A square metal plate of side behaves like an ideal black surface

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

Problem

A square metal plate of side 0.40 m0.40\,\text{m} behaves like an ideal black surface. It is maintained at 1200 K1200\,\text{K} in a large room whose walls are at 300 K300\,\text{K}. (a) Calculate the rate at which the plate emits thermal radiation at this temperature. Use σ=5.67×10−8 W m−2 K−4\sigma = 5.67 \times 10^{-8}\,\text{W m}^{-2}\,\text{K}^{-4}. (b) The plate is later heated so that its rate of emission becomes exactly double the value found in part (a). Determine the new steady temperature of the plate, assuming the room temperature remains 300 K300\,\text{K} and continues to be neglected in the calculation of emission.

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