# Earth’s surface absorbs an average of about 960. W/m2 from the Sun’s irradiance. The power absorbed is Pabs = (960. W/m2) (Adisc), where Adisc = π(RE)2 is Earth’s projected area. An equal amount of power is radiated so that Earth remains in thermal equilibrium with its environment at nearly 0 K. Estimate Earth’s surface temperature by setting the radiated power from Stefan’s law equal to the absorbed power and solving for the temperature in Kelvin. In Stefan’s law, assume e = 1 and take the area to be A = 4π(RE)2, the surface area of a spherical Earth. (Note : Earth’s atmosphere acts like a blanket and warms the planet to a global average about 30 K above the value calculated here.)

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Earth’s surface absorbs an average of about 960. W/m2 from the Sun’s irradiance. The power absorbed is Pabs = (960. W/m2) (Adisc), where Adisc = π(RE)2 is Earth’s projected area. An equal amount of power is radiated so that Earth remains in thermal equilibrium with its environment at nearly 0 K. Estimate Earth’s surface temperature by setting the radiated power from Stefan’s law equal to the absorbed power and solving for the temperature in Kelvin. In Stefan’s law, assume e = 1 and take the area to be A = 4π(RE)2, the surface area of a spherical Earth. (Note : Earth’s atmosphere acts like a blanket and warms the planet to a global average about 30 K above the value calculated here.)

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Step 1

Write the expression for the power absorbed by the Earth’s surface from the Sun’s irradiance.

Step 2

Write the expression for the Stefan’s law for the power dissipated from a body.

Step 3

As mentioned in the question, power absorbed is equal to the power ...

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