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Basic Physics of the Incandescent (Lightbulb) Dan MacIsaac, Gary Kanner,andGraydon Anderson

ntil a little over a century ago, artifi- transferred to electronic excitations within the Ucial was based on the emis- solid. The excited states are relieved by pho- sion of radiation brought about by burning tonic emission. When enough of the radiation fossil fuels—vegetable and animal oils, emitted is in the so that we waxes, and fats, with a wick to control the rate can see an object by its own visible , we of burning. Light from coal gas and natural say it is incandescing. In a solid, there is a gas was a major development, along with the near-continuum of electron energy levels, realization that the higher the temperature of resulting in a continuous non-discrete spec- the material being burned, the whiter the trum of radiation. and the greater the light output. But the inven- To emit visible light, a solid must be heat- tion of the incandescent electric lamp in the ed red hot to over 850 K. Compare this with Dan MacIsaac is an 1870s was quite unlike anything that had hap- the 6600 K average temperature of the ’s Assistant Professor of pened before. Modern lighting comes almost photosphere, which defines the color mixture Physics and at entirely from sources. In the of and the visible spectrum for our Northern Arizona University. United States, about a quarter of electrical eyes. It is currently impossible to match the He received B.Sc. (physics) consumption is attributed to lighting, half of color mix of sunlight with any filament and B.Ed. (math and sci- that in incandescent . So an understand- because we have no substance that can be ence ) degrees ing of the basic electrical and optical charac- heated to this temperature and remain solid. from Mount Allison Univ- ersity, an M.A. ( edu- teristics of the lightbulb is an appropriate sub- Of all solid filament materials, has cation) from the University ject for study in the introductory physics class. the highest known melting temperature (3680 of British Columbia, and an The first incandescent lamps consisted of a K) and the lowest rate of evaporation (vapor M.S. (physics) and Ph.D. filament of wire in an evacuated ) of the pure . Carbon can with- (science education) from bulb, two ends of the wire being brought out stand higher temperatures without melting, Purdue University. His inter- through a sealed cap and then to the electric but evaporates too rapidly. Compounds and ests are in physics educa- supply. A major improvement was the devel- alloys (usually and nitrides) tion research and high- opment of metallic filaments, particularly with higher melting temperatures and lower school teacher preparation, those made of tungsten, now used almost evaporation rates exist, but these are brittle and his hobbies include exclusively in lightbulbs. and tend to disassociate at these very high classical trumpet and motor- Incandescent lighting is very economical temperatures. cycle riding. and nonhazardous to manufacture, although Tungsten’s high and low Department of Physics less energy efficient than other lighting tech- vaporization pressure make it the metal of and Astronomy 1 Northern Arizona nologies. The vapor fluorescent choice, but the vaporization pressure limits University tube is more efficient; however, many states maximum useful filament temperature to Flagstaff, AZ 86011-6010 are passing restrictive regulations regarding about 3000 K. It is extremely difficult to [email protected] disposal of such tubes. Currently, the most maintain an average temperature higher than efficient commercial light source (in terms of about 2900 K in standard incandescent bulbs, visible light output to input energy) is the resulting in radiation distributions like those high-pressure . shown in Sidebar 1. At these temperatures, only a small fraction of the radiated energy Incandescent Lighting occurs in the visible wavelengths—less than occurs when electrical 10%, with most remaining energy radiated resistive heating creates thermally excited away at (IR) wavelengths. Hence, atoms. Some of the thermal kinetic energy is incandescent filaments are quite inefficient

520 THEPHYSICSTEACHER Vol. 37, Dec.1999 Basic Physics of the Incandescent Lamp (Lightbulb) Bulb envelope Fill gas for visible light production, and their light is quite reddish-yellow. Low-temperature fila- ments (2500 to 2700 K) are particularly rich in red spectral energy and tend to bring out red in skin complexions, making people appear healthier. Higher temperature fila- ments (2800 to 2900 K) are relatively richer in blue wavelengths, and are paradoxically Filament called “cooler” in the color sense. Lead-in While far from ideal for visible light emis- Wires sion, these filament temperatures are still enormous (about 3000 K, or 5000 ЊF), likely the hottest phenomenon we will closely encounter in our lifetimes, unless we are Glass rod welding. Achieving and sustaining these tem- peratures requires many technical innova- tions (Fig. 1). Lighting manufacturers describe the effi- Fuse Exhaust ciency measurement orefficacyof incandes- Tube cent lamps as the amount of visible light pro- duced in lumens per watt (LPW) of electrical Base power consumed. A bar of tungsten heated to its melting point has a theoretical maximum efficacy of 52 LPW. Practical studio flood Gary S. Kanneris a visiting Assistant Professor at the Eyelet lamps achieve 33 LPW, standard 60-W household lamps with a rated lifetime of 1000 Department of Physics and Astronomy at Northern Fig. 1. Components of a standard household lightbulb hours achieve 14.5 LPW, or 870 lumens total. Arizona University while on of 60 W, 120 VAC. Looking at the Lightbulb leave of absence from Los • Bulb envelopeis made of soft soda-lime glass; Alamos National Laboratory, top operating temperature ~ 400 ЊC. A lightbulb’s glass envelope is designed to where he has been a techni- keep water vapor and oxygen away from the • Fill gas—usually to retard filament evapo- cal staff member in a metal- ration with some nitrogen to eliminate arcing— filament, which would otherwise oxidize the lurgy group, after having circulates by convection. metal within seconds. Household bulbs are served as postdoc there for • Exhaust tube extends through bulb base and is usually made of soda-lime glass. Silica and several years. He received used to evacuate, flush, and fill bulb before being Pyrex™ (borosilicate) can be used for higher a B.A. in physics from sealed off. temperatures, to improve durability, or for Brandeis University, an M.S. in physics from Brown • Base, made of aluminum and brass, is - transparency. The intricate coiled- ed to the bulb; cement failure is first sign of bulb’s coil mechanical design of the filament is University, and a Ph.D. in overheating. physics from the University designed to retain as much thermal energy as of Utah. His research inter- • Eyelet is contact point to which electrical hot wire possible while increasing surface area and ests are in optical properties is soldered. Electrical return wire is soldered to aspect ratio (Fig. 2). The lead-in threaded side portion of base. of , and he wires that support the filament and conduct likes to compete in • Fuseprotects household circuit by melting if fila- current to it retain their strength at high tem- ment arcs. triathlons. peratures. The National Electric Code speci- Department of Physics • Glass rodwith button that supports wires placed fies that the lead-in wire soldered to the eye- in it. and Astronomy let (the bottom brass button) must incorporate Northern Arizona • Lead-in wiresmade ofthree welded metal sec- a short fuse element and then be connected to University tions carry current to and from filament, passing Flagstaff, AZ 86011-6010 through glass seals called the stem press. Wires the “hot” ac connection. Return is through the are designed to match expansion coefficient of threaded aluminum side of the base. All mod- the glass. ern household bulbs over 25 W are internally • Coiled-coil tungsten filamentis designed to fused. When properly installed, it is the hot maintain temperature and glows yellow/orange side that is fused (hence the current use of hot at 3000 K (5000 ЊF). Filament is supported by mechanical clamps to lead-in and tie wires. polarized plugs for lamps). An electrostatically applied inside coat of fine silica powder called standard coat

Basic Physics of the Incandescent Lamp (Lightbulb) Vol. 37, Dec. 1999 THEPHYSICSTEACHER 521 Fig. 2. Scanning electron micrograph (SEM) of a coiled-coil filament from a 60-W lamp (500X magnifi- cation). Filament winding is an incredi- ble technical feat; readers are encour- aged to break a bulb and examine the fila- ment closely with a hand lens.

spreads the brilliant filament light diffusely cacy for melting tungsten will be surpassed. by Mie scattering.2 In high-temperature bulbs, an additional may be used to Filament Coils keep the base cool by preventing radiative The automated mass of Graydon Anderson com- warming and restricting the convection flow incandescent filaments intended for operation pleted his Ph.D. in physical of the “fill gas” throughout the base. at over 2500 K is a significant technical chemistry at Cornell Most modern bulbs use argon as the inert achievement. Just drawing brittle tungsten University in 1975. For most fill gas, with a small amount of nitrogen to into wire required the development of a spe- of the time since then he impede arcing. Argon’s high molecular cial process involving doping with potassium, has worked as an experi- mentalist at the Los Alamos weight and low retards pressing and tungsten ingots, then National Laboratory on a the tungsten’s evaporation and insulates the swaging, lubricating, and finally drawing the very diverse set of projects, filament, thereby allowing for high tempera- wire. The filament coils are made by first coil- including isotope sepa- tures. The preferred gas is too expen- ing finedrawn tungsten wire around a molyb- ration, sensing of high-ener- sive, except for specialty lamps where long denum wire called a mandrel, then gy particle beams, and the life span is a priority (traffic-signal lights, for the assembly in a hydrogen-filled furnace. measurement of the physi- example). Orienting the filament vertically to Annealing removes internal stresses and cal properties of supercriti- align it with circulating streams in the fill gas allows the assembly to be coiled a second cal fluids. Outside of work, helps maintain consistent filament tempera- time around a retractable stainless-steel man- he enjoys the study of the ture. Pressure of the fill gas is about 80% of drel and then cut to length. A second anneal- physics of everyday events atmospheric pressure when cold, rising to ing is followed by an immersion in acid to and common objects, and 3 has a special interest in atmospheric when in use, thereby reducing dissolve the inner molybdenum mandrel. making physics comprehen- strain on the glass envelope. Lightbulbs The filament is then ready for mounting by sible to nonspecialists. smaller than 25 W require no fill gas,just a mechanical clamping to two lead-in wires. These pedagogical inter- partial free of oxygen and water Filaments gradually degrade, and light- ests, as well as his long- vapor. bulbs darken as tungsten evaporates from the term passion for photogra- Traditional lightbulb design is intended to filament surface to be deposited on the inner phy, led to the present col- maximize filament temperature, lifetime, surface of the glass envelope. In the univer- laboration. mechanical integrity, and efficacy. Some day, sally familiar upright bulb envelope (called Los Alamos National filament lamp systems will exceed the theo- the A envelope shape by manufacturers), con- Laboratory retical maximum efficacy of melting tungsten vection currents in the fill gases will carry the Los Alamos, NM 87545 because of new reflective bulb coatings. Such tungsten atoms to the top of the envelope to coatings (which reflect IR energy back into accrete and blacken the bulb. Tungsten evap- the bulb to further heat the filament) are cur- orates from the filament at higher temperature rently under development, and when suffi- locations, creating a cycle: cient IR energy is reclaimed into visible since filament hot spots evaporate faster, wavelengths, the theoretical maximum effi- locally thinned filament locations will devel-

522 THEPHYSICSTEACHER Vol. 37, Dec.1999 Basic Physics of the Incandescent Lamp (Lightbulb) op higher electrical resistances that rise in temperature, A Student Experiment thereby reinforcing localized evaporation. A simple measurement can show the dramatic effect of At startup, tungsten filaments are so cool that the initial temperature on resistivity of tungsten. Measure the resis- “inrush current” is 10 times greater than operating current, tance of a 60-W bulb with an ohmmeter. The built-in volt- leading to strong magnetic forces between adjacent coils age is provided by a 1½-V battery. The resistance will be of the filament. This thermal and mechanical stress about 18 ⍀. Consider, however, that when the bulb is used ensures that most degraded household bulbs will fail or in a 120-V circuit, its resistance must be R = (120 V)2/60 “burn out” in their first second of cold startup. Expensive W = 240 ⍀. The current surge when the bulb is first turned quartz infrared lamps counter this effect by preheating on is about 7 A. with a low voltage during startup. Acknowledgments The Tungsten Halide Cycle The authors wish to acknowledge the comments and The blackening of a bulb due to evaporated tungsten discussion of the PHYS-L list subscribers Joseph Bellina, deposits can be reduced or eliminated by introducing David Bowman, Leigh Palmer, Brad Shue, Larry Smith, traces of a gas such as or . These and Brian Whatcott. In particular we recognize the cogent engage in a temperature-dependent cycle with critique and guidance of Lance Kaczorowski, PHYS-L tungsten vapor in which tungsten halide forms at lower subscriber and lighting engineer. PHYS-L is an internet temperatures (on the inside of the bulb envelope). mailing list devoted to physics and physics education. See Tungsten halide dissociates at the higher temperatures on http://purcell.phy.nau.edu/PHYS-L for details. the filament. This halide cycle will return tungsten atoms Photography by Dan Boone, Imaging Specialist at the from the fill gas and the silica envelope to the filament. Bilby Research Center, Northern Arizona University; scan- While bulb blackening is tremendously reduced, tungsten ning electron microscopy by Marilee Sellers, Manager of is unfortunately not returned to the thinnest parts of the fil- the Electron Facility, Northern Arizona ament—the only halogen that can do this is fluorine, University. which is not yet safely controllable. filaments not only canbe run hotter and References more efficiently, but mustbe run at higher temperatures to 1.See, for instance, OSRAM Sylvania publications: initiate and sustain the halogen cycle. Therefore, for halo- Bulletin IN002 (Incandescent Lamp gen bulbs, a very small tubular envelope made of fused sil- Manufacture); Engineering Bulletin IN003 ica (a noncrystalline quartz) is operated at temperatures up (Incandescent Lamps); Engineering Bulletin 0-349 to 1200 ЊC (depending on bulb type and wattage), togeth- (Tungsten Halogen Lamps); and the 1996 catalogs for Light Products and Large Lamps. See also the General er with a high-pressure fill gas (about five atmospheres). Electric publicationIncandescent Lamps. To ensure full lamp life, halogen filaments should be run at least 20 minutes to initiate the halogen gas cycle and 2.E. Hecht, Optics(Addison Wesley, 1987), p. 539. fill-gas convection. Compared with non-halogen bulbs 3.A standard 60-W 120 VAC lamp fila- ment starts as a 53.3-cm length of tungsten wire having whose envelopes are made of soda-lime glass and are typ- 5 ically operated at 200 to 400 ЊC, these bulbs are much a 46-micron (4.6ϫ 10 m) diameter. It is first wound into a coil of 1130 turns 8.3 cm in length over a greater and explosion hazards.4 molybdenum mandrel and then coiled a final time to 2 Halogen lamps are often not tolerant of changing orien- cm in length around a steel mandrel. tations because of their strong dependence on convection 4. Underwriter Laboratories refuses to certify halogen gas currents. Halogen lamps are whiter and hotter (usually torchiere (floor standing) lamps over 300W as safe. 3000 to 3500 K) than ordinary bulbs, and the system is http://gohper.fiu.edu/orgs/ehs/halogen.htm suggests more efficient (10 to 12% of the spectral energy is in visi- that consumers replace bulbs over 300 W in such ble wavelengths). Halogen lamps have become standard in lamps. For further safety, high-wattage halogen lamps automobile and projector bulbs, and for photo- should also have glass bulb shields. graphic use. 5.B. Merik in Light and Color of Small Lamps(General Electric publication). 6.Handbook of Chemistry and Physics, 75th ed. (Chemical Rubber Company, Boca Raton, 1994), p. 10- 296.

Basic Physics of the Incandescent Lamp (Lightbulb) Vol. 37, Dec. 1999 THEPHYSICSTEACHER 523 Sidebar 1. Incandescent Lamp Emission Curves

To calculate the portion of light emitted 12 at visible wavelengths, we compare the fila- 2.5 x 10 2800K (60W bulb) ment to a theoretical blackbody radiator. The 2870K (100W bulb) rate P at which any object emits energy via 2900K (150W bulb) r 2.0 visible region )

electromagnetic radiation is dependent upon 3 m

its area and temperature to the fourth power: /

␴⑀ 4 W P = A T , where in SI units P is power ( 1.5 r obj r )

radiated in watts, ⑀is the emissivity (⑀= 1 T , for a theoretically perfect radiator (or a ( 1.0 I “blackbody”), Aobj is the object’s surface area in m2, and Tis temperature of that area in kelvin. 0.5 At a particular wavelength ␭, the radia- U.V. Infrared tion emitted by a perfect blackbody radiator 0 is described by Planck’s radiation law: 0 1000 2000 3000 4000 5000 6000 ␲ 2 Wavelength (nm) ␭ ᎏ2 hᎏc ᎏ1ᎏ I(, T) = 5 –hc/␭kT ␭ e –1 Fig. 1. Blackbody radiation curves for three different temperatures, corresponding where T is the temperature (in K), h is to lamps of different power ratings. Shaded area shows wavelength region of visible light. For clarity, the area in the visible region for a 150-W bulb is shown, which Planck’s constant, cis the speed of light, and entirely overlaps respective areas of 60- and 100-W bulbs. kis Boltzmann’s constant (1.3 ϫ10-23J/K). I(␭,T) is known as the spectralexitance, which is a flux W/m2 • T4). In this calculation we have made two ide- of power per unit area per unit wavelength, and there- alizations: first we ignored the transmissivity of the fore has SI units of W/m3. Figure 1 shows the spectrum glass envelope; its effect on visible light would be of I(␭,T) for perfect blackbodies at three different tem- small. The portion of light emitted in the visible range peratures corresponding to the operating temperatures is about 10%. Second, by treating tungsten as a black- of tungsten bulbs operating at 60, 100, and 150 W.1 body, we have also ignored the emissivity ⑀, which is Only a small fraction of a bulb’s intensity is emitted dependent on both wavelength and temperature. The at visible wavelengths (390 to 780 nm), as indicated by emissivity of tungsten decreases the emission by a sub- the shaded area in Fig. 1. This fraction was determined stantial amount (more than a factor of two in the visi- (Table I) for three bulbs by numerically computing the ble) and shifts the maximum of I(␭, T) slightly towards area A(T) under each curve in the visible region and shorter wavelengths.5However, since the spectrum of then dividing that area by the total radiant flux ⑀for tungsten is approximately independent of Tfor I(T) for each temperature. I(T) is given by the Stefan- lightbulb operating temperatures, the spectrum of I(␭, Boltzmann law: T) for tungsten will behave like a blackbody of a some- ϱ what different T. Additionally, the ratio of ␭ ␭ ␴ 4 I(T)= ΎI(,T)d= T Acurve(T)/I(T) is still close to 10% for real tungsten 0 because the blue shift of I(␭,T) due to ⑀is small. where ␴is the Stefan-Boltzmann constant (5.67ϫ10-8

Power Temperature Visible flux Total radiant % Emission density A(T) flux I(T) in visible (W) (K) (105W/m2) (106W/m2) A(T)/I(T) 60 2800 3.389 3.49 9.7

100 2870 4.124 3.85 10.7

150 2900 4.474 4.01 11.2

Table I. Lightbulb characteristics at visible wavelengths, as determined from Planck’s radiation law and the Stefan-Boltzmann law (assumes ⑀= 1).

524 THEPHYSICSTEACHER Vol. 37, Dec.1999 Basic Physics of the Incandescent Lamp (Lightbulb) Sidebar 2. Optical and Electrical Properties of an Incandescent Lamp

We measured the current-voltage characteristics of a " clear" lamp GE®60-W “crystal clear” incandescent lamp to show optical pyrometer how the filament resistance increases dramatically as the filament heats up. The clear glass bulb envelope also allowed us to simultaneously measure the temperature of the filament using an optical pyrometer. Apparatus setup is shown in the figure. at 60 Hz was supplied to the bulb by a Variac that could adjust the voltage from 0 to 140 V. Digital multimeters (Tektronix DM501) simultaneously i measured the voltage and current supplied to the fila- rms ment. Filament temperature was measured using a Leeds ammeter and Northrup model 8622-C optical pyrometer. V In an optical pyrometer, the image of the object rms voltmeter whose temperature is to be measured is superimposed on the image of a standard filament inside of the pyrometer. 0-120V A red filter limits the bandwidth to the wavelength 60 Hz region of 0.65 microns. The operator varies the current in the standard filament until it appears to have the same This equation can be solved to determine the true brightness as the unknown object. For this reason, the corrected value of Tfor the graybody given the bright- measured temperature is often referred to as the bright- ness temperature TB measured by the pyrometer and nesstemperature. The current-adjusting dial is calibrat- the value of the emissivity of the source, ⑀. A small ed to directly read out the “effective blackbody temper- complication in our lamp experiment: the glass enve- ature” of the unknown object. lope reduces the brightness of the filament by approx- Usually, the object to be measured is not a true black- imately 8%, due to 4% reflection losses at each glass body, necessitating a correction to the temperature deter- surface. However, this can easily be treated as an effec- mination. In effect, we ask the question, “What temper- tive reduction in the emissivity of the source. ature would a graybody (an imperfect blackbody) with Reference 6 gives the emissivity of tungsten at 0.65 emissivity ⑀require in order to be as bright at ␭= 0.65 microns and at temperatures near 2900 K as ⑀= 0.420. ␮ m as a blackbody at temperature TB?” The answer We calculate an effective emissivity for a filament in a ⑀ comes from the Planck distribution law. Equating the glass envelope using eff= (0.92)(0.420) = 0.386. ⑀ brightness of a graybody with an equivalent blackbody, Knowing eff, TB, and the constants, we numerical- we get ly solve the equation for the values of corrected fila- ment temperature Tas shown in Table II. The results of 2␲hc2⑀ 1 2␲hc2 1 our measurements and the applied corrections due to ᎏᎏ ᎏᎏ = ᎏᎏ ᎏ the effective emissivity are given in the table. Note the ␭5 ehc/␭kT–1 ␭5 ehc/␭kTB –1 large increase (14.4ϫ) in the filament resistance between room temperature and the normal operating point of the lamp.

rms voltage rms current Power Filament Apparent Corrected (volts) (amperes) (watts) resistance blackbody filament (ohms) temperature temperature TB(kelvin) T (kelvin) 0 0 0 16.85 -NA- 297 70.27 0.3710 26.07 189.4 2223 2459 79.99 0.3976 31.80 201.2 2278 2526 90.00 0.4234 38.11 212.6 2373 2644 100.04 0.4479 44.81 223.3 2468 2762 109.97 0.4710 51.80 233.5 2563 2882 119.95 0.4931 59.15 243.3 2588 2913

Table II. Current-voltage-resistance-temperature characteristics of a clear 60-W incandescent lightbulb.

Basic Physics of the Incandescent Lamp (Lightbulb) Vol. 37, Dec. 1999 THEPHYSICSTEACHER 525