Star A and star B are both perfect black bodies

PHYSICS · Subjective · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics

Problem

Star A and star B are both perfect black bodies. The surface temperature of star A is

T_A = 6000\,\text{K}

, while that of star B is

T_B = 7500\,\text{K}

. The radius of star B is

0.80

times the radius of star A. (a) Write an expression for the luminosity

L

of a spherical black-body star in terms of its radius

R

and surface temperature

T

. (b) Hence calculate the ratio

\dfrac{L_B}{L_A}

. (c) If the luminosity of star A is

3.9 \times 10^{26}\,\text{W}

, estimate the numerical value of the luminosity of star B.