The Stefan-Boltzmann Law stipulates that the maximum rate at which radiation is released by an object is proportional to the fourth power of its surface temperature, measured in Kelvin.I have to go through a bunch of problems similar to this one, so if some kind person could show me how to go about it I'm sure I could figure out the rest on my own. Any takers? I'll love you forever...M = σ T^4Where M is the maximum rate at which radiation is emitted by the surface; σ is the Stefan-Boltzmann constant, (5.67 x 10^-8 W/m^-2 K^-4) ; and T is the surface temperature of the object, K. W/m = Watts per meter.

K = ℃ + 273

The mean global air temperature is (we'll go with today's temperature) 20℃.

What is the maximum rate of emission in terms of W/m^-2?

## Saturday, September 22, 2007

### I need help

Hey, you. I am calling upon YOU to help me out for once in your life. I need some math help. I didn't think doing a degree in geography would entail much math, but I was wrong. I have not done anything math-related in years and not being able to manage this is making me very irritated because the problems I am trying to work out are not complicated in the slightest. They're very basic algebra, just plugging numbers into formulas. I hate that I can't figure this stuff out, because I was good at math in high school. I can explain Husserl's transcendental époché or Althusser's interpellation of the subject in my sleep (and I do, in my dreams!) but I can't do simple algebra. Makes me feel dumb. Here's a sample of what I'm being asked to work out:

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## 3 comments:

I'll help!

First, I think you have some units and constants mixed up in your type-up of the problem. The Stefan-Boltzmann constant (we'll call it s) = 5.670 × 10−8 W/m^2·K^4.

One way to go about these problems is to look at the units. You'll notice that the Stefan-Boltzmann constant is in W/(m^2 K^4), and it is going to be multiplied by a temperature in K to the 4th degree (or K^4). That means that unit will divide out, leaving you with W/m^2 for M.

Are you sure it didn't ask for the emission rate in Watts per meter squared?

Anyway, T = temperature. In this case, 20 C, or when you convert to Kelvin, 293. (T in Kelvin = 20 C + 273 = 293 K)

M = 5.67*10^-8 * 293^4

Cross out the appropriate units, and tada! You have an emissions rate in W/m^2.

-Gina

Email me if that didn't make sense and I'll try to do better.

Thanks so much Gina!

Aha! That's why I wasn't getting the right answers. There's a typo in my textbook where it shows the Stefan-Boltzmann constant. A 4 instead of an 8. And yes, it is supposed to be in W/m^2.

Let me try this out on a few and I'll get back with you.

Thanks again. You're the best.

Yay, it works! I was starting to freak out. Of all the places that there could be a typo...

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