A red-giant star initially possesses a radius of and an effective surface temperature of
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
A red-giant star initially possesses a radius of 2.5R⊙ and an effective surface temperature of 3.4×103K. Astronomers predict that during the next phase of its evolution the star’s surface temperature will rise to 5.1×103K while its total luminosity remains effectively constant.
(a) Derive an expression for the star’s final radius in terms of its initial radius and the two surface temperatures.
(b) Using the result from part (a), calculate the numerical value of the final radius in meters and in solar-radius units.
(c) Determine the factor by which the star’s average surface energy emission per unit area changes between the two stages. Provide a brief interpretation of this change in terms of stellar surface conditions.