An Earth-sized exoplanet has a radius of and orbits a Sun-like star at a distance…
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
An Earth-sized exoplanet has a radius of 6.0×106m and orbits a Sun-like star at a distance where the star’s radiation intensity (power per unit area incident on a surface perpendicular to the rays) is 900Wm−2. The planet’s Bond albedo is 0.30, meaning that it reflects 30\% of the incident stellar radiation. Assume the planet behaves as a uniform emitter over its entire surface, that its atmosphere does not trap infrared radiation, and that its surface emissivity is initially ε=1.0.
(a) Calculate the total power from the star that is absorbed by the planet.
(b) Write an expression for the total power the planet emits as thermal radiation at an unknown surface temperature T. Identify the geometric factor associated with emission.
(c) Using the condition for radiative equilibrium, determine the planet’s equilibrium surface temperature. Express your answer in kelvins.
(d) Suppose volcanic activity releases gases that reduce the planet’s average surface emissivity to ε=0.90 while all other properties remain the same. State qualitatively and quantitatively (no new calculation required) how the equilibrium temperature would change and explain your reasoning.