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As the radiation pressure scales as the fourth power of the temperature, it becomes important at these high temperatures. In the Sun, radiation pressure is still quite small when compared to the gas pressure. In the heaviest non-degenerate stars, radiation pressure is the dominant pressure component. [25]
Bartoli in 1876 had derived the existence of radiation pressure from the principles of thermodynamics. Following Bartoli, Boltzmann considered an ideal heat engine using electromagnetic radiation instead of an ideal gas as working matter. The law was almost immediately experimentally verified.
Radiation pressure affects the effective force of gravity on the particle: it is felt more strongly by smaller particles, and blows very small particles away from the Sun. It is characterized by the dimensionless dust parameter β {\displaystyle \beta } , the ratio of the force due to radiation pressure to the force of gravity on the particle:
In forming the stellar structure equations (exploiting the assumed spherical symmetry), one considers the matter density (), temperature (), total pressure (matter plus radiation) (), luminosity (), and energy generation rate per unit mass () in a spherical shell of a thickness at a distance from the center of the star.
The first Friedmann equation is often seen in terms of the present values of the density parameters, that is [7] =, +, +, +,. Here Ω 0,R is the radiation density today (when a = 1 ), Ω 0,M is the matter ( dark plus baryonic ) density today, Ω 0, k = 1 − Ω 0 is the "spatial curvature density" today, and Ω 0,Λ is the cosmological constant ...
The consideration begins by noting the relation between the radiation pressure P rad and luminosity. The gradient of radiation pressure is equal to the momentum transfer absorbed from the radiation, giving: =, where c is the velocity of light.
The equation of state for ordinary non-relativistic 'matter' (e.g. cold dust) is =, which means that its energy density decreases as =, where is a volume.In an expanding universe, the total energy of non-relativistic matter remains constant, with its density decreasing as the volume increases.
Acoustic radiation pressure is the apparent pressure difference between the average pressure at a surface moving with the displacement of the wave propagation (the Lagrangian pressure) and the pressure that would have existed in the fluid of the same mean density when at rest.