Problem

Calculate the temperature the entire sky would ha…

03:05

Problem 63 Hard Difficulty

A large body of lava from a volcano has stopped flowing and is slowly cooling. The interior of the lava is at $1200^{\circ}{C}$ , its surface is at $450^{\circ}{C},$ and the surroundings are at $27.0^{\circ} {C}$
(a) Calculate the rate at which energy is transferred by radiation from 1.00 $\mathrm{m}^{2}$ of surface lava into the surroundings, assuming the emissivity is $1.00 .$ (b) Suppose heat conduction to the surface occurs at the same rate. What is the thickness of the lava between the $450^{\circ} \mathrm{C}$ surface and the $1200^{\circ} \mathrm{C}$ interior, assuming that the lava's conductivity is the same as that of brick?

Answer

$T_{s k y}=127^{\circ} \mathrm{C}$

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Physics 101 Mechanics

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Chapter 14

Heat and Heat Transfer Methods

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Video Transcript

So to solve this question, we're going to use Steven Woodsman. So for the part A were given that surface temperature is 4 50 degree Celsius, so we must convert it to kill him. This converted for 50 plus 2 73 it's 7 23 kid, and the temperature of surrounding his 2070 losers years. That is 300 Kelvin. And we are asked the rate at which energy is transferred by radiation. So will use Steven Woodsman Law. Sigma Absalon, eh? Times temperature off the body or the lower in this case to the four minus temperature off. Surrounding to the food we are given Stephen Bozeman Constant, which is 5.67 times 10. Power needed to eight. Absalon is one because temperature is they high. Since it's not given to us, we can safely assume that area is given to us s one. Me too square. So 7 23 to the four minus 300 24 Let's do this difference first. So the answer here is to 65 billions. Oh, oh, it isn't finished yet. We have to multiply it by 5.67 times 10 power. Negative eight. So the answer will be 15,000 and 34 Jules per seconds. So let's convert it. Let's write it in terms off proper significant digits. That is three significant digits. So answer here will be. Q. Divided by T is equal to 1.5 times 10 powerful, 1.50 times 10 power for Jews per seconds or what answer given below the question is wrong. So let's all for the party hard, be asks. Suppose he'd conduction to self surface, Of course. At the same time, what is the thickness between the lower off 12 distances on foot? Full 50 degree Celsius. Let's use the formula for conduction of heat. Que es delta t divided by thickness. They're supposed to find thickness d. So let's substitute the values Day is equal to We know Cube. I t well, okay, you know, a K is 0.184 given in the textbook area we know is one meter square, as questions stays change in temperature is a difference. In the temperature is 1200 miners for 50 which is 7 50 in this case, you don't need to convert it to kill him, because it's the difference in the temperature On cue by T is as we found before 1.5 times 10 power for so value of B. Let me calculate this point when it full times 7 15 invited. So the value here is 0.0 92 meters. If you converted two centimeters it with the 20.92 meters Oh, I'm sorry. The value here is supposed to be 00.84 point 184 So let me correct that. So it will be 0.84 So let me do this calculation again. Answer here is not 0.9 to what it is equal to 0.42 meters. So the answer is 4.2 centimeters. Sorry about that. So the thickness is 4.2 centimeters.

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