Thermal Properties of Mat question bank (Physics)

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.)

Consider a rectangular sheet of solid material of length $\ell=9 \mathrm{~cm}$ and width $\mathrm{d}=4 \mathrm{~cm}$. The coefficient of linear expansion is $\alpha=3.1 \times 10^{-5} \mathrm{~K}^{-1}$ at room temperature and one atmospheric pressure. The mass of sheet $\mathrm{m}=0.1 \mathrm{~kg}$ and the specific heat capacity $\mathrm{C}_{\mathrm{v}}=900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$. If the amount of heat supplied to the material is $8.1 \times 10^2 \mathrm{~J}$ then change in area of the rectangular sheet is :-