Need help on this Light bulb Filament Temperature with emissivity and δ given

[sickid]

Hi, I am stuck on this question, any help would be appreciated. Thanks!

1. The tungsten filament of a certain 100 W light bulb radiates 2.85 W of light. (The other 97.15 is carried away by convection and conduction) The filament has surface area of 0.400 mm^2 and an emissivity of 0.952. Find the filament's temperature in kelvin. (melting point of tungsten is 3683 K) Take δ 5.6696 X 10^-8 W/m^2.K^4

I tried to use the formula: P=eδAT^4 but I still can't get the right answer. I tried to do a search on internet, come across a lot of problem related to the above mentioned but the resistence and ohm is known. If you could point me to the right way, providing the right formula would be very much appreciated.

 

[andrevdh]

What temperature did you get?

 

[kyle8921]

Sure, let me help you with this question. First, let's start by understanding the given information. We know that the light bulb is emitting 2.85 W of light, which means that the remaining 97.15 W is being carried away by convection and conduction. We also know the surface area of the filament (0.400 mm^2) and its emissivity (0.952).

To solve for the filament's temperature, we can use the Stefan-Boltzmann law, which states that the power radiated by an object is proportional to the fourth power of its absolute temperature (in kelvin). In other words, the formula you mentioned, P=eδAT^4, is correct.

To use this formula, we need to rearrange it to solve for the temperature (T). It should look like this: T = (P/eδA)^1/4. Now, we can plug in the values we know: T = (2.85/0.952 x 5.6696 x 10^-8 x 0.000000400)^1/4 = 2,949 K.

However, this is not the final answer yet. We need to convert this temperature from kelvin to Celsius by subtracting 273.15. This gives us a final temperature of 2675.85°C. Since the melting point of tungsten is 3683 K (3409.85°C), this temperature seems reasonable.

I hope this helps you understand the problem and how to solve it. It's important to remember to always double-check your units and make sure they are consistent. Keep practicing and you'll get the hang of it!