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.)

Question

Aicharya · Accepted Answer

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

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is $1727^{\circ}…

Solution