# Energy of black body

1. Jan 21, 2017

### kubajed

1. The problem statement, all variables and given/known data
I need to calculate radiation power of ball in range 400nm-800nm.
T=10000K
d=1um.

2. Relevant equations
I think I need to use Planck equation and integrate that.

3. The attempt at a solution
I look for equations and laws and try to do my equation (above). If this is correct, I ask for help with calculate that.

2. Jan 21, 2017

### haruspex

3. Jan 21, 2017

### kubajed

Thanks. Problem is that I don't know how to calculate integrate.

4. Jan 21, 2017

### zexxa

If you have not learnt how to integrate you should consider reading up or watching some explanatory videos on YouTube. I suppose that if the question expects to you integrate for your solution you should have been taught it at some point before.

But if you do know how to integrate, and your only problem is that you are not confident if you did it right, we can help you here if you show us how you did it so we can correct your mistakes (and you can learn from it too!).

5. Jan 21, 2017

### kubajed

I don't know how to integrate. That isn't a homework for all. It's an extra exercise for me. I hope that you will help me with it.
I do calculations in Mathematica. I put that:
Integrate[((2*Pi*6.63*10^-34*(3*10^9)^2)/x^5)*(1/(E^(6.63*10^-34*3*10^9/x*1.38*10^-23*10000))-1)*1.256*10^-11, {x,4*10^-7,8*10^-7}].
I use my equation just multiplied by c/4 and area of ball. Result is -4.31119.
This site: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/radfrac.html claim that result is 0.00269. Where I am wrong?

Last edited: Jan 21, 2017
6. Jan 21, 2017

### haruspex

7. Jan 22, 2017

### kubajed

Which one of them is that what I am looking for? On this site is calculator too. It claims that result is 6.77561e+07 W/m2/sr. My site: 2.1447e+08 W/m2.

8. Jan 23, 2017

### kubajed

I have other question: how much photons (in visible range) will be registered in detector located 10cm far with diameter 1mm in 100ps?

9. Jan 23, 2017

### haruspex

Those seem about right for the radiance. It asks for the power. The emitter is a tiny ball. Using https://astrogeology.usgs.gov/tools/thermal-radiance-calculator/, I get more like 2.2E-4W.

(There's something I'm not understanding in this topic. I see radiance quoted as W·sr−1·m−2. Suppose the ball's surface has a radiance R and radius r. It has a surface area 4πr2, so that satisfies the m−2. What solid angle should I use to satisfy the sr−1? 2π, on the basis that each area element is emitting into a half space? Doesn't really make sense to me.
I note that one of your results quotes sr−1 but the other doesn't, and the ratio is about π.)