# Problem: During the day, heat from the Sun is absorbed by the Earth's surface.Part (a) Calculate the rate, in watts, at which this heat transfer through radiation occurs (almost entirely in the infrared) from 1.0 m2 to the atmosphere at night. Assume the emissivity is 0.90, the temperature of the surface of the Earth is 15°C, and that of outer space is 2.7 K.Part (b) The intensity of the Sun's radiation at the Earth's distance is about 800 W/m2, but only half of the incoming radiation is actually absorbed by the Earth's surface. What fraction of the rate of radiation absorption by the Earth's surface during the day is reemitted at night?Part (c) What is the maximum magnetic field strength, in microteslas, of the outgoing radiation, assuming it is a continuous wave?

###### FREE Expert Solution

Part (a)

From Stefan-Boltzmann law, the rate of heat radiation is:

$\overline{){\mathbf{j}}{\mathbf{=}}{\mathbf{\sigma \epsilon A}}{\mathbf{\left(}}{{{\mathbf{T}}}_{{\mathbf{2}}}}^{{\mathbf{4}}}{\mathbf{-}}{{{\mathbf{T}}}_{{\mathbf{1}}}}^{{\mathbf{2}}}{\mathbf{\right)}}}$ ###### Problem Details

During the day, heat from the Sun is absorbed by the Earth's surface.

Part (a) Calculate the rate, in watts, at which this heat transfer through radiation occurs (almost entirely in the infrared) from 1.0 m2 to the atmosphere at night. Assume the emissivity is 0.90, the temperature of the surface of the Earth is 15°C, and that of outer space is 2.7 K.

Part (b) The intensity of the Sun's radiation at the Earth's distance is about 800 W/m2, but only half of the incoming radiation is actually absorbed by the Earth's surface. What fraction of the rate of radiation absorption by the Earth's surface during the day is reemitted at night?

Part (c) What is the maximum magnetic field strength, in microteslas, of the outgoing radiation, assuming it is a continuous wave?