Technology & Engineering
Wien's Law
Wien's Law states that the wavelength at which an object emits the most radiation is inversely proportional to its temperature. In other words, as the temperature of an object increases, the peak wavelength of its emitted radiation shifts to shorter wavelengths. This principle is fundamental in understanding the relationship between temperature and the color of light emitted by objects, and it has important applications in fields such as astronomy and thermal imaging.
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3 Key excerpts on "Wien's Law"
eBook - PDF- D. Ter Haar(Author)
- 2016(Publication Date)
- Pergamon(Publisher)
PART 2 This page intentionally left blank I On an Improvement of Wien's Equation for the Spectrum f M . PLANCK THE interesting results of long wave length spectral energy measurements which were communicated by Mr. Kurlbaum at today's meeting, and which were obtained by him and Mr. Rubens, confirm the statement by Mr. Lummer and Mr. Pringsheim, which was based on their observations that Wien's energy distribution law is not as generally valid, as many have supposed up to now, but that this law at most has the character of a limiting case, the simple form of which was due only to a restriction to short wave lengths and low temperatures. J Since I myself even in this Society have expressed the opinion that Wien's Law must be necessarily true, I may perhaps be permitted to explain briefly the relationship between the electromagnetic radiation theory developed by me and the experimental data. The energy distribution law is according to this theory deter-mined as soon as the entropy S of a linear resonator which interacts with the radiation is known as function of the vibrational energy U. I have, however, already in my last paper on this subject 1 stated that the law of increase of entropy is by itself not yet sufficient to determine this function completely; my view that Wien's Law would be of general validity, was brought about rather by special considerations, namely by the evaluation of an infinitesimal increase of the entropy of a system of n identical f Verh. Dtsch. Phys. Ges. Berlin 2, 202 (1900). % Mr. Paschen has written to me that he has also recently found appreciable deviations from Wien's Law. 79 The expression on the right-hand side of this functional equation is certainly the above-mentioned change in entropy since n identical processes occur independently, the entropy changes of which must simply add up.
eBook - PDFEinstein's Other Theory
The Planck-Bose-Einstein Theory of Heat Capacity
- Donald W. Rogers(Author)
- 2020(Publication Date)
- Princeton University Press(Publisher)
Four The Planck Equation I n 1893 W. W ien proposed on theoretical grounds that the intensity of blackbody radiation relative to its maximum intensity, I T : I max T , is the same function of / max for all values of T , where max is the wavelength of maximum intensity at any selected T . By 1896 Paschen provided extensive experimental corroboration of Wien’s law of intensity ratios. In time, the theoretical foundations of this contention were to be discarded in favor of a much more radical theory, and Wien’s general equation for energy density as a function of wavelength was to be relegated to the status of an approximate solution to the problem. Nevertheless, Wien’s provisional theory and the ratio laws were the first significant steps toward a theory of blackbody radiation. 4.1 The Paschen-Wien Law To see how the Paschen-Wien law works, consider the two experimental blackbody radiation spectra shown in figure 4.1.1, observed at different temperatures. First, replace on the horizontal axis with the ratio / max . This “nor-malizes” the two curves so that the peak of each falls at / max = 1 0. Now we attempt to “normalize” the heights of the two curves by plotting the ratio u , T / u max , T (which is equivalent to plotting I T : I max T ) on the vertical axis (figure 4.1.2). Behold, it works! Both normalized curves are the same. The peak of both curves is at the ratio u , T / u max , T = 1 0. This is a very important discovery. By Wien’s law, if we can find the dis-tribution function for one temperature, we have the distribution function for all temperatures. As a consequence of the Paschen-Wien law, max T = const ≡ b W . In 1897 Lummer and Pringsheim published an excellent value of b W = 0 294 cm deg (modern value, b W = 0 290 cm K = 2 898 × 10 − 3 m K). We shall see that this law can be derived from the distribution function of u versus or, equivalently, u versus . We now meet the central problem of finding what that distribution function is.
eBook - PDFFrom Atoms to Galaxies
A Conceptual Physics Approach to Scientific Awareness
- Sadri Hassani(Author)
- 2010(Publication Date)
- CRC Press(Publisher)
The first theoretical attempts to derive the intensity distribu-tion function were made by Ludwig Boltzmann and others. Boltzmann deserves particular attention because his method brought both electromagnetism and thermodynamics into the treatment of heat radiation. He showed in 1884 that electromagnetic radiation possesses pressure and, when combined with the second law of thermodynamics, it connects the en-ergy flux J e (energy radiated from each unit area of the radiator per second), sometimes called brightness , to the temperature by the formula J e = σT 4 , where σ is a constant and T is the temperature of the radiator in Kelvin. σ has been measured accurately with a value of 5 . 67 × 10 -8 in the scientific units we use in this book. So we write this equation as Stefan-Boltzmann law. J e = 5 . 67 × 10 -8 T 4 (20.1) and call it the Stefan-Boltzmann law , because the equation had been discovered empir-ically by Joseph Stefan in 1879. There is no wavelength in this equation because it gives the total energy flux with contributions coming from all wavelengths. 1 As noted above, the Sun is not a “good” black body, but approximates it fairly well. 286 Chapter 20 Birth of Quantum Theory 0.5 1 1.5 2 2.5 3 Figure 20.2: A typical black body radiation curve. The length of the wavelength at which the maximum occurs is inversely proportional to the temperature. What do you know? 20.3. By what factor does the brightness of a BBR increase if you double its temperature? 20.1.2 Wien’s Displacement Law The next step was taken by Wilhelm Wien (1864–1928). Instead of the total energy density as given by the Stefan-Boltzmann law, Wien was interested in the distribution of energy among wavelengths. In a typical investigation, one plots the intensity of various wavelengths emitted by a black body as a function of wavelength. The resulting graph will look similar to the one plotted in Figure 20.2. This so-called black body radiation curve typically Black body radiation curve.
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