An astronomer observes a red-giant star that has recently completed a phase of rapid…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
An astronomer observes a red-giant star that has recently completed a phase of rapid expansion. During the expansion, the star’s total power output remained essentially constant while its radius doubled.
Answer the following questions about the star’s surface properties and emitted spectrum. Assume the star behaves as an ideal blackbody.
(a) Qualitatively determine whether the star’s surface temperature after the expansion is greater than, less than, or equal to its surface temperature before the expansion. Provide a clear justification based on the given information.
(b) Based on your answer to part (a), state how the wavelength at which the star’s emission is most intense changed (shifted toward longer wavelengths, shorter wavelengths, or remained the same). Explain your reasoning.
(c) On a set of axes with wavelength on the horizontal axis and spectral intensity on the vertical axis, sketch two smooth curves—one representing the star before expansion and one after expansion. Label each curve clearly. Your sketch should accurately depict the qualitative changes described in parts (a) and (b).
(d) Provide a concise verbal explanation connecting your results in parts (a) through (c) to the physical relationship among power output, surface area, surface temperature, and the shape of a blackbody spectrum.