The length of the filament is 0.2 m.
To find the answer, we need to know about the Stefan - Boltzmann law.
What's Stefan - Boltzmann law?
- It states that the intensity of power radiated from a body is propertional to the fourth power of temperature of the object.
- Mathematically, I= e×σ×T⁴
- I= intensity, e= emissivity, σ= a constant with value 5.67×10^(-8) W/(m²K⁴), T= temperature
- As intensity= power/area, so power= area ×e×σ×T⁴
What's the length of the filament having diameter 0.1 mm, temperature 2500K, emissivity 0.35 and radiating power of 40W?
- Here, e= 0.35, T= 2500K, power= 40W
- If L= length of the filament, its area = (2πd/2)L= πdL
- So, power= π×d×L ×e×σ×T⁴
L= power/(π×d×e×σ×T⁴)
= 40/(π×0.0001×0.35×5.67×10^(-8)×2500⁴)
= 0.2m
Thus, we can conclude that the length of the filament is 0.2 m.
Learn more about the Stefan - Boltzmann law here:
brainly.com/question/18273651
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