Thermodynamics HW Solutions 878

# Thermodynamics HW Solutions 878 - Chapter 11 Fundamentals...

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Chapter 11 Fundamentals of Thermal Radiation 11-35 A small surface is subjected to uniform incident radiation. The rates of radiation emission through two specified bands are to be determined. A = 1 cm 2 45 ° Assumptions The intensity of incident radiation is constant. Analysis ( a ) The rate at which radiation is incident on a surface per unit surface area in the direction ( θ , φ ) is given as φθθ θφ d d I dA Q d dG i i sin cos ) , ( = = & The total rate of radiation emission through the band between 0 ° and 45 ° can be expressed as 2 sin cos ) , ( 2 0 45 0 1 π φθ θθ i i I d d I G = = ∫∫ == since the incident radiation is constant ( I i = constant), and 2 / ) 0 sin 45 (sin sin cos 2 sin cos 2 2 45 0 2 0 45 0 πθ πφ = = = = d d d Approximating a small area as a differential area, the rate of radiation energy emitted from an area of 1 cm 2 in the specified band becomes W 3.46 = × × = = = ) m 10 1 )( sr W/m 10 2 . 2 ( 5 . 0 5 . 0 2 4 2 4 1 1 , dA I dA G Q i i
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