The number of thermal photons refers to the number of photons (particles of light) present in a system at thermal equilibrium, which is when the system is in a state of constant temperature and energy distribution.
The number of thermal photons can be calculated using the Planck distribution, which relates the energy and frequency of a photon to the temperature of the system. This distribution is described by the Planck's law formula: N(ν,T) = (8πν^2 / c^3) * (1 / (e^(hν/kT) - 1)), where N is the number of photons, ν is the frequency, T is the temperature, c is the speed of light, h is Planck's constant, and k is Boltzmann's constant.
The number of thermal photons in a system is affected by the temperature, the size of the system, the type of material the system is made of, and the frequency range being considered. Higher temperatures, larger systems, and materials with a higher number of energy levels can result in a higher number of thermal photons.
The number of thermal photons and thermal radiation are directly proportional, as thermal radiation is the emission of photons from a system at thermal equilibrium. In other words, the more thermal photons present in a system, the higher the amount of thermal radiation emitted.
The number of thermal photons is directly related to the total energy of a system, as each photon carries a specific amount of energy. The higher the number of thermal photons, the higher the total energy of the system. This is described by the equation E = hν, where E is the energy, h is Planck's constant, and ν is the frequency of the photon.