Converting Lumens to Joules for 1cm Plastic/Glass Sphere

[OpenLaszlo]

(Note that this is not a homework question, but rather something I'm pursing in my leisure)

I'd to do a quick calculation to see what sort of power I would need to raise the temperature of a small sphere (1cm diameter, made of plastic or glass) with an absorption coefficient of about .5. I was thinking about using a bright LED flashlight (1200-2000 lumens) to do this. However, I'm having trouble computing how much energy I would be depositing on the sphere (I assume just the front surface). Essentially, I'd like to convert a certain exposure time (maybe 15s or so of illumination) into the units of Joules so I can roughly estimate the temperature change via Q=m*c_p*delta T.

I realize that the first step should be to convert lumens to candelas, which could be done if I can measure the beam angle of the flashlight. Once I have my number in candelas, however, I'm not really sure where to go. I've found a converter online at http://www.unitconversion.org/unit_converter/luminance.html which converts candela/m^2 to Watts/cm^2 per steradian (at 555nm). I'm unsure as to how they arrived at this conversion factor and was hoping someone might be able to lend a little insight.

Thanks!

 

[Andy Resnick]

That seems complicated. Why not just measure the power of your flashlight (say it emits a few mW), estimate how much of that is absorbed by the object (if you held the light directly against the sphere, it would absorb a mW or so), and from that you can calculate how much energy is absorbed after a given amount of time.

Note- converting from lumens to watts is not trivial. And I see that consumer LED specs don't distinguish between power draw and emitted power. So maybe you have to slog through a conversion of lumens to watts, which is nontrivial except for narrowband sources (like lasers). FWIW, a 100W incandescent bulb emits only 1750 lm

http://members.misty.com/don/bulb1.html

Sounds like the easiest thing is to go backwards- shine the light on the sphere, measure the increase in temperature, and infer the light output.