### Temperature of a 100 W Lightbulb Filament

```Temperature of a 100 W Light
Bulb Filament
Joran Booth and Peter Hyatt
ME 340
Winter 2009
Heat Transfer Problem
oMeasured the electrical power dissipated
oMeasured the bulb surface temperature
and the ambient temperature
oMeasured the diameter of the light bulb
oMeasured the thickness of the glass
ASSUMPTIONS:
oNear vacuum inside the light bulb
oGeometry is a sphere
oThe radiation is a point source
oFilament treated as a sphere
oAll electrical work converted to heat
Solution
Tavg
ρ
cP
μ
ν
k
α
Pr
beta
332
1.0549
1008
2.00E-05
1.91E-05
2.87E-02
2.72E-05
0.703
3.01E-03
Øfil = 0.06149
Øinner = 0.0595
Øouter =
0.06
kN =
2
σ=
Tin =
TS =
T∞ =
5.67E-08
368
368
300
hr1 =
hr2 =
h=
Nu =
481.0875139
8.111165792
6.56E+00
13.71767276
R1 =
R2 =
R3 =
R4 =
-0.0434
7.00E-01
0.00028
53.901
Ra =
8.34E+05
R5 =
43.6038
kglass =
81
q=
96 W
Afil =
0.00283
εglass =
0.95
Rtotal =
24.8045
without R1
εW =
0.38
Tfilament =
2681
K
Ts =
2681
Aglass = 2.97E-03
Tfilament= ?
knitrogen
= 81
W/m·K
As, ε
Ts =
95ºC

Online sources show:
T = 2550ºC
60 mm Ø
0.5 mm
thick
Glass
qin = 96
W
Results
Degrees Kelvin
Area vs. Temperature
12000
11709
11000
10000
9000
8000
7000
6000
5000
4316
4000
3000
2681
2000
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02
Area versus
Temperature
Meters squared
Degrees Kelvin
Emissivity vs. Temperature
5100
5000
4900
4800
4700
4600
4500
4400
4300
4200
5010
4983
Emissivity vs.
Temperature
4316
0.15
0.2
0.25
0.3
Emissivity
0.35
0.4
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
qid=20080508134327AAlv437 .
 Fundamentals of Heat and Mass Transfer,
Incropera, 6th Edition.
 http://members.misty.com/don/bulb1.html

Degrees Kelvin
Area vs. Temperature
3000
2950
2934
2900
2850
2800
2750
2700
2650
2643
2615
2600
2550
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02
Area vs. Temperature
Meters squared
Degrees Kelvin
Emissivity vs. Temperature
2645
2644
2644
2644
2644
2644
2643
2643
2643
2643
2643
Both graphs based on assumption of
pure nitrogen inside bulb with no
convection
2644
Emissivity vs.
Temperature
2643
0.15
0.2
0.25
0.3
Emissivity
2643
0.35
0.4
Calcuations
Assuming a vacuum
A1 =
2.97E-03ε1 =
A1 =
2.97E-05ε1 =
Ts =
Ts =
0.38Ts =
2681K A1 =
2.97E-05ε1 =
4316K A1 =
2.97E-05ε1 =
2681
0.38Ts =
Ts =
4320
Ts =
0.38Ts =
4316K A1 =
2.97E-07ε1 =
5010K A1 =
2.97E-05ε1 =
4320
0.27Ts =
Ts =
4320
Ts =
0.38Ts =
11709K
11690
0.18Ts =
4983K
4984
Assuming nitrogen filled
A1 =
2.97E-03ε1 =
Ts =
A1 =
2.97E-05ε1 =
Ts =
0.38Ts =
2615K A1 =
2615
0.38Ts =
2643
2.97E-05ε1 =
Ts =
2643K A1 =
2.97E-05ε1 =
Ts =
0.38Ts =
2643K A1 =
2643
0.27Ts =
2643
2.70E-07ε1 =
Ts =
2643K A1 =
2.70E-05ε1 =
Ts =
0.38Ts =
2934K
2933.96
0.18Ts =
2644
2644K
```