Astronomers observe a transient “hot spot” on the surface of a distant star

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

Problem

Astronomers observe a transient “hot spot” on the surface of a distant star. The spot is circular, has a radius of

4.0\times10^{6}\,\text{m}

, and maintains an approximately uniform surface temperature of 8200 K for 5.0 min before fading. The surrounding stellar surface remains at its normal temperature of 5800 K. Take

\sigma = 5.67\times10^{-8}\,\text{W}\,\text{m}^{-2}\,\text{K}^{-4}

. (a) Calculate the instantaneous radiant power produced by the hot spot while it is at 8200 K. (b) Determine the total extra thermal energy (beyond what the same region would emit at 5800 K) radiated by the spot during the 5.0 min interval. (c) Earth receives about

1.7\times10^{17}\,\text{J}

of solar energy each second. Express the energy found in part (b) as an equivalent number of seconds of Earth-received solar energy. Discuss briefly what this comparison reveals about the flare’s magnitude.

Related theory

Browse the problem library