Re: luminous efficiency

[Larry Woolf <larry.woolf@GAT.COM>]

Carl Mungan wrote:
> > > I agree that higher wattage means higher
> > > filament temperature, which tends to increase the light output in the
> > > visible by Wien's law.
Then Larry Woolf  wrote:
> > The light output also increases because of the increasing filament
diameter
> > and length (higher surface area for light emission) for larger wattage
> > bulbs:
> >
> > 25 W            0.0030 cm dia   56 cm length        ratio=1.0
> > 75 W            0.0053 cm dia   55 cm length            3.2
> > 100 W           0.0064 cm dia   58 cm length            4.4
> > 200 W           0.0102 cm dia   72 cm length            9.0
Then Carl E. Mungan responded:
> True, but I was thinking specifically of increasing the luminous
> efficiency
> which is the ratio of visible output in lumens to electrical
> power in watts.
> Note that most of the change in filament size alters both of these values
> proportionately. Specifically, I added a fourth column to your
> table above,
> namely the ratio of diameter squared to length, normalized to
> unity for the
> first entry. This ratio tracks pretty closely with the power, as you can
> see, the discrepancy indicating some variation in resistivity with
> temperature.
>
> However, another factor which does change the luminous efficiency is the
> variation in emissivity with temperature.

Your comment immediately above is re: P=V^2/R  = (V^2 *A)/(rho*L) so yes,
the electrical power dissipated in the filament will be proportional to
D^2/L.

I was looking at the (light) power emitted by the filament: P~A*(T^4). The
filament temperature does increase somewhat as the bulb wattage increases,
which increases the relative proportion of light emitted in the visible
region, as Carl noted earlier in his comment about Wien's Law.  However, the
total visible light output increases to a significant extent because of the
increase in emitting surface area of the filament, which is proportional to
diameter*length. From the calculation below, it appears that about 50% of
the light emission increase results from the increase in emitting area, the
remainder then is due to an increase in filament temperature (or emissivity
change).

25W     D*L = 0.168             Ratio = 1
75W     D*L = 0.292             Ratio = 1.7
100W    D*L = 0.371             Ratio = 2.2
200W  D*L = 0.734               Ratio = 4.4

Larry Woolf
General Atomics
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