A solar sail is made of aluminized Mylar having an emissivity of 0.03 and reflec

Question

A solar sail is made of aluminized Mylar having an emissivity of 0.03 and reflecting 98% of the light that falls on it. Suppose a sail with area 1.50 km2 is oriented so that sunlight falls perpendicular to its surface with an intensity of 1.40 103 W/m2. To what temperature will it warm before it emits as much energy (from both sides) by radiation as it absorbs on the sunny side? Assume the sail is so thin that the temperature is uniform and no energy is emitted from the edges. Take the environment temperature to be 0 K. ____ K A solar sail is made of aluminized Mylar having an emissivity of 0.03 and reflecting 98% of the light that falls on it. Suppose a sail with area 1.50 km2 is oriented so that sunlight falls perpendicular to its surface with an intensity of 1.40 103 W/m2. To what temperature will it warm before it emits as much energy (from both sides) by radiation as it absorbs on the sunny side? Assume the sail is so thin that the temperature is uniform and no energy is emitted from the edges. Take the environment temperature to be 0 K. ____ K A solar sail is made of aluminized Mylar having an emissivity of 0.03 and reflecting 98% of the light that falls on it. Suppose a sail with area 1.50 km2 is oriented so that sunlight falls perpendicular to its surface with an intensity of 1.40 103 W/m2. To what temperature will it warm before it emits as much energy (from both sides) by radiation as it absorbs on the sunny side? Assume the sail is so thin that the temperature is uniform and no energy is emitted from the edges. Take the environment temperature to be 0 K. ____ K

Explanation / Answer

Pabsorbed = 0.03 * (1.4 * 103) * (1.5 * 103)2 = 9.45 * 107 W

Sail radiates equally from both sides 2 * (1.50 km)2 = 4.5 * 106 m2

Prad = sigma Ae(T4 - 0) = (5.669 * 10-8 * 4.5 * 106 * 0.03) T4 = (7.65 * 10-3 W/K4) T4

Prad = Pabsorbed

(7.65 * 10-3 W/K4) T4 =  9.45 * 107

T = 333 K

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