For example 100 watt incandescent bulb produces 1600 lumens.
Led 23 watt can produce 1600 lumens.
Is there minimum amount of watts needed ?
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Yes, there is a fundamental limit. It comes down to two factors:
The first question is straightforward - by conservation of energy, 1W of electrical energy can yield at most 1W of light energy.
The second question is not so straightforward, and depends on the spectrum of the light. The lumens is a unit in photometry, the science of measuring light intensity as perceived by the human eye. By the early 20th century, the notion of perceived intensity was quantified in numerous experiments with human subjects, and a standards body called CIE defined the standard luminosity function to summarize all the findings. The luminosity function defines the number of lumens per watt of light energy for different wavelengths, answering our second question. The function has a peak at 555 nm (green), where its value is 683 lm/W.
Thus, a perfectly efficient light source at 555 nm could produce 683 lm/W - this is the theoretical maximum allowed by the laws of physics. If you wanted white light source, then the maximum is lower (depending on the shade of white) - another answer has quoted 250 lm/W from this document.
Yes there is
the thermodynamic law of Conservation of Energy.
Light is a form of energy, and you can't get more energy out than is put into the system.
This paper http://physics.ucsd.edu/~tmurphy/papers/lumens-per-watt.pdf puts the number at about 250 lm/W for "white" light
I believe the question has been answered (earlier), but not explicitly. The question seems to be if an incandescent bulb requires 100 watts to produce 1690 lumens and an LED 23 watts to produce 1600 lumens, what is the theoretical minimum number of watts required to produce 1600 lumens.
Using Jason and Sergei's answers (and Tom Murphy's paper already linked above), the answer is that an ideal white light source, that is, a 5800 K blackbody truncated to 400 nm - 700 nm range only in emission, would require 3.98 mW minimum per lumen (i.e., at least 3.98 mW to produce 1 lumen of ideal white light as defined). Therefore, the theoretical minimum watts to produce 1600 lumens is 3.98 mW x 1600 = 6.37 watts.