Question

The Earth has an average temperature of 58.3 ̊F, and radius of 6.38 x 106 m, and an emissivity of 0.986. The Sun has an average temperature of 9941 ̊F, and radius of 6.09 x 1012 m, and an emissivity of 0.986. Calculate the energy emitted by the Earth and the Sun in one day.

Answer 1

Average temperature of Earth T_E=58.3⁰F

first of all we will convert this temperature into kelvin scale-

And average temperature of sun in kelvin-

Total power emitted by any body having surface area A,Emissivity e and temperature T kelvin is-

              -------------------------------------(1)

Where =stephen-Boltzmann constant=5.67 x 10^-8W/m²K⁴

^{For earth total radiated radiated(Energy radiated per second-}

now 1day=24 hours=24x60x60seconds=8.64x10⁴s

So total energy emitted in 1 day-

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Calculations for Sun

^{For earth total radiated radiated(Energy radiated per second-}

where e=emissivity of sun

So total energy emitted in 1 day by sun-