A star with surface area normally radiates uniformly at a temperature of

PHYSICS · Single correct · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A star with surface area 5.0×1012 m25.0\times10^{12}\,\text{m}^{2} normally radiates uniformly at a temperature of 5.0×103 K5.0\times10^{3}\,\text{K}. During a brief flare, the surface temperature jumps to 6.0×103 K6.0\times10^{3}\,\text{K} and remains at that value for 15 min15\,\text{min} before returning to normal. Assuming the surface area stays unchanged and using σ=5.67×10−8 W m−2 K−4\sigma = 5.67\times10^{-8}\,\text{W}\,\text{m}^{-2}\,\text{K}^{-4}, what is the additional energy radiated by the star because of the flare (compared with the energy it would have emitted had the flare not occurred)? (a) 1.7×1022 J1.7\times10^{22}\,\text{J} (b) 3.3×1023 J3.3\times10^{23}\,\text{J} (c) 1.7×1023 J1.7\times10^{23}\,\text{J} (d) 1.3×1023 J1.3\times10^{23}\,\text{J}

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