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29 September, 16:24

The intensity of electromagnetic waves from the sun is 1.4kW/m2 just above the earth's atmosphere. Eighty percent of this reaches the surface at noon on a clear summer day. Suppose you think of your back as a 26.0 cm * 52.0 cm rectangle. How many joules of solar energy fall on your back as you work on your tan for 0.90 h?

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  1. 29 September, 18:01
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    Answer: The answer is 4.9 * 10^5 J

    Explanation:

    Recall that,

    Power (P) = Energy (E) / time (t)

    Hence,

    Energy (E) = Power (P) * time (t)

    First, we will determine the power, P

    From, Intensity (I) = Power (P) / Area (A)

    Power is then given by

    Power (P) = Intensity (I) * Area (A)

    From the question, the intensity of electromagnetic waves from the sun is 1.4kW/m2, but only 80% of this reaches the surface at noon.

    Hence,

    Intensity (I) = 80% of 1.4kW/m2

    I = 0.8 * 1.4 * 10^3 W/m2

    I = 1120 W/m2

    For the area,

    Area of rectangle (A) = length * breadth

    A = 26.0 * 10^-2 m * 52.0 * 10^-2 m

    A = 0.1352 m2

    Hence,

    Power (P) = 1120 W/m2 * 0.1352 m2

    P = 151.424 W

    Now, to the energy,

    From,

    Energy (E) = Power (P) * time (t)

    P = 151.424 W

    From the question,

    t = 0.90 h = (0.9 * 60 * 60) s = 3240s

    Hence,

    E = 151.424 * 3240

    E = 490613.76 J

    E = 4.9 * 10^5 J
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