Blundell Thermal Physics · Problem 23.1

Photons

Physics — Statistical Mechanics · stefan-boltzmann-grey-body

Problem

The temperature of the Earth's surface is maintained by radiation from the Sun. By making the approximation that the Sun is a black body, but now assuming that the Earth is a grey body with albedo

A

(this means that it reflects a fraction

A

of the incident energy), show that the ratio of the Earth's temperature to that of the Sun is given by

T_{\text{Earth}} = T_{\text{Sun}}(1-A)^{1/4}\sqrt{\frac{R_{\text{Sun}}}{2D}},\tag{23.65}

where

R_{\text{Sun}}

is the radius of the Sun and the Earth–Sun separation is

D

Related theory

Stefan Boltzmann Law Radiation Pressure

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