed on thisstove, how long will it take to boilaway all the water?

34. An electric immersion heater is ratedat 0.200 kW of power. How long willit take to boil 100 cm3 of water at aninitial temperature of 20.0 °C?

Additional Problems35. Using the specific heat of copper in

British engineering units determinehow many Btu's are required to raisethe temperature of 30 lb of copperfrom 70.0 °F to 300 °F?

36. A 890-N man consumes 3000 kcal offood per day. If this same energywere used to heat the same weight ofwater, by how much would thetemperature of the water change?

37. An electric space heater is rated at1.50 kW of power. How many kcal ofthermal energy does it produce persecond? How many Btu's of thermalenergy per hour does it produce?

+38. A 0.055-kg mass of lead at an initialtemperature of 135 °C, a 0.075-kgmass of brass at an initialtemperature of 185 °C, and a0.0445-kg of ice at an initialtemperature of —5.25 °C is placedinto a calorimeter containing 0.250kg of water at an initial temperatureof 23.0 °C. The aluminumcalorimeter has a mass of 0.085 kg.Find the final temperature of themixture.

39. A 100-g lead bullet is fired into afixed block of wood at a speed of 350m/s. If the bullet comes to rest in theblock, what is the maximum changein temperature of the bullet?

+40. A 35-g lead bullet is fired into a 6.5-kg block of a ballistic pendulum thatis initially at rest. The combinedbullet-pendulum rises to a height of0.125 m. Find (a) the speed of thecombined bullet-pendulum after thecollision, (b) the original speed of thebullet, (c) the original kinetic energyof the bullet, (d) the kinetic energyof the combined bullet-pendulumafter the collision, and (e) how muchof the initial mechanical energy wasconverted to thermal energy in thecollision. If 50% of the energy lostshows up as thermal energy in thebullet, what is the change in energyof the bullet?

+41. After 50.0 g of ice at 0 °C is mixedwith 200 g of water, also at 0 °C, inan insulated cup of 15.0-cm radius, apaddle wheel, 15.0 cm in radius, isplaced inside the cup and set intorotational motion. What force,applied at the end of the paddlewheel, is necessary to rotate thepaddle wheel at 60 rpm, for 10.0minutes such that the finaltemperature of the mixture will be15.0 °C?

I

r

+42. A 75.0-kg patient is running a feverof 105 °F and is given an alcohol rubdown to lower the body temperature.If the specific heat of the humanbody is approximately 0.830 kcal/(kg °C), and the heat of vaporizationof alcohol is 203 kcal/kg, find (a) theamount of heat that must be removedto lower the temperature to 102 °Fand (b) the volume of alcoholrequired.

43. How much thermal energy isrequired to heat the air in a housefrom 15.0 °C to 20.0 °C if the houseis 14.0 m long, 9.00 m wide, and 3.00m high?

44. A classroom is at an initialtemperature of 20 °C. if 35 studentsenter the class and each liberatesheat to the air at the rate of 100 W,find the final temperature of the airin the room 50 min later, assumingall the heat from the students goesinto heating the air. The classroom is10.0 m long, 9.00 m wide, and 4.00m high.

45. How much fuel oil is needed to heata 100-gal tank of water from 40.0 °Fto 180 °F, if oil is capable ofsupplying 140,000 Btu of thermalenergy per gallon of oil?

46. How much fuel oil is needed to heata 570-liter tank of water from10.0 °C to 80.0 °C if oil is capable ofsupplying 3.88 X 107 J of thermalenergy per liter of oil?

47. How much heat is necessary to melt100 kg of aluminum initially at atemperature of 20 °C? The meltingpoint of aluminum is 660 °C and itsheat of fusion is 90 kcal/kg.

+48. If the heat of combustion of naturalgas is 1000 Btu/ft3, how many ft3 areneeded to heat 26 ft3 of water from60.0 °F to 180 °F in a hot waterheater if the system is 75% efficient?

49. If the heat of combustion of naturalgas is 3.71 X 107 J/m3, how manycubic meters are needed to heat0.580 m3 of water from 10.0 °C to75.0 °C in a hot water heater if thesystem is 63% efficient?

+50. If the heat of combustion of coal is12,000 Btu/lb, how many pounds ofcoal are necessary to heat 26 ft3 ofwater from 60 °F to 180 °F in a hotwater heater if the system is 75%efficient?

51. If the heat of combustion of coal is2.78 X 107 J/kg, how manykilograms of coal are necessary toheat 0.580 m3 of water from 10.0 °Cto 75.0 °C in a hot water heater ifthe system is 63% efficient?

422 Thermodynamics

+52. The solar constant is the amount ofenergy from the sun falling on theearth per second, per unit area and isgiven as SC = 1350 J/(s m2). If anaverage roof of a house is 60.0 m2,how much energy impinges on thehouse in an 8-hr period? Express theanswer in joules, kWhr, Btu, andkcal. Assuming you could convert allof this heat at 100% efficiency, howmuch fuel could you save if #2 fueloil supplies 140,000 Btu/gal; naturalgas supplies 1000 Btu/ft3; electricitysupplies 3415 Btu/kWhr?

53. How much thermal energy can youstore in a 2000-gal tank of water ifthe water has been subjected to atemperature change of 70.0 °F in asolar collector?

54. How much thermal energy can youstore in a 5680-liter tank of water ifthe water has been subjected to atemperature change of 35.0 °C in asolar collector?

55. The refrigerating capacity of someolder air conditioners were rated interms of tons. A 1-ton air conditionerextracted enough thermal energy tofreeze 1 ton of water at 32 °F perday. How much thermal energy isnecessary to freeze 1 ton of water? Ifit takes 24 hr to freeze this water,how much power is expended in Btu/hr and watts? Compare this value tothe rating of modern air conditioners.

56. A 5.94-kg lead ball rolls withoutslipping down a rough inclined plane1.32 m long that makes an angle of40.0° with the horizontal. The ballhas an initial velocity o0 = 0.25 m/s.The ball is not perfectly sphericaland some energy is lost due tofriction as it rolls down the plane.The ball arrives at the bottom of theplane with a velocity v = 3.00 m/s,and 80.0% of the energy lost showsup as a rise in the temperature of theball. Find (a) the height of theincline, (b) the initial potentialenergy of the ball, (c) the initialkinetic energy of translation, (d) theinitial kinetic energy of rotation,(e) the initial total energy of the ball,(f) the final kinetic energy oftranslation, (g) the final kineticenergy of rotation, (h) the final totalmechanical energy of the ball at thebottom of the plane, (i) the energylost by the ball due to friction, and(j) the increase in the temperature ofthe ball.

+57. The energy that fuels thunderstormsand hurricanes comes from the heatof condensation released whensaturated water vapor condenses toform the droplets of water thatbecome the clouds that we see in the

sky. Consider the amount of aircontained in an imaginary box 5.00km long, 10.0 km wide, and 30.0 mhigh that covers the ground at thesurface of the earth at a particulartime. The air temperature is 20 °Cand is saturated with all the watervapor it can contain at thattemperature, which is 17.3 X 10"3kg of water vapor per m3. The air inthis imaginary box is now lifted intothe atmosphere where it is cooled to0 °C. Since the air is saturated,condensation occurs throughout thecooling process. The maximum watervapor the air can contain at 0 °C is4.847 X 10"3 kg of water vapor perm3. (The heat of vaporization ofwater varies with temperatures from600 kcal/kg at 0 °C to 540 kcal/kgat 100 °C. We will assume anaverage temperature of 10.0 °C forthe cooling process.) Find (a) thevolume of saturated air in theimaginary box, (b) the mass of watervapor in this volume at 20.0 °C,(c) the mass of water vapor in thisvolume at 0 °C, (d) the heat ofvaporization of water at 10.0 °C, and(e) the thermal energy given off inthe condensation process, (f) Discussthis quantity of energy in terms ofthe energy that powersthunderstorms and hurricanes.

30 m

10 km

Interactive Tutorialsy 58. Find the total amount of thermal

energy in joules necessary to convertice of mass m-, = 2.00 kg at an initialtemperature ts = —20.0 °C to waterat a final water temperature of t,„ =88.3 °C. The specific heat of ice is c-,= 2093 J/kg °C, water is c„ = 4186J/kg °C, and the latent heat offusion of water is Lf = 3.34 X 105J/kg-

y 59. If a sample of lead shot of mass ms= 0.080 kg and initial temperaturetis = 100 °C is placed into a mass ofwater mw = 0.100 kg in analuminum calorimeter of mass mc =

0.060 kg at an initial temperature /iw= 20.0 °C, what is the finalequilibrium temperature of thewater, calorimeter, and lead shot?The specific heats are water cw =4186 J/kg °C, calorimeter cc = 900J/kg °C, and lead sample cs = 129.8J/kg °C.

y60. Temperature Conversion Calculator.The Temperature ConversionCalculator will permit you to converttemperatures in one unit to atemperature in another unit.

y 61. Specific heat. A specimen of lead,ws = 0.250 kg, is placed into anoven where it acquires an initialtemperature tis = 200 °C. It is thenremoved and placed into acalorimeter of mass mc = 0.060 kgand specific heat cc = 900 J/kg °Cthat contains water, m„ = 0.200 kg,at an initial temperature tm =10.0 °C. The specific heat of water isc„ = 4186 J/kg °C. The finalequilibrium temperature of the waterin the calorimeter is observed to betfyt = 16.7 °C. Find the specific heatcs of this sample.

y 62. Find the total amount of thermalenergy in joules necessary to convertice of mass mi = 12.5 kg at an initialtemperature t„ = —25.0 °C tosuperheated steam at a temperaturetss = 125 °C. The specific heat of iceis ci = 2093 J/kg °C, water is cw =4186 J/kg °C, and steam is cs =2013 J/kg °C. The latent heat offusion of water is L, = 3.34 X 10sJ/kg, and the latent heat ofvaporization is L, = 2.26 X 106J/kg.

y63. A mixture. How much ice at aninitial temperature of tu =— 15.0 °C must be added to amixture of three specimens containedin a calorimeter in order to make thefinal equilibrium temperature of thewater t,„ = 12.5 °C? The threespecimens and their characteristicsare sample 1: zinc; msl = 0.350 kg,cs, = 389 J/kg °C, initialtemperature thl = 150 °C; sample 2:copper; ms2 = 0.180 kg, cs2 = 385J/kg °C, initial temperature ris2 =100 °C; and sample 3: tin; ms3 =0.350 kg, cs3 = 226 J/kg °C, initialtemperature /is3 = 180 °C. Thecalorimeter has a mass mc = 0.060kg and specific heat cc = 900J/kg °C and contains water, m„ =0.200 kg, at an initial temperature ft„= 19.5 °C. The specific heat ofwater is c„ = 4186 J/kg °C.

Chapter 14 Temperature and Heat 4 2 3