# Black Body Radiation

LHarriger
I was looking over the calculation leading to the thermal average number of photons s in a mode of frequency w in a black body. The approach was pretty straightfoward: Calculate the partition function Z based on quantized energies of a harmonic oscillator, then use this to calculate:
$<s> \ = \ \sum_{i=0}^{\infty}{s P(s)} \ \ \Longrightarrow \ \ \ <s> \ = \ \frac{1}{e^\frac{\hbar\omega}{\tau}-1}$
I had no problem understanding the derivation. However, this result is independent of the size of the black body. For the life of me, I don't see how this could be the case. I assume that when we talk about the number of photons in a mode we are talking about the number of photons that would be emmitted for the energy of that mode to vanish. It seems to me that the larger the body, the more photon will sit in that mode. For instance, a big anvil held at a given temperature should radiate more than a penny. I am clearly missing something, could someone clue me into my cluelessness.

## Answers and Replies

Staff Emeritus
$<s>=\frac{1}{e^\frac{\hbar\omega}{\tau}-1}$