Two stars, X and Y

PHYSICS · Subjective · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

Two stars, X and Y, behave as perfect blackbodies. Star X has twice the radius of star Y. The wavelength corresponding to maximum emission is

400\,\text{nm}

for X and

700\,\text{nm}

for Y. (i) Determine the ratio of their surface temperatures

T_X:T_Y

. (ii) Calculate the ratio of their total luminosities

L_X:L_Y

. (iii) If both stars are located at the same distance from the Earth, which star would appear brighter? Justify your answer quantitatively.