#2075 please, the answer is 5800k. please work out and show steps Most of us thi

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#2075 please, the answer is 5800k. please work out and show steps

Most of us think of ourselves as the final triumph of biological evolution; we are convinced that we have come to stay as rulers of the earth. I wonder why. Gigantic reptiles, dinosaurs ruled the earth for millions of years but failed to retain their supremacy...Man has ruled only for a fraction of one million years... We have fought against the wild beasts... and won. But we have not yet conquered the microbe. We have also to fight against famine, against vice, against bellicose tendencies to self-destruction. These fights have not yet been won; the issue is still in doubt...The dinosaurs could not escape their fate. We can. We face the future with a weapon not given to the earlier rulers of the world --- I mean scientific knowledge, and the capacity for increasing it indefinitely by scientific research. Sir James Jeans, d. 1946. English physicist, astronomer. Writer. Calculate the temperature of the sun's surface from the fact that the "solar constant" (=energy per unit time per unit area in all wavelengths incident at right angle on the earth's surface) is 324 cal/sec/m^2. Assume the sun to be a perfect radiator (it doesn't look black, of course, because it's hot enough to emit visible wavelengths), and take the sun's diameter to be 1.4 times 10^9 m, and earth-sun distance 1.5 times 10^11 m; the earth's diameter (1.3 times 10^7 m) can be neglected in the earth-sun distance. The result obtained by this method will be slightly low because energy reflected by the earth's atmosphere is not considered. Calculate the temperature of the sun's surface from the fact that the wavelength of greatest intensity in the solar spectrum is 471 nm. (This value is corrected for the fact that some wavelengths are more strongly absorbed than others ("differential absorption") in the earth's atmosphere.) Compare this result with that of the previous problem. For the region of the black body radiation curves where lambda T is small, show that the Wien

Explanation / Answer

Find the power output, P, of the Sun using I = P/(4.pi.d^2) where
I =324 cal/s/m^2 = 1356W/m^2
d = 1.5*10^11m

Find the surface area of the sun, A = 4.pi.r^2 where
r =7*10^8 m

Use the Stefan-Boltzmann Law to find the absolute temperature T :
P/A = 5.670x10^-8 x T^4

I*4pi*d^2/4pi r^2 = 5.67e-8*T^4

1356*(1.5e11)^2/(7e8)^2 = 5.67e-8 T^4

T^4 = [1356*(1.5e11)^2/(7e8)^2]/[5.67e-8] = 1.09815e15

T = 5757 K

Rounding it off T = 5800 K

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