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welcome to our fourth example video. Where we're going to consider are more correct equation for radiation which, if you recall, is e sigma a multiplied by t to the fourth. Mine is the temperature of your surroundings to the fourth power. Now, if you were to apply this to our previous problem of the sun and finding its surface temperature by looking at how much energy from the sun reaches the Earth, you would have found that it wouldn't make much difference if you went through and did the calculation you'd find the surface temperature of the earth is about 6000 Kelvin. Well, the temperature of it's arousing surroundings are about three Calvin. So even if you include this, you don't get a significant change in your calculation of the surface temperature of the sun s. Oh, what if though we looked at a couple of temperatures that are a little closer to each other so we can really see this effect? For example, let's consider the human head and how much heat it's giving off to its surroundings. So you know how your mother always used to tell you to put a hat on. We are doing that problem. So we have a cold temperature around your head, will say 12 degrees Celsius. And you didn't put a hat on because you didn't listen to your mother. In fact, you even shaved your head. So now you can. We have a temperature of your body, which is going to be about 37 degrees Celsius. Is core human body temperature. So there's our T, H and R T C. And we're in this case are T and R T s. Our area then is going to be approximately four pi times the radius of our head, which will estimate to be six centimeters Sigma is a constancy, universal constant. We don't need to worry about it. But what about the imbecility? I mentioned in the previous video that since our head absorbs most light that hits us, we tend to have any missive ity that's pretty close to one. Generally, it's estimated to be approximately 0.95 Given these numbers, then the rate at which heat is leaving our body is equal to to your 0.95 multiplied by 5.67 times 10 to the negative eight watts per kilogram or watts per meter squared Kelvin to the fourth multiplied by our area, which is going to be for pi times 0.6 m squared, multiplied by t fourth. So that's going to be remember, we have to convert this into Kelvin because we're actually taking it to the fourth power and then subtracting. If we were just taking the difference and then going to the fourth power, we could have left it in terms of Celsius. As it is, though, our temperature is about 37 degrees Celsius. Remember, that's 2 73 then plus 37. So that's going to end up being 300 20. Kelvin. Let's check that. Something about that's not right. Yep, 310. Calvin. There we go. So we have 310 Calvin to the fourth, minus 12, which is going to be 285. Calvin to the fourth. And here we have the rate at which heat is leaving your head. Obviously, the holder gets the faster heat will go out through your head. Uh, though this is a bit of a misnomer. That heat leaves your head faster than any other part of your body. In fact, it just tends to be the part of your body that's uncovered the most, which is why it tends to get cold the most. Andi. That's generally why he leaves your head faster than any other part of your body. Um, though it does have a lot of blood vessels in it that contribute to that.

University of North Carolina at Chapel Hill