Image Caption 1: The compounded helix structure (called a coiled coil) of the tungsten (symbol W, Z=74) filament of a 200-watt incandescent light bulb.

Features:

The total length of a filament is of order 0.5--1 meters and its diameter is typically of order 0.050 mm = 500 microns (μm). The image scale is about 10 mm it seems.
The melting point of tungsten is 3695 K = 3422°C (at about STP) which is the highest of all pure metals. The high melting point is why tungsten can be used for filaments which typically work in the temperature range 2000--3300 K (see Wikipedia: Incandescent light bulb: Construction).
Filaments look white hot due to the psychophysical response of human eye photopic vision (i.e., human eye vision under well lit conditions) (see Temperature of a "White Hot"Object, Carine Fang, 2001; Wikipedia: Thermal radiation: Subjective color to the eye of a black body thermal radiator; Wikipedia: Red heat). However, for their working temperature range 2000--3300 K (see Wikipedia: Incandescent light bulb: Construction), they have a blackbody spectrum peak in the range ∼ 0.88--1.45 μm which is in the infrared 0.7 μm -- 0.1 cm (see Wikipedia: Wien's law).
Actually, incandescent light bulbs are NOT very efficient. Only ∼ < 5 % of the output energy comes out as visible band (fiducial range 0.4--0.7 μm = 4000--7000 Å) (see Wikipedia: Incandescent light bulb: Efficacy, efficiency). The low electrical efficiency is illustrated by Image 2 where one can see that most of the energy of the blackbody spectrum is in the infrared 0.7 μm -- 0.1 cm.
Image Caption 2: The short wavelength part of the near blackbody spectrum of a 25-watt incandescent light bulb. Shown are the ultraviolet band (fiducial range 0.01--0.4 μm) (very low), visible band (fiducial range 0.4--0.7 μm = 4000--7000 Å), and part of the infrared band (fiducial range 0.7 μm -- 0.1 cm). The temperature of the filament may be ∼ 2000 K (see Wikipedia: Incandescent light bulb: Construction).
To explicate the low electrical efficiency of the incandescent light bulbs, note that the filament radiates to good approximation like a blackbody radiator, and so obeys to good approximation Wien's law and the Stefan-Boltzmann law. Because of Wien's law, the filament has to be at ∼ 2000--3300 K (see Wikipedia: Incandescent light bulb: Construction) to radiate significantly in the visible band and that's low enough NOT to melt the tungsten, but so low that only ∼ < 5 % of the output energy is in the visible band (fiducial range 0.4--0.7 μm = 4000--7000 Å) (see Wikipedia: Incandescent light bulb: Efficacy, efficiency).
Most of the output energy comes out in the infrared band (fiducial range 0.7 μm -- 0.1 cm) and dissipates into heat energy in the surroundings (i.e., into waste heat).
Because of low electrical efficiency, incandescent light bulbs might be phased out in the near future in favor of fluorescent lamps and light-emitting diodes (LEDs).
Why is the coiled coil filament is used? It gives a larger radiating surface area per volume than any other practical radiating filament allowing the filament to output a high radiant flux (AKA radiant power) without having the filament temperature exceed the melting point of tungsten. One has give an explication with to show that this is so.
Explication:
1. In general, radiating strength for an object increases at least roughly as its surface-area-to-volume ratio increases all other things being equal, particularly with volume equal.
2. The smallest surface-area-to-volume ratio is for a sphere (more exactly a solid sphere (AKA ball)) which you might have guessed since a sphere seems maximally compact. (see Wikipedia: Surface-area-to-volume ratio). So a sphere seems a good standard of comparison for the surface-area-to-volume ratio of any other object of the same volume.
3. The surface-area-to-volume ratio of a long cylinder (so long that its end areas are negligible) in ratio to surface-area-to-volume ratio a sphere of the same volume as the cylinder and depending only on cylinder parameters is derived as follows:
```
  R = (2πaL)/(4πr**2)    cylinder to sphere surface area ratio where "a" is cylinder radius,
                               L is cylinder length, and r is sphere radius.

  πa**2*L = (4π/3)*r**3  equating cylinder volume to sphere volume to solve sphere radius.
  r = [(3/4)*a**2*L]**(1/3)    sphere radius r.
 
  R = (1/2)*(4/3)**(2/3)*[aL/(a**2*L)**(2/3)]   cylinder to sphere surface area ratio with r eliminated.

  R = (1/2)*(16/9)**(1/3)*(L/a)**(1/3)          simplied cylinder to sphere surface area ratio.

  R = (2/9)**(1/3)*(L/a)**(1/3)                 exact formula.
 
  R  = (0.6057 ...)(L/a)**(1/3)                 exact formula with decimal fraction coefficient .  
```
4. From the R formula, you see you can make the ratio R arbitrarily large by increasing L/a in ideal theory keeping volume fixed (and therefore amount of tungsten used fixed in a filament). In practice, there are limitations on the how large L/a can be.
5. Now both a cylinder and a sphere of tungsten will have the same output radiant flux (AKA radiant power) for input electrical power (wattage) by conservation of energy ideally in theory. But to make up for its relatively low radiating surface area, the sphere will radiate at a much higher temperature than the cylinder. So you would have to keep the temperature of the sphere much lower than you would for the cylinder, and so keep its output radiant flux (AKA radiant power) lower and the amount of radiant flux (AKA radiant power) in the visible band (fiducial range 0.4--0.7 μm = 4000--7000 Å) probably very low.
6. Note cylinder filament is wrapped into coiled coil filament to make the cylinder filament compact, but NOT as compact as a sphere of the same volume.

Images:

Credit/Permission: User:Lander777, 2007 / Public domain.
Image link: Wikipedia: File:Filament.jpg.
Credit/Permission: © User:Thorseth, 2015 / CC BY-SA 4.0.
Image link: Wikimedia Commons: File:Spectral power distribution of a 25 W incandescent light bulb.png.

local link: light_incandescent_filament.html

Electromagnetic Radiation file

light_incandescent_filament.html