# AP Physics Heat Transfer and Thermal Expansion

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1 AP Physics Heat Transfer and Thermal Expansin Heat Flw: Heat can flw frm ne system t anther nly if there is a temperature difference between the tw systems. The greater the difference in temperature, the faster heat will flw. temperature difference Ht Cld r H TC The directin f heat flw is frm a high temperature system t a lw temperature system. Heat can nly flw in this directin. There is n lgical reasn fr this; after all, isn t it reasnable t think that in the winter heat culd flw frm the cld utside int the warm inside f yur huse? It wuld cut yur energy bill. Unfrtunately, that will never happen. Heat flws frm the high temperature system t the lw temperature system. When an bject absrbs heat, its particles must smehw gain kinetic energy. They d this by absrbing heat. There are three ways that heat can be transferred between systems: cnductin, radiatin, and cnvectin. The teacher hpes that yu are familiar with these. This is the kind f stuff that yu d in elementary science classes. Nnetheless, they will be described belw. Heat Transfer: Materials that allw heat t flw thrugh them easily are called heat cnductrs, materials which d nt allw heat t flw thrugh them are called heat insulatrs. Cnductin is heat transfer by direct cntact between tw systems. When yu sit n a really ht car seat and burn yur hide, yu have gained heat via cnductin. Heat will flw frm the ht system t the cld system until thermal equilibrium is reached. At that pint heat will n lnger flw. What happens in cnductin is that the particles in the ht bject, placed against the cld bject, have cllisins with the particles in the cler system. In these cllisins, the particles in the high temperature system lse energy and the particles in the lw temperature system gain energy. The thermal energy transfers thrugh the cl system via cllisins between the particles until the particles in the tw systems have the same average kinetic energy. We say that the systems have reached thermal equilibrium when this happens. Radiatin is heat transfer via electrmagnetic waves. A great deal f the energy frm the sun reaches the earth in the frm f electrmagnetic waves. They travel thrugh space. When yu g utside n a warm spring day and bask in the warmth f the sun, yu are absrbing heat that has radiated frm the sun. Electric space heaters that have thse glwing red heat elements prvide mst f their heat via radiatin in the same way. Mst f the heat that yu get frm a fireplace (r a camp fire fr that matter) arrives via radiatin. The electrmagnetic waves travel thrugh space and are absrbed by the system, the absrbed energy is cnverted int the kinetic energy f the particles makes them mve back and frth. Cnvectin is heat transfer via fluid flw. A fluid absrbs heat at ne lcatin and then flws t anther place where it transfers the heat it absrbed t sme ther system. Cnvectin is used t heat hmes via frced air furnaces. A large fan blws warm air int the rms f the huse thrugh ducts. Cler air is drawn in thrugh grates and returned t the furnace fr heating. Ovens d mst f their heating via cnductin. An element in the bttm f the ven heats air. The heated air then circulates arund and arund in the ven transferring heat t the fd yu want t ck. 210

2 It is quite cmmn t have multiple frms f heat transfer in a system. Burning gasline in a car engine heats the engine blck by cnductin. Water is circulated thrugh water channels in the engine blck absrbing heat via cnductin. It then carries the heat t the radiatr this is cnvectin. The heat is then transferred frm the water t the radiatr via cnductin. Air circulates thrugh the radiatr remving heat via cnductin (when the air is in direct cntact with the metal fins f the radiatr). The heated air then departs, remving the heat frm the radiatr via cnvectin. Heat Transfer by Cnductin: Materials that allw heat t flw thrugh them easily are called heat cnductrs, materials which d nt allw heat t flw thrugh them are called heat insulatrs. Heat cnductrs are things like metals. Metals are gd cnductrs because f the nature f the chemical bnd that binds the atms tgether. These bnds are called metallic bnds. The significant thing abut the bnds are that sme f the electrns f each atm are nt bund t any ne particular atm they re kind f like cmmunity electrns belnging t everyne. They are very lsely held and can mve arund thrughut the metal. These are knwn as free electrns. The free electrns carry the heat frm ne part f the metal t anther. They d this via cllisins wherein ne electrn gives sme f its energy t anther. This can happen very quickly s that the heat transfers quite easily. Insulatrs d nt have handy little particles that can cllide with each ther transferring energy frm ne place t anther. There are n free electrns t d this. If it is a slid, then the electrns are ging t be tightly held via cvalent r inic bnds. Gases make very gd insulatrs because there aren t many particles t carry the energy frm ne place t anther. Clearly a vacuum wuld be even better! Mst insulatrs are actually materials that have lts f little pckets f air (r a fancy gas) in them. The gas slws the flw f heat dwn. Therms bttles are very interesting. Yu can put a ht fluid in the thing and it will stay ht r yu can put a cld fluid in it and the fluid will stay cld. The questin is this, Hw des the bttle knw what t d? Maybe a micrchip thingee? Hmmm. Well, actually, therms bttles are very simple devices. The have an external metal r plastic bdy, inside f this bdy is a glass bttle. Really gd therms bttles have a vacuum between the uter case and glass bttle. The glass bttle is mirrred. Heat is kept frm flwing by the vacuum which prevents cnductin and cnvectin. The mirrr surface prevents heat flw by radiatin the mirrr reflects the electrmagnetic waves (infrared waves, right?). S therms bttles d a pretty gd jb f blcking the flw f heat cming either int r ut f the bttle. S it can keep ht things ht and cld things cld withut micrprcessrs. Let us lk at a slab f material. One side f the material is at a high temperature and the ther side is expsed t a lw temperature. Because f the temperature difference, heat will flw thrugh the slab. The rate at which heat is transferred thrugh an bject is prprtinal t the amunt f heat that travels thrugh the bject divided by the time: H t Where H is the heat flw rate, is the quantity f heat transferred, and t is the time. The amunt f heat that makes it thrugh depends n thickness f the substance, the area f the bject, and the thermal prperties f the material. The thermal prperties are expressed in what is called the thermal cnductivity f the substance. Each material has its wn value fr its thermal cnductivity. This thermal cnductivity is a measure f the ability f a substance t transfer heat. The symbl fr thermal cnductivity is 211 T H A L T C

3 k. Materials that have a large value fr k are gd heat cnductrs, materials with lw k values make gd insulatrs. The heat flw rate fr the slab is given by this equatin: H ka L Where H is the heat flw rate, k is the thermal cnductivity, A is the area, is the temperature difference, and L is the thickness f the material. H will have units f J/s, J/min, Cal/h, etc. Since H ka L and H, Then = H t s, substituting in fr H, we get: t k At L This wuld give us the amunt f heat flw that wuld ccur in a given time. S what can we see frm this equatin? Well, the heat is directly prprtinal t the temperature difference and the area. It is indirectly prprtinal t the thickness f the slab. Duble the area, duble the heat flw. Duble the temperature difference, duble the heat flw. Etc. Hwever if yu duble the thickness, the heat flw decreases by tw s it is nly ne half f what it was befre. k can have many different units. Tw cmmn W J units are r m K m s C Thermal Cnductivities J/s m C Aluminum 238 Cpper 397 Gld 314 Irn 79.5 Lead 34.7 Silver 427 Air Fiberglass Hydrgen Drywall 0.16 Brick 0.71 Asbests 0.25 Cncrete 1.3 Glass 0.84 Crk Rubber 0.2 Water 0.60 Wd 0.10 Generally ne lks up the required k values. One culd als wrk them ut experimentally. A brick ven is 15.0 cm thick. The inside temperature is C. The utside temperature is 25.0 C. Hw much heat is lst frm ne side f the ven in ne hur? The side measures 85.0 cm x 60.0 cm. Thermal cnductivity f brick? Use 0.71 J/s m C. k At J C 25.0 C m 0.60 m s L ms C 0.15 m J kj 212

4 Thermal Expansin: When heat is added t a system, the particles gain kinetic energy. Since their average kinetic energy increases, the temperature increases. Since the particles have increased their kinetic energy, they mve faster and further. Each particle takes up mre rm, s the bject as a whle expands. It expands in all directins. Engineers and architects have t allw fr the expansin f materials with temperature increases when they design things r else the whle thing culd break apart n a cld r ht day. Lng structures like bridges have expansin jints t allw fr the expansin f the structure with changing temperatures. Many devices make use f the expansin f materials. Bimetallic strips are used t cntrl the peratin f cling r heating devices. A bimetallic strip is made f tw metals that are bnded tgether. Each metal expands a different amunt, s ne f the metals expands mre than the ther. This causes the strip t curve when the temperature changes. This can be used t switch electrical circuits n and ff, cntrlling an air cnditiner r a heater. There are three types f thermal expansin that can ccur: linear, area and vlume. We begin with linear expansin. Essentially, if a rd is heated up r cled dwn, the rd will expand r cntract respectively. Linear Expansin: The change in length f a heated rd is given belw: Where ΔL is the change in length, α is the cefficient f linear expansin, L 0 is the riginal length f the rd, and is the temperature difference in the material. The change in length f a rd is directly prprtinal t the temperature difference in the material and the cefficient f linear expansin. Generally ne lks up the value f α, but it culd be slved fr if enugh infrmatin is given. A cpper (α = 1.7 x 10-5 C 0-1 ) pipe is 90 m lng at 20 0 C. What is its new length when steam passes thrugh the pipe at C? m Area Expansin: The change in area f a heated surface is given belw: 2 Where ΔA is the change in area, α is the cefficient f linear expansin, A 0 is the riginal area f the surface, and is the temperature difference in the material. Vlume Expansin: The change in vlume f a heated bject is given belw: Where ΔV is the change in vlume, β = 3α is the cefficient f vlume expansin, V 0 is the riginal vlume f the bject, and is the temperature difference in the material. 213

5 Dear Dctr Science, At hme we play this little game f placing an ice cube n a smth table and then shaking sme salt n tp f it. After abut 30 secnds the ice is stuck t the table. It smetimes requires a lt f frce t disldge it. Why des this happen? --- jhn lutz frm Seattle, WA Dr. Science respnds: I share yur queer idea f fun. My lab assistant and I used t sprinkle salt n slugs, until smene reprted us fr mllusk abuse, and we were frced t take sensitivity training s mind numbing it almst cst me my sanity. In yur little game, the ice sticks t the table because salt is a natural aphrdisiac, causing the ice t mate with the table. Yes, salty water is randy water, which is why the sea is s ften used as a symbl f rmance. Peple sigh when they lk ut at the sea, and ften feel a lump in their, uh, thrat and an ache in their heart, bth f which are ften signs f zne pisning, caused by temperature inversins trapping smg alng the shreline, but yu prbably knew that already. Dear Dctr Science, The defrster in my car desn't wrk very well and I'm ften frced t scrape the frst ff the inside f my windshield while I'm driving. Why is there always mre frst directly in frnt f me than in any ther area f the windshield? -- Brian Price frm Nrflk, VA Dr. Science respnds: Yur car is trying t kill yu. If I were yu, I'd trade it in as sn as pssible. This defrster malfunctin is nly the tip f the iceberg, s t speak. One day the brake pedal will be suspiciusly sft, and then when yu're heading int a curve yu'll find yu have n brakes at all. I nce heard f a Saab that fried its wner with the driver's seat warmer. By the way, never stick yur head thrugh a sun rf, even in jest. Thse things can clse very quickly, even with n ne at the cntrl. Yes, new cars are intelligent, flashy, and unbelievably malevlent. 214

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