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Calculate the temperature the entire sky would have to be in order to transfer energy by radiation at 1000 ${W} /{m}^{2}$ $-$ about the rate at which the Sun radiates when it is directly overhead on a clear day. This value is the effective temperature of the sky, a kind of average that takes account of the fact that the Sun occupies only a small part of the sky but is much hotter than the rest. Assume that the body receiving the energy has a temperature of $27.0^{\circ} \mathrm{C}$

$401 \mathrm{~K}$

Physics 101 Mechanics

Chapter 14

Heat and Heat Transfer Methods

Thermal Properties of Matter

Cornell University

University of Michigan - Ann Arbor

Hope College

McMaster University

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for 64. We will know what's the temperature of the sky? They're just averaging out the whole temperature of this guy. Even the sun makes it hot in one spot. This is an overall average. So what temperature would risk? I have to be thio transfer energy by radiation at a rate of 1000 watts per meter squared, and the object receiving that energy is at 27 degrees Celsius. What? Somebody is my equation here? Um, the rate that's gonna be the 1000 Watts course. That's, um Bolton. It's constant. Always 5.67 times 10 to the negative. Um, the sky The sun will consider it to be a a black body. So it's gonna have em acidity of one. The area. Remember here, this was 1000 wants her meter cubed, so this is per meter cubed. Someone put an area of one meter cubes in here. Um, here, this would be in a tea, too. That's the temperature of the environment. So in this case, that's the sky. That's what I'm looking for and were given that the object has a temperature of 27 Celsius. Remember, that always has to be in Kelvin, though, so I'm gonna add the 2 73 0.15 to that. So this temperature is now 300 point one's life? Um, only do me, Matthew. I'm gonna make sure that I distribute this. So I have 1000 equals. Well, just this 5.67 times. 10 two, then 8/8 times C two raised to the fourth power. And then you do this minus for 60 point to. That's what I get only multiplied here. So I'm gonna add for 60.2 to both sides. So over here, 1460 0.2 is equal to this by 0.67 times 10 to the negative, eighth t to to the fourth power I'm gonna divide. And then that I'm going to read. Just raised to the 1/4 power. It's just like taking the fourth of root of that. And I get a temperature. T too, is 401 that will be killed

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