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 95% of the light that falls on it. Suppose a sail with area 1.08 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 to be 0 K. (Use = 5.6696 10-8 W/m2 · K4 for the Stefan-Boltzmann constant.)

_______K

Explanation / Answer

Power absorbed = I * a * A, where I is the intensity, a is the absorbance, and A is the surface area

Power emitted = e * (2 * A) * sigma * T^4 (from Stefan-Boltzmann Law. Note the factor of 2 because it is emitting from both sides of the sail).

Power absorbed = Power emitted

Therefore I * a * A = e * (2 * A) * sigma * T^4, (a = 1- r = 1 - 0.95 = 0.05)

Solving for T,

T = [ I * a / (2 * e * sigma) ] ^ (1/4)

I get 506.566 K.

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