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Hey everyone, this is question number 60 in chapter 14.
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In this problem, we're talking about the sun.
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We're given the surface temperature, the estimated radiation, and we're told that it acts like an ideal black body.
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And then we're asked to find the diameter.
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So with surface temperature, radiation, we should immediately thinking the radiation equation, the stefan boltzman equation equals emissivity times sigma, which is that constant, a surface area, and t to the fourth, which is surface temperature.
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So we have everything for this equation except a, but if we find surface area, we can then find radius or diameter.
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So we can rearrange this equation and solve for a.
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So a equals h over e sigma t to the fourth.
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Can plug in our numbers for this.
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I'm going to start on the bottom.
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E, so an ideal black body, that means it has an emissivity of one.
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Our constant, 5 .67 times 10 to the minus 8th, watts per meter squared times k to the fourth, and then times t, surface temperature to the fourth, we're given 5 ,800 kelvin to the 4th, over.
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Over h, which is our radiation, which we're given as 3 .92 times 10 to the 26th...