Problem

. Basal metabolic rate. The energy output of an a…

04:39

Problem 85 Hard Difficulty

$\bullet$ The effect of urbanization on plant growth. A study published in July 2004 indicated that temperature increases in urban areas in the eastern United States are causing plants to bud up to 7 days early compared with plants in rural areas just a few miles away, thereby disrupting biological cycles. Average temperatures in the urban areas were up to 3.5 $\mathrm{C}^{\circ}$ higher than in the rural areas. By what percent will the radiated heat per square meter increase due to such a temperature difference if the rural temperature was $0^{\circ} \mathrm{C}$ the average?

Answer

5.23$\%$

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Physics 101 Mechanics

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Video Transcript

Yes, over these. For these questions, we can use such formula, which is? He can't go to the surface area. Tester Inclusivity sense us, Evan Constant intense toe temperature to about for is this is associate with Stepped on Bozeman's fall. Okay, And we're looking for we're rate. Oh, now will present where? The radio he per square meter increase due to such difference between a rural area and the other. What is he is talking about the radio per square meter. There is it's issue over a issue here stands for the key currents around the urban area. Asia is a surface area so h over a means the he radiate per square here. Okay, in a chart here, stand for the heater on the rule here and the A here is the same to steal the service area. Okay, so this will give us both my ego too. E has the sigma. She's with Paul for okay and see years The temperature on the urban area and a T prime here is the temperature on the rule area. So we know that the temperature at the rural area is zero degrees Celsius which is 273 Calvin. And the temperature from the urban area is 3.5. Results is higher than it real area, which is three point fighting resources. And they'll give us 200 and 76. 45 degree. I mean, sorry, Calvin, in unique help. Okay, so we're looking for 4% increase. Tells the difference between the urban area. And they're a rural area, which means that we're looking for Sash about it, which is the He couldn't per meter square from the urban area. You went by the he occurrence from square meter around the rule area. And over No, he radiates per square meter from the rural area times 100%. And this whole thing is the the value we're looking forward to soft. Okay, so how can we do it? Well, remember h you over a Was he going to e sigma t to about four years in music? But he is equally walk. Okay, So you re plugging valuable got one times sick man is 5.67 times a potential. Borrow a what's per meter? Uh, see, at least for meter square times, Calvin to the power for times 276 point by Calvin. Cool crowd here sometimes cow into the power four times. 200 and 76.5. Calvin to a power of four. Okay. And the he read a per square meter on the rule area. This people to HR over a Okay. Sigma t prime for okay, You know what? Actually, we don't really need to expand this. Sorry about this, because eventually you'll see e sigma. We'll cancel out. Okay, So if we plugging from trying always, um, symbols on his equations back into the the question here, we'll get boob e cigna t to about four. My eyes E Sigma Tito Power prime t Prime to a power for over e seeking my t prime toe. How for And it would take You see, come out will get you Sigma Times t to the power or minus t prime to about four over e sigma t prime to a power for and the e cig. Moken. So out. I will get, uh, got to tie 100% here. Yeah, did you say and I will get t to about four minus t prime to power for over de private up power for times 100% and we plug in value. Now we'll get 276 point by Calvin, which is a temperature of on the urban area. Two of our four minus 273 Children to about four, which is the temperature on the rule area over 273. Calvin to the power for times 100%. We'll get the values of spow 5.23 per se. Okay, so let's, uh, percent increase due to a difference from the rule area in the urban area. Okay. And thank you.

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