How to determine temperature of filament?

[HHeCNeOSiFe]

I was wondering in class today how I could determine the temperature of a filament in an incandescent light bulb? Mainly then so I could determine the thermal energy outputted through radiation. So after school I used a test circuit.

I started with the Stefan-Boltzmann law which is Q = (ε)(σ)(T⁴)(A)(t)
First I substituted 60s into the equation as my time, 0.191 as my emissivity constant and for Area I measured 1.1x10^-5m²

So finally I got Q = (60s)(0.191)(5.670367 W/m²K⁴*10^-8)(1.1x10^-5m²)(T⁴) ⇒ Q = 7.1480646402×10^-12(T⁴)

I am so close to my answer but I simply don't know how to figure out how to get temperature from my knowledge of circuits!
I had my powersource to stay at 4.0 Volts and my lightbulb was 1.44 Watts type so we just turn that into
1.44W = 4.0V(I) ⇒ (1.44W/4.0V) = I ⇒ 0.36 amperes = I
and for resistance it is just 4.0V = 0.36A(R) ⇒ 4.0V/0.36A = R ⇒ 11Ω ≅ R.

From there I have no idea of how to determine the temperature of the filament so any and all help would be appreciated, thank you!

 

[Simon Bridge]

Welcome to PF;
The temperature of a glowing object is usually estimated from its spectrum.
You could calculate it from theory from specific heat, and the rate that heat is radiated away (if the filament is in vacuum)... knowing that this is a steady state.