A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is \(1727^{\circ} \mathrm{C}\) and power radiated by the wire is 94.2 W. Its emissivity is \(\frac{x}{8}\) where \(x=\)_______
(Given \(\sigma=6.0 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}, \pi=3.14\) and assume that the emissivity of wire material is same at all wavelength.)

\(\mathrm{L}=10 \mathrm{~cm}, \mathrm{~d}=0.5 \mathrm{~mm}, \mathrm{~T}=1727^{\circ} \mathrm{C}=2000 \mathrm{~K}\)
Power, \(\mathrm{P}=94.2 \mathrm{~W}\)
\(\mathrm{P}=\varepsilon \sigma \mathrm{AT}^4\)
\(94.2=\varepsilon \times\left(6 \times 10^{-8}\right)(\pi \mathrm{dL})(2000)^4\)
\(94.2=\varepsilon \times\left(6 \times 10^{-8}\right)(3.14)(0.5)\left(10^{-3}\right)\)
\(\left(10 \times 10^{-2}\right)(2000)^4\)
\(\varepsilon=\frac{94.2}{(94.2)(16)}=\frac{5}{8}\)