a) If the Sun\'s emissivity is E = 1.0, what total power does it radiate? Consid

Question

a) If the Sun's emissivity is E = 1.0, what total power does it radiate?

Consider a disk witli the same radius as the Earth's (RE = 6.4 x 106 m) and the same

distance to the Sun (r = 1.50 x 1011 m), that is oriented with its surface perpendicular

to the direction of the Sun. For light with wavelengths that correspond to (visible) Sunlight,

the disk's emissivity is Evis = 0.25.

b) What is the total power of Sunlight that is absorbed by the disk?

The disk reradiates this power back to outer space as infrared light.

c) If the disk's emissivity for infrared light wavelengths is EIR = 1.0, what will the disk's

temperature be?

Explanation / Answer

A)W =total power = sigma (A)T^4 = 5.67*10^-8 *(pi*49*10^16)(5723)^4 = 9.363*10^25 W

B)using kirchoff law...emmisivity = absorbtivity....the total power that is coming to disk is the power coming in the solid angle 2pi(1-cosd) where d is half angle of cone ...cos d = r/sqrt(r^2+Re^2) so (1-cos d) =1- .9999573 =4.27*10^-5

and in 4pi ,W power is emitted...so in given solid angle W/2 (1-cos d) = 2*10^21 W

so the absorbed power = .25 *2*10^21 = 5*10^20 W

C) as the disk has 2 surfaces through which to radiate... P = 2 sigma(A)T^4

=> 5*10^20 = 2 (5.67*10^-8)(pi(6.4*10^6)^2) T^4

=> T = 2420 K

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.