Density of black body radiation

In summary, the density of black body radiation is the amount of electromagnetic radiation emitted by a perfect black body per unit volume and per unit frequency. It is directly proportional to the fourth power of the temperature according to Planck's law and is important in astronomy for understanding the thermal properties of celestial objects. The density varies with frequency, following a bell-shaped curve with higher frequencies having higher densities. It can be measured experimentally using specialized instruments such as a spectrometer or radiometer.
  • #1
asub
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I came across a formula that gives radiant energy density as 4 * sigma * T^4 / c. I am trying to figure out how this formula follows from Stefan-Boltzmann law. Shouldn't it be 4*pi instead of just 4? I am also wondering why one can just stick in c.

TIA
 
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  • #3


The formula you have come across is known as the Planck law and it describes the spectral density of black body radiation at a given temperature T. The constant sigma represents the Stefan-Boltzmann constant, and c represents the speed of light. The factor of 4 in the numerator is a result of integrating over all angles in 3-dimensional space, which is why it is not 4*pi as you suggested. This factor of 4 is a fundamental part of the Planck law and is derived from the geometry of the radiation emitted from a black body.

Additionally, the presence of the speed of light in the formula is a result of the fact that radiation travels at the speed of light. This is why it is not simply multiplied by 4, but rather divided by c. This factor accounts for the fact that the radiation is spread out over a larger area as it travels away from the black body.

In summary, the formula you have encountered is a fundamental law in physics and is derived from the Stefan-Boltzmann law. The factors of 4 and c are necessary components that account for the geometry and speed of light in the radiation emitted from a black body. I hope this helps clarify your understanding of the density of black body radiation.
 

1. What is the definition of density of black body radiation?

The density of black body radiation refers to the amount of electromagnetic radiation emitted by a perfect black body per unit volume and per unit frequency. It is often measured in units of energy per unit volume per unit frequency, such as joules per cubic meter per hertz.

2. How is the density of black body radiation related to temperature?

According to Planck's law, the density of black body radiation is directly proportional to the fourth power of the temperature. This means that as the temperature increases, the density of radiation also increases exponentially.

3. Why is the density of black body radiation important in astronomy?

The density of black body radiation plays a crucial role in understanding the thermal properties of celestial objects. By measuring the density of radiation emitted by a celestial object, astronomers can determine its temperature, composition, and other important characteristics.

4. How does the density of black body radiation vary with frequency?

The density of black body radiation follows a bell-shaped curve, known as the Planck distribution, with the peak of the curve shifting to higher frequencies as the temperature increases. This means that the density of radiation is higher at higher frequencies, or shorter wavelengths.

5. Can the density of black body radiation be measured experimentally?

Yes, the density of black body radiation can be measured using specialized instruments, such as a spectrometer or a radiometer. These instruments can detect and measure the intensity of radiation at different frequencies, allowing for the calculation of the density of black body radiation.

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