A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is 1727°C and power radiated by the wire is 94.2 W. Its emissivity is where x = ________. (Given and assume that the emissivity of wire material is same at all wa

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Solution

Q.
A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is 1727°C and power radiated by the wire is 94.2 W. Its emissivity is $\frac{x}{8}$ where x = ________.

(Given $σ = 6.0 \times 10^{- 8} {Wm}^{- 2} K^{- 4}, π = 3.14$ and assume that the emissivity of wire material is same at all wavelength.) [2025]

Ans.
(5)

L = 10 cm, d = 0.5 mm, T = 1727°C = 2000 K

Power, P = 94.2 W

$P = ε σ A T^{4}$

$94.2 = ε \times (6 \times 10^{- 8}) (π d L) {(2000)}^{4}$

$94.2 = ε \times (6 \times 10^{- 8}) (3.14) (0.5) (10^{- 3}) (10 \times 10^{- 2}) {(2000)}^{4}$

$ε = \frac{5}{8} \Rightarrow x = 5$

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