Number Density vs Energy Density of Radiation and Matter

This is why the energy density decreases at a faster rate for radiation compared to matter. In summary, the number densities of radiation and matter change at the same rate due to expansion, but the energy densities are different due to the different ways in which energy is stored.
  • #1
cp05
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I was going through my notes preparing for finals (this is my last one hooray!), and I saw that the Number Density of radiation and matter changes at the same rate (N=Na^-3) while the energy density is different (E=Ea^-3 for matter, E=Ea^-4 for radiation). I think I get why the energy densities for matter/radn are different (matter exists in 3 dimensions...while radiation exists in 4 because of time...is that remotely correct?), but I don't understand why the number densities are the same.

Thanks for the help!
 
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  • #2
The reason why the number densities of radiation and matter are the same is because they are both affected by expansion at the same rate. As space expands, the number of particles of matter and radiation in a given volume decreases, resulting in a decrease in the number density of both. The energy densities are different because the energy of matter is stored in mass, which does not change with the expansion of space, while the energy of radiation is stored in photons, which do change with the expansion of space.
 

1. What is the difference between number density and energy density of radiation and matter?

Number density refers to the number of particles per unit volume, while energy density refers to the amount of energy per unit volume. In the context of radiation and matter, number density refers to the number of particles of radiation or matter per unit volume, while energy density refers to the amount of energy carried by those particles per unit volume.

2. How are number density and energy density related?

Number density and energy density are related through the equation E = n * h * ν, where E is the energy density, n is the number density, h is Planck's constant, and ν is the frequency of the radiation. This equation shows that as the number density increases, so does the energy density.

3. What factors affect the number density and energy density of radiation and matter?

The number density and energy density of radiation and matter are affected by several factors, including temperature, pressure, and the type of particles present. As temperature and pressure increase, the number density and energy density also increase. Additionally, different types of particles (such as photons or protons) will have different number and energy densities.

4. How does the number density and energy density of radiation and matter change with distance?

The number density of radiation and matter typically decreases with distance, since particles spread out as they travel. However, the energy density can remain constant or even increase with distance, as the energy of the particles is conserved even as their number density decreases.

5. How are the number density and energy density of radiation and matter measured?

The number density of radiation and matter can be measured using counting techniques, such as counting the number of particles in a given volume. Energy density can be measured using a variety of methods, including calorimetry and spectrophotometry. These techniques involve measuring the amount of energy present in a given volume or frequency range.

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