Wattage of a light bulb?

Question

The temperature at which pure tungsten melts is about 3400 K. Assuming the filament of an incandescent light bulb has an operating temperature safely below this value, say 2900 K, at what wavelength does its spectrum peak? The filament has a diameter of 0.3 mm and a length of 10 cm. What is the wattage of the light bulb?

Answer 1

Peak wavelength can be found from Wien's Displacement law:
λ(max) = b/T,
where b = 2.898 x 10^6 nm·K

To find power, apply the Stefan-Boltzmann law : P = σ·A·T^4.
σ = 5.670×10^−8 W/m^2·K^4.

Figure the area in square meters and plug that and the temperature into the equation.
(edited to add area to equation).

Answer 2

That is more of a physics question, or even engineering. And not a simple one either. You need to calculate how fast a filament of that size made of that material looses heat at that temperature and then convert that heat loss to units of Watts.