Blackbody problem

First was the blackbody problem. A blackbody is a theoretical object that emits and absorbs radiation. When heated, the intensity... 

Although historians of science have studied the breakthrough that led to quantum mechanics, nobody can be exactly sure what was in Planck s orderly, disciplined mind when he devised the equation that revolutionized physics. He tackled the blackbody problem in several ways, but nothing worked. Finally, he tried an idea that was contradictory to all established concepts at the time What if energy was not continuous What if blackbodies absorbed and emitted it in little chunks He wrote down his equation ... 

The corpuscular view was revived in a different form early in twentieth century with Planck s solution of the blackbody problem and Einstein s adoption of the photon model in 1905. Milloni [6] has emphasized the fact that Einstein s famous 1905 paper [7] Concerning a heuristic point of view toward the... 

Planck presented his solution to the blackbody problem at the December 1900 meeting of the Berlin Physical Society. At the time, no one, probably not even Planck himself, grasped the implications of the simple equation he used to solve it. His equation was considered to be a nice mathematical trick but one with no particular physical significance. It was useful, but did not necessarily represent the way the blackbodies actually worked. 

The Rayleigh-Jeans picture of the radiation field as an ensemble of different modes of vibration confined to an enclosure was applied to the blackbody problem in Chapter 1. The quantum theory of radiation develops this correspondence more explicitly, identifying each mode of the electromagnetic field with an abstract harmonic oscillator of frequency coa- The Hamiltonian for the entire radiation field can be written... 

Planck had a firm belief that all physical phenomena must eventually succumb to analysis, and he chose to work on the blackbody problem. He tackled the problem from the standpoint of classical thermodynamics because he was familiar with the area and classical thermodynamics does not assume the existence of atoms (and atoms were still controversial among physicists at the time). Planck knew that if heat were added to a blackbody cavity, then there had to be an entropy change, so he tried to calculate an expression for entropy that would match experimental observations. But his efforts resulted in failure until he did what he characterized as an act of desperation. He assumed that the energy of the light was not continuous but came in discrete packets, called quanta, and that the size of these packets became larger at shorter wavelengths. He did some creative curve fitting (technically known as interpolation ), and his formulation fit. 

Planck was a thermodynamicist, and having studied under Kirchhoff (of spectroscope fame) in Berlin, he was aware of the blackbody problem and approached it from a thermodynamic point of view. The exact derivation is not difficult but is omitted here texts on statistical thermodynamics include it as a matter of course. Planck treated light as interacting with electric oscillations in matter. He supposed that the energy of these oscillations was not arbitrary, but proportional to their frequency v ... 

Several questions present themselves immediately How good does the initial guess have to be How do we know that the procedure leads to better guesses, not worse How many steps (how long) will the procedure take How do we know when to stop These questions and others like them will play an important role in this book. You will not be surprised to leam that answers to questions like these vary from one problem to another and cannot be set down once and for all. Let us start with a famous problem in quantum mechanics blackbody radiation. 

No object can radiate more energy than can a blackbody at the same temperature, because a blackbody ia equiUbrium with a radiation field at temperature T radiates exacdy as much energy as it absorbs. Any object exhibiting surface reflection must have emissivity of less than 1. Pyrometers are usually caUbrated with respect to blackbodies. This can cause a serious problem ia use. The emissivities of some common materials are fisted ia Table 4. 

Nd YAG and the lifetime measurement is made by the use of the phase-locked detection of fluorescence lifetime (PLD) scheme. By reference to the use of the fluorescence lifetime measurement, the problems, in pyrometry, of emissivity, and sight path factor in the blackbody radiation measurement could be corrected in such a scheme having an internal self-calibration. ... 

One of the problems which must be solved for quantitative measurements by emission is the need for a blackbody source at the temperature of measurement. And a variety of blackbody references have been used including a V-shaped cavity of graphite 164), a metal plate covered with a flat black paint1S6 160) and a cone of black paper l53). However, none of these methods of producing a blackbody reference spectrum are adequate. In most cases the efficiency of the reference has not been established. The most recent recommendation 1S0) is an aluminium cup painted with an Epley-Parsons solar black lacquer which has an emittance of greater than 98% over the infrared spectral range. 

It was an act of desperation. For six years I had struggled with the blackbody theory. I knew the problem was fundamental, and I knew the answer. I had to find a theoretical explanation at any cost, except for the inviolability of the two laws of thermodynamics. 

The authors note that the use of little or no solvent in the reactions helped mitigate Raman spectroscopy s problems with sensitivity. Subtraction of the initial spectrum from each subsequent spectrum in a complete time series removed the signal from unchanged species, such as solvent and other additives. Though no problems were observed from elevated temperature, blackbody radiation, or the duty cycle of the microwave, the authors caution that more experiments on those factors are needed. 

In dealing with problems of solar radiation, as opposed to blackbody radiation, the effect of the solid angle in which the radiation is confined has been examined (2-4) by considering the volume density of photons to be reduced. Landsberg(6) considers dilute radiation in the sense that the spectral distribution is retained but the radiation density is reduced. This leads to defining the temperature of a spectral component as... 

A serious problem of using an Nd YAG laser to excite FT-Raman is the difficulty of attempting to study samples at temperatures > 150°C. The thermal blackbody emission from the sample becomes more intense (broad background) than the Raman signal. The S/N ratio is lowered, and the detector becomes saturated. 

Problem A copper-constantan thermocouple is in an inert-gas stream at 350 K adjacent to a blackbody surface at 900 K. The heat transfer coefficient from the gas to the thermocouple is 25 W/(m2K). Estimate the temperature of the bare thermocouple, (e = 0.15 for copper-constantan.)... 

The diagram for this problem is shown in the sketch. Because the room is large it may be treated as a blackbody also. We shall analyze the problem by calculating the heat transfer for each wavelength band and then adding them together to obtain the total. The network for each band is a modification of Fig. 8-60, as shown below for black furnace and room. We shall make the calculation for unit area then... 

The large room acts like a blackbody at 20°C, so for analysis purposes we can assume the hole is covered by an imaginary black surface S at 20°C. We shall set the problem up for a numerical solution for the radiosities and then calculate the heat-transfer rates. After that, we shall examine an insulated-surface case for this same geometry. 

This prediction was based on the notion that a blackbody is composed of tiny oscillators that produce a continuum of waves, like those you get when you pluck the strings of a violin. But the spectrum physicists predicted for blackbody radiation—an infinite amount of high-energy radiation—and the experimental data did not fit. They were not even close. And this was the problem that Max Planck was working on in 1900. 

Planck s resolution of the problem of blackbody radiation and Einstein s explanation of the photoelectric effect can be summarized by a relation between the energy of a photon to its frequency ... 

Describe blackbody radiation, and discuss how related paradoxes of classical physics were resolved by quantum mechanics (Section 4.2, Problems 9 and 10). 

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