Temperature of a 100 W Light Bulb Filament

Temperature of a 100 W Light Bulb Filament Joran Booth and Peter Hyatt ME 340 Winter 2009

Heat Transfer Problem o. Measured the electrical power dissipated o. Measured the bulb surface temperature and the ambient temperature o. Measured the diameter of the light bulb o. Measured the thickness of the glass ASSUMPTIONS: o. Near vacuum inside the light bulb o. Geometry is a sphere o. The radiation is a point source o. Filament treated as a sphere o. All electrical work converted to heat

Solution Tavg ρ c. P μ ν k α Pr beta 332 1. 0549 1008 2. 00 E-05 1. 91 E-05 2. 87 E-02 2. 72 E-05 0. 703 3. 01 E-03 Øfil = 0. 06149 Øinner = 0. 0595 Øouter = 0. 06 k. N = 2 σ= Tin = TS = T∞ = 5. 67 E-08 368 300 hr 1 = hr 2 = h= Nu = 481. 0875139 8. 111165792 6. 56 E+00 13. 71767276 R 1 = R 2 = R 3 = R 4 = -0. 0434 7. 00 E-01 0. 00028 53. 901 Ra = 8. 34 E+05 R 5 = 43. 6038 kglass = 81 q= 96 W Afil = 0. 00283 εglass = 0. 95 Rtotal = 24. 8045 without R 1 εW = 0. 38 Tfilament = 2681 K Ts = 2681 Aglass = 2. 97 E-03 Ts = 95ºC sources show: T = 2550ºC cuu Va m Tfilament= ? knitrogen = 81 W/m·K As , ε 60 mm Ø 0. 5 mm thick Glass �Online qin = 96 W

Results Degrees Kelvin Area vs. Temperature 12000 110000 9000 8000 7000 6000 5000 4000 3000 2000 1 E-07 11709 Area versus Temperature 4316 2681 1 E-06 1 E-05 1 E-04 1 E-03 Meters squared 1 E-02 Emissivity vs. Temperature 5200 Degrees Kelvin 5000 4983 5010 4800 4600 4400 4316 4200 4000 3800 0, 15 0, 25 0, 35 Emissivity 0, 45 Emissivity vs. Temperature

Conclusions and Recommendations �The temperature is between 4500 to 2500˚C. �Main contributors to Tfilament: ◦ Surface Area of Filament ◦ Vacuum v. Conduction thru gas �Measure different filament styles �Verify/modify assumptions with other measurements

Appendix �http: //answers. yahoo. com/question/ind ex? qid=20080508134327 AAlv 437. �Fundamentals of Heat and Mass Transfer, Incropera, 6 th Edition. �http: //members. misty. com/don/bulb 1. h tml

Additional Graphs Area vs. Temperature 3050 Degrees Kelvin 2950 2934 2850 2750 2643 2615 Area vs. Temperature 2550 2450 1 E-07 1 E-06 1 E-05 1 E-04 1 E-03 Meters squared 1 E-02 Emissivity vs. Temperature Both graphs based on assumption of pure nitrogen inside bulb with no convection 2645 Degrees Kelvin 2644 2643 2642 0, 15 0, 25 0, 3 Emissivity 0, 35 0, 4 Emissivity vs. Temperature

Calcuations Assuming a vacuum A 1 = 2. 97 E-03ε 1 = A 1 = 2. 97 E-05ε 1 = Ts = 0. 38 Ts = 2681 K A 1 = 2. 97 E-05ε 1 = 4316 K A 1 = 2. 97 E-05ε 1 = 2681 0. 38 Ts = 4320 Ts = 0. 38 Ts = 4316 K A 1 = 2. 97 E-07ε 1 = 5010 K A 1 = 2. 97 E-05ε 1 = 4320 0. 27 Ts = 4320 Ts = 0. 38 Ts = 11709 K 11690 0. 18 Ts = 4983 K 4984 Assuming nitrogen filled A 1 = 2. 97 E-03ε 1 = Ts = A 1 = 2. 97 E-05ε 1 = Ts = 0. 38 Ts = 2615 K A 1 = 2615 0. 38 Ts = 2643 2. 97 E-05ε 1 = Ts = 2643 K A 1 = 2. 97 E-05ε 1 = Ts = 0. 38 Ts = 2643 K A 1 = 2643 0. 27 Ts = 2643 2. 70 E-07ε 1 = Ts = 2643 K A 1 = 2. 70 E-05ε 1 = Ts = 0. 38 Ts = 2934 K 2933. 96 0. 18 Ts = 2644 K