Question

A wire of length \(L\) and diameter \(d\) is used in a bulb. The temperature of wire is \(T\) and power radiated by the wire is \(P\). Its emissivity is (\(σ\) = Stefan's constant) (Assume that emissivity of wire material is same at all wavelength)

• A. \(\frac{P}{σT^4πdL}\)
• B. \(\frac{P}{σT^2πdL}\)
• C. \(\frac{P}{σT^2πd^2L^2}\)
• D. \(\frac{P^2}{σT^4πdL}\)

Hint:

Use the Stefan-Boltzmann law $P=e\sigma AT^4$ with the curved surface area $\pi dL$.

Answer 1

The Correct Option is A

Step 1: Write the law
\(P=e\sigma AT^4\) where \(A\) is the radiating surface area.

Step 2: Surface area
The wire is a cylinder of diameter \(d\) and length \(L\), so the curved area is \(A=\pi dL\).

Step 3: Solve for \(e\)
\(e=\frac{P}{\sigma T^4\pi dL}\). Option (A).

Final Answer:
The emissivity is \(\frac{P}{\sigma T^4\pi dL}\), option (A). \[ \boxed{\text{(A)}} \]