A solar sail is made of aluminized Mylar having an emissivity of 0.0300 and refl

Question

A solar sail is made of aluminized Mylar having an emissivity of 0.0300 and reflecting 97.0% of the light that falls on it. Suppose a sail with area 1.00 km^2 is oriented so that sunlight falls perpendicular to its surface with an intensity of 1.40 X 10^3 W/m^2. 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.

Explanation / Answer

Emissivity of solar sail, e = 0.03

Area of sail, A = 1.0 k m^2 = 1.0 x10^ 6 m^2

Intensity of the sun light, I = 1.4 x 10^ 3 W / m^2

Stefans constant,   ? =  5.6696 x 10^ -8 W / m^2 . K^4

Solution:

The rate of energy absorption is,

           P = [(100-97)%]IA = [(100-97)%](1.4 x 10^ 3 )(1.0 x10^ 6) = 4.2x107 W

Consider the sail radiates equally from both sides, so A = 2(1.0 x10^ 6) = 2 x10^ 6

From stefan's law, we have, P = Ae ? T^4

Thus, the temeprature is,

    T = [ P / e ?A ]1/4 = [4.2x107/ 0.03*5.6696*10^ -8*2 x10^ 6] = 333.34 K = 333 K    (rounded)

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