The filament of an incandandescent light bulb is a very thin solid cylindrical s

Question

The filament of an incandandescent light bulb is a very thin solid cylindrical shape, with a total length of 350 mm and a diameter of 0.42 mm. The filament is made of tungsten which has a melting point of about 3965 K and emissivity of about 0.04. It has a temperature of about 3000 °C when on and fully warmed up. To save space, the filament is then loosely coiled (into a larger hollow cylinder)- this is simply to save space, but you may assume these coils are packed loosely enough so the total surface area of the filament can radiate to the environment. The filament is inside a glass bulb filled with argon gas (this serves to reduce the evaporation rate of the filament.) Photo: Incandescent light bulb filament magnified 50 times. Note the break in the middle- this filament is burnt out. a.) What is the total surface area of the filament? (Not including endcaps.) m2 b.) What is the size of the radiative power output of the bulb? (i.e. what is the wattage reading on the light bulb's package, assuming you use it as recommended?) IPI- Why don't conduction and convection play much of a role in the heat transfer from the filament? c.) What is the peak wavelength emitted by this light bulb? How does this compare to visible light? Is this bulb "energy efficient"? d.) What is the lowest peak wavelength you could get out of this light bulb before the filament melted? nm nm

Explanation / Answer

surface area A = 2*pi*r*L

r = radius = D/2

D = diameter = 2r = 0.42mm = 0.42*10^-3 m

L = length of the filament = 350 mm =350*10^-3 m

surace area = pi*D*L = pi*0.42*10^-3*350*10^-3 = 0.0004618 m^2 <<<<-------ANSWER

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b)

radiation power P = e*sigma*A*T^4

sigma = stefans constant = 5.67*10^-8 W/m^2K^4

e = emissivity = 0.04

T = 3000 + 273 = 3273 K

power = 5.67*10^-8*0.04*0.0004618*3273^4 = 120.2 W

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c)

From wein's displacement law of radiation

lambda*T = constant = 2.9*10^-3

wavelength = lambda = 2.9*10^-3/T

for peak wavelength    T = 3273 K

lambda = 2.9*10^-3/3273 = 886 nm <<<<-------ANSWER

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(d)

for lowest peak   T = 3965 K

lambda = 2.9*10^-3/3965 = 731 nm   <<<<-------ANSWER

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