An Introduction to Modern Astrophysics · Problem 9.5

The Interiors of Stars — Carroll & Ostlie

Physics — Astrophysics · stefan-boltzmann-derivation

Problem

Consider a spherical blackbody of radius RR and temperature TT. By integrating Eq. (9.8) for the radiative flux with Iλ=BλI_\lambda = B_\lambda over all outward directions, derive the Stefan–Boltzmann equation in the form of Eq. (3.17). (You will also have to integrate over all wavelengths and over the surface area of the sphere.)

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