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Radiative transfer

Blackbody

An isotropic blackbody surface has outward flux $F=\pi\int B_\nu\,d\nu=\sigma T^4$. A sphere of radius $R$ therefore has luminosity
$$
L=4\pi R^2\sigma T^4.
$$


Luminosity of a spherical blackbody

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 68 / 2 / Solution

Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 315 / 4 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 315 / 4 / c / Solution

Luminosity of a spherical blackbody

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Luminosity of a spherical blackbody

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