A rectangular steel plate is kept at a uniform temperature of in a large laboratory…

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A rectangular steel plate 60 cm×40 cm60\,\text{cm}\times40\,\text{cm} is kept at a uniform temperature of 1000 K1000\,\text{K} in a large laboratory whose walls are at 300 K300\,\text{K}. One half of the plate is coated with a matt black paint of emissivity ε1=0.90\varepsilon_{1}=0.90 and the other half remains polished with emissivity ε2=0.40\varepsilon_{2}=0.40. Assume each half has uniform emissivity. Use σ=5.67×10−8 W m−2 K−4\sigma = 5.67\times10^{-8}\,\text{W\,m}^{-2}\,\text{K}^{-4}. (i) Derive an expression for the total net power radiated by the entire plate in terms of its dimensions, emissivities and temperatures of the plate and surroundings. (ii) Calculate the numerical value of the total net power radiated by the plate.

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