Question

The Stefan-Boltzmann law is a statement on the total black-body power R (energy radiated per second) emitted per unit area. R = c/4 u(v,T), here c is the speed of light, which converts energy per unit volume to power per unit area. The law is R = σT⁴: In other words, it is the integral of Plank's law u(v, T) over the frequency v (or the wavelength λ., u(λ, Τ')) times c/4. Choose the form you like and integrate over appropriate variable (v or λ.).

[infinity]
By change of the integration variable to x reduce the integral to constants times ∫ x³ dx / eˣ - 1 = π⁴/15 Obtain σ and evaluate its numerical value include units.
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Answer 1

The Stefan-Boltzmann law relates the rate of energy radiated by a blackbody to its temperature. The law can be expressed as R = σT⁴, where R is the total power emitted per unit area, σ is the Stefan-Boltzmann constant, and T is the temperature in Kelvin. To obtain the value of the Stefan-Boltzmann constant, we integrate Planck's law of blackbody radiation and solve for σ.

Step-by-step explanation:

The Stefan-Boltzmann law is a fundamental concept in physics that relates the rate at which a blackbody radiates energy to its temperature.

It states that the total power emitted from a unit area is proportional to the fourth power of the absolute temperature. The law can be expressed as R = σT⁴, where R is the total power, σ is the Stefan-Boltzmann constant, and T is the temperature in Kelvin.

To obtain the value of the Stefan-Boltzmann constant, we integrate Planck's law of blackbody radiation over the appropriate variable, which can be either frequency (v) or wavelength (λ). By changing the integration variable to x, we can reduce the integral to a known function ∫ x³ dx / eˣ - 1 = π⁴/15. Finally, we solve for σ and evaluate its numerical value, taking into account the units. The Stefan-Boltzmann constant is approximately 5.670 × 10⁻⁸ W/(m² · K⁴).