Is the luminous efficiency of a 5000 K incandescent greater than that of a 3000 K bulb?

Question

The color temperature represents the color of light emitting from an ideal black body, when heated to said temperature in kelvin, and how an incandescent bulb emits light is close to a black body.

Does this mean a 5000 K incandescent bulb has higher filament temperature when powered than a 3000 K? Does a 5000 K incandescent bulb use more power than a 3000 K (EDIT: under the same brightness in lumens)? Does a 5000 K incandescent bulb produce less brightness than a 3000 K when at the same wattage?

Answer 1

The color temperature represents the color of light emitting from an ideal black body, when heated to said temperature in kelvin

Correct. But the bulb's color temperature may not coincide exactly with the filament temperature. Standard bulb glass absorbs ultraviolet light, which skews the color temperature lower. However we are usually only interested in visible light (ie. what the human eye sees) so this has little practical effect except in situations where the proportion of ultraviolet light is important.

Does this mean a 5000 K incandescent bulb has higher filament temperature when powered than a 3000 K?

Not necessarily. An incandescent filament run at 5000 K would produce much more visible light for the same power input as a 3000 K filament, due to the larger proportion of energy radiated in the visible region. But it would quickly burn out.

So how are 5000 K incandescent bulbs a thing? By placing a 'blue' (actually cyan) filter over the bulb. This increases the color temperature by absorbing longer wavelengths. Here is an example:-

OSRAM COOL BLUE ADVANCE H7 5000K

This bulb puts out less visible light than an equivalent unfiltered bulb of the same wattage.

Now you may ask, what is the point of making a headlight bluer if it reduces the light output? Wouldn't that just make the road ahead harder to see? Not necessarily. Most of the human eye has a higher density of rods (monochrome sensors, more sensitive to green light) than cones (color sensors), and the rods are more sensitive at low light. 5000 K is closer to daylight, so objects appear closer to their expected colors than they would in 'warmer' light. Filtering out excessive red light makes the perceived image sharper and easier to see, particularly in the peripheral area that is important for driving safety.

Answer 2

If you took some incandescent light bulb and applied a voltage to it such that its filament glows at 3000K and you measured the power consumed by this light bulb;
then, with this same light bulb, you adjust the voltage until its filament glows at 5000K and again measure the power consumed;
then yes you'll almost certainly observe that this particular bulb consumes more power at 5000K than it does at 3000K.

But you'd be ignoring the fact that at 5000K the bulb was also emitting more light than it was at 3000K.

So the really useful measurement here would be the efficiency of the light bulb - how does its light output change as a function of power consumed at those different color-temperature values?
I don't have the data, but my intuition says that at lower color-temperatures the light bulb will be turning a greater fraction of its power consumed into heat instead of light, resulting in lower efficiency at lower color-temperatures.

But then you'd also have to consider if the heat output of the light bulb is actually useful too. I've read anecdotes where traffic-lights were 'upgraded' from incandescent bulbs to LEDs - but this was in an area which sees significant snowfall during winter. The old incandescent bulbs warmed the traffic lights enough to mostly keep the snow melted while the new LEDs did not - resulting in the 'upgraded' lights no longer being visible...

Answer 3

To add to the answer by brhans, which is mostly correct, I will mention that an incandescent bulb draws far more power at lower light levels, due to the lower filament resistance. That's why some say it's not worth it to shut the light off when exiting a room and coming back 10seconds later. As others have stated, though, the question does not give adequate information. If we presume the same quantity of photons emitted from a linear source, we ought factor in the photon energy based on light wavelength. Tables exist for that.

Answer 4

What filament material can remain solid at 5000K for long enough to make a useful incandescent bulb?

The nearest I can think of is an old-style photographic flashbulb, where the filament is magnesium. And the answer is, it uses less electrical power because the main energy source is the burning magnesium itself. Of course, it only lasts for 20 milliseconds or so...