Converting Lumens to Joules for 1cm Plastic/Glass Sphere

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SUMMARY

This discussion focuses on converting lumens to joules to estimate the temperature change of a 1cm diameter plastic or glass sphere when illuminated by a bright LED flashlight (1200-2000 lumens). The user seeks to calculate the energy deposited on the sphere over a 15-second exposure time using the formula Q=m*c_p*delta T. Key steps include converting lumens to candelas by measuring the beam angle and using an online converter for candela/m² to watts/cm² per steradian. An alternative approach suggested is to measure the power output of the flashlight directly and calculate energy absorption based on temperature increase.

PREREQUISITES
  • Understanding of thermal energy transfer principles (Q=m*c_p*delta T)
  • Knowledge of photometric units (lumens, candelas)
  • Familiarity with LED flashlight specifications and power output
  • Basic skills in measurement techniques for temperature change
NEXT STEPS
  • Learn how to measure beam angle for accurate lumens to candelas conversion
  • Research the relationship between lumens and watts for LED lights
  • Explore methods for measuring temperature change in small objects
  • Investigate online converters for photometric unit conversions
USEFUL FOR

Individuals interested in thermodynamics, optical engineering, or anyone conducting experiments involving light absorption and temperature changes in small objects.

OpenLaszlo
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(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!
 
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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.