Black Body Radiation Calculation: Unveiling My Cluelessness

In summary, the conversation discusses the calculation leading to the thermal average number of photons in a mode of frequency w in a black body. The result is calculated by using the partition function and is independent of the size of the black body. However, this seems to conflict with the idea that a larger black body should have more photons in a mode. It is concluded that the probability density function is based on the fraction of the population within an incremental range and the number of photons would be greater in a larger population.
  • #1
LHarriger
69
0
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:
[itex]<s> \ = \ \sum_{i=0}^{\infty}{s P(s)} \ \ \Longrightarrow \ \ \ <s> \ = \ \frac{1}{e^\frac{\hbar\omega}{\tau}-1}[/itex]
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.
 
Science news on Phys.org
  • #2
A probability density function is based on the probability of a fraction of that population being within an incremental range.

The numbers are very large of course - say for a solid, on the order of 1022 atoms / gram.

Pick a fraction like 1000 / 1023 which is the same as 10000 / 1024. The fractions of particles are the same, but obviously 24 atoms radiate 10 times the energy of 1023 atoms. The frequency distribution would the be same, the intensity, number of photons would be greater by a factor of 10 in the larger population.
 
  • #3
Astronuc said:
[The] number of photons would be greater by a factor of 10 in the larger population.

That was my conclussion too. My problem is that it seems, at least to me, that this conclussion conflicts with the result:
[itex]<s>=\frac{1}{e^\frac{\hbar\omega}{\tau}-1}[/itex]
which states that the average number of photons in a mode is independent of the size of the black body.
 

1. What is black body radiation?

Black body radiation is the electromagnetic radiation emitted by a perfect black body, which is an object that absorbs all incoming electromagnetic radiation and emits it in a continuous spectrum.

2. How is black body radiation calculated?

The calculation of black body radiation is based on Planck's law, which describes the spectral energy density of black body radiation at a given temperature. It involves using mathematical equations to determine the intensity of radiation at different wavelengths.

3. What factors affect black body radiation?

The temperature of the black body is the main factor that affects black body radiation. As the temperature increases, the intensity of radiation also increases. Other factors that can affect black body radiation include the material of the black body and the surface area.

4. How is black body radiation important in science and technology?

Black body radiation is important in various fields of science and technology, such as astronomy, thermodynamics, and materials science. It helps scientists understand the behavior of objects at different temperatures and is also used in the design of energy-efficient devices such as solar panels.

5. Is black body radiation a real phenomenon?

Yes, black body radiation is a real phenomenon that has been observed and studied by scientists for centuries. It is a fundamental concept in physics and has been validated by numerous experiments and observations.

Similar threads

Replies
2
Views
6K
  • Thermodynamics
Replies
1
Views
1K
  • Quantum Physics
Replies
12
Views
1K
Replies
4
Views
1K
Replies
7
Views
1K
Replies
14
Views
993
  • Introductory Physics Homework Help
Replies
10
Views
778
  • Special and General Relativity
Replies
1
Views
468
  • Thermodynamics
Replies
6
Views
2K
Back
Top