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 x/8 where x= -. (Given σ=6.0 × 10 -8 Wm -2 K -4 , π=3.14 and assume that the emissivity of wire material is same at all wavelength.)

Physics · Heat Transfer

JEE Main 2025 — 7 April, Morning Shift — Question 70

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 $x=$ $\qquad$ -.

(Given $\sigma=6.0 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}, \pi=3.14$

and assume that the emissivity of wire material is same at all wavelength.)

Numerical answer — enter this value.

$A=\pi D \times \ell=\pi \times 5 \times 10^{-4} \times 10 \times 10^{-2} \mathrm{~m}^{2}$

\begin{aligned} & \Rightarrow \quad P=\sigma e A T^{4} \\ & \Rightarrow \quad 94.2=\frac{\sigma x}{8}\left(5 \pi \times 10^{-5}\right) \times(2000)^{4} \\ & \Rightarrow \quad x=\frac{94.2 \times 8}{5 \times 3.14 \times 10^{-5} \times(2000)^{4} \times 6.0 \times 10^{-8}} \\ & \Rightarrow \quad x=5 \end{aligned}

Answer key and solution verified before publishing.

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