Temperature of a thin bulb filament

[Baibhab Bose]

In my assignment question, the length L and radius r is given and asked to find out how the Temperature of a thin bulb filament which depends on those two parameters. and the answer is r^(1/4)*L^(-1/2). I can't figure out how. Which relation is involved?

 

[trurle]

For constant voltage at ends,
T~r^1/4L^-1/2
Use Stefan-Boltzmann law and neglect ambient temperature.

 

[Baibhab Bose]

For constant voltage at ends,
T~r^1/4L^-1/2
Use Stefan-Boltzmann law and neglect ambient temperature.

I still can't get this. Stefan Boltzmann law states only Power radiated= σT^4. But where do we get the L and r?

 

[trurle]

I still can't get this. Stefan Boltzmann law states only Power radiated= σT^4. But where do we get the L and r?

L and R affect both radiated power (by Joule-Lenz law) and surface area of filament which affect radiated power density

 

[Baibhab Bose]

Okay! Got it! Thank you so much!

 

[DrClaude]

This question should have been asked in the homework forum. Filling out the homework template would have been useful.

Thread closed,