What Is a Blackbody, Really?

· blackbody radiation

Let us check how the notion of blackbody is defined in physics literature. Wikipedia tells us:

  • blackbody absorbs all incident radiation.
  • A black body is an ideal emitter: it emits as much or more energy at every frequency than any other body at the same temperature.
  • An approximate realization of a black body is a hole in the wall of a large enclosure (cavity). Any light entering the hole is reflected indefinitely or absorbed inside and is unlikely to re-emerge, making the hole a nearly perfect absorber, as illustrated in the following figure: 

Is this a good definition from scientific point of view? No, it is not! Why? Because it is not constructive in the sense of  offering a realistic concrete model of blackbody. Instead it is described implicitly by

  1. property: “best” absorber-emitter
  2. cavity containing nothing.

To describe an object by its properties is more vague than showing a concrete object with the properties. It may be that there is nothing with the specified properties and then one may be talking about the empty set which is meaningless from scientific point of view

It is thus desirable present a concrete physical example of a blackbody which has a mathematical model. In my new proof of Planck’s Law I have considered such a concrete model in the form of a vibrating string subject to small radiative damping defined by two parameters \gamma and \frac{T}{h}:

  • radiative damping coefficient \gamma
  • cut-off frequency \frac{T}{h}
  • T is a common temperature of all frequencies and h a precision parameter.

In this model the dependence of \gamma is eliminated by calibrating temperature so that \gamma T  is constant, and the only effective parameter is the precision parameter h defining the cut-off frequency \frac{T}{h}.

The new proof of Planck’s Law shows that this model is an ideal absorber-emitter and since the emitted energy increases with the cut-off frequency, a model with maximal cut-off- smallest h can be chosen as a concrete example of a reference blackbody satisfying the defining properties of a blackbody of being an ideal absorber-emitter and emitting maximal energy.

In other words: As a concrete physical model of a blackbody, we may take a well-tempered Steinway Grand Piano:

1 Comment

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  1. cementafriend

    The definition in Perry’s Chemical Engineering (7th Edition) refined by the esteemed late Professor Hoyt Hottel, is as follows:” Blackbody Radiation -Engineering calculations of thermal radiation from surfaces are best keyed to the radiation characteristics of the blackbody, or ideal radiator. The charcteristic properties of the blackbody are that it absorbs all the radiation incident on its surface and that the quality and intensity of the radiation it emits are completely determined by its temperature. The total radiative flux throughout a hemisphere from a black surface of area A and its absolute temperature T is given by the Stefan-Boltzman law
    Q=A* sigma* (T^4)” This is in line with Stefan’s orginal work based on measurements of surfaces in a vacuum.
    The S-B law does not apply to a cavity nor does it apply to a gas. Mathematical assumptions and manipulations have been made to apply the S-B law to pseudo surfaces (eg the sun’s visible projection) and to pseudo average temperatures but that does not mean that is a physical reality. The moon has a surface and has no atmosphere. It appears that new measurements have found that the average temperature over full rotations around the sun are less than previously estimated from use of the S-B equation and sun’s estimated radiation flux.

    I am sure you look occasionally at Tallbloke’s blog (he is an engineer and the site is followed by some knowledgeable engineers) Note the following http://tallbloke.wordpress.com/2012/04/02/a-model-of-lunar-temperature/#more-5647
    All the best Cementafriend

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