The emissive properties of a black body are determined by means of quantum theory and are confirmed by experiment. The black body is so called because. 12- Stephan's Law for Black Body Radiation Object: Measure how the current through an electric light bulb varies as the applied voltage is changed. This will allow you to establish Stephan's Law for Black Body Radiation. Introduction: When an electric current flows through the.
An apparatus can be set up to detect the radiation from an object maintained at temperature T 1. (Since a warm body gives off radiation in all directions, some sort of shielding must be put in place so the radiation being examined is in a narrow beam.) Placing a dispersive medium (i.e. A prism) between the body and the detector, the wavelengths ( λ) of the radiation disperse at an angle ( θ). The detector, since it’s not a geometric point, measures a range delta- theta which corresponds to a range delta- λ, though in an ideal set-up this range is relatively small. The total intensity radiated over all wavelengths (i.e. The area under the R( λ) curve) increases as the temperature increases. This is certainly intuitive and, in fact, we find that if we take the integral of the intensity equation above, we obtain a value that is proportional to the fourth power of the temperature.
Specifically, the proportionality comes from Stefan’s law and is determined by the Stefan-Boltzmann constant ( sigma) in the form:. I = σ T 4. The value of the wavelength λ max at which the radiancy reaches its maximum decreases as the temperature increases. The experiments show that the maximum wavelength is inversely proportional to the temperature. In fact, we have found that if you multiply λ max and the temperature, you obtain a constant, in what is known as Wein’s displacement law: λ max T = 2.898 x 10 -3 mK. The box is filled with electromagnetic standing waves. If the walls are metal, the radiation bounces around inside the box with the electric field stopping at each wall, creating a node at each wall.
The number of standing waves with wavelengths between λ and dλ is N( λ) dλ = (8 π V / λ 4) dλwhere V is the volume of the box. This can be proven by regular analysis of standing waves and expanding it to three dimensions. Each individual wave contributes an energy kT to the radiation in the box.
From classical thermodynamics, we know that the radiation in the box is in thermal equilibrium with the walls at temperature T. Radiation is absorbed and quickly reemitted by the walls, which creates oscillations in the frequency of the. The mean thermal kinetic energy of an oscillating atom is 0.5 kT. Since these are simple harmonic oscillators, the mean kinetic energy is equal to the mean potential energy, so the total energy is kT. The radiance is related to the energy density (energy per unit volume) u( λ) in the relationship R( λ) = ( c / 4) u( λ)This is obtained by determining the amount of radiation passing through an element of surface area within the cavity.
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