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:

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.

M = σ T^4

Where 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?
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...


Anonymous said...

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.


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

Matthew said...

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.

Matthew said...

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