Sham Wow Of Physics

"Blackbody radiation" or "cavity radiation" refers to an object or system which absorbs all radiation incident upon it and re-radiates energy which is characteristic of this radiating system only, not dependent upon the type of radiation which is incident upon it. The radiated energy can be considered to be produced by standing wave or resonant modes of the cavity which is radiating.

The amount of radiation emitted in a given frequency range should be proportional to the number of modes in that range. The best of classical physics suggested that all modes had an equal chance of being produced, and that the number of modes went up proportional to the square of the frequency

But the predicted continual increase in radiated energy with frequency (dubbed the "ultraviolet catastrophe") did not happen. Nature knew better.

Definition Provided by Hyperphysics

Stefan Boltzmann Law

For Black Bodies

The Stefan–Boltzmann law, also known as Stefan's law, states that the total energy radiated per unit surface area of a black body per unit time (known variously as the black-body irradiance, energy flux density, radiant flux, or the emissive power), P, is directly proportional to the fourth power of the black body's thermodynamic temperature T (also called absolute temperature):

p = σ A T4

For Grey Bodies

A more general case is of a grey body, the one that doesn't absorb or emit the full amount of radiative flux. Instead, it radiates a portion of it, characterized by its emissivity, e:

p = e σ A T4

The irradiance p has dimensions of energy flux (energy per time), and the SI units of measure are joules per second per square metre, or equivalently, watts per square metre. The SI unit for absolute temperature T is the kelvin. e is the emissivity of the grey body; if it is a perfect blackbody,  e = 1. Still in more general (and realistic) case, the emissivity depends on the wavelength, e = e(λ).

Emissivity

The emissivity of a material (usually written ε or e) is the relative ability of its surface to emit energy by radiation. It is the ratio of energy radiated by a particular material to energy radiated by a black body at the same temperature. A true black body would have an ε = 1 while any real object would have ε < 1. Emissivity is a dimensionless quantity.

In general, the duller and blacker a material is, the closer its emissivity is to 1. The more reflective a material is, the lower its emissivity. Highly polished silver has an emissivity of about 0.02.

Definition provided by Wikipedia

Example - Radiation from the surface of the Sun

If the surface temperature of the sun is 5800 K and if we assume that the sun can be regarded as a black body the radiation energy per unit time can be expressed by modifying (1) like

p / A = σ T4

= (5.6703 10-8 W/m2K4) (5800 K)4

= 6.42 107 W/m2

Example Provided by Engineering Toolbox

Example - Radiation from a Sphere

A solid sphere (emissivity = 0.65) has a radius of 5cm is heated to 873 K and suspended from a thin wire in the center of the room whose temperature is 295 K.  At what rate is heat released to the room

p = e σ A T4

p = (0.65)(6.57x10^-8)(4 x 3.14 x 0.05^2)(873)^4

p = 672 watts

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Example - Radiation transfer to a loaf of bread from an oven

Calculate the net heat transfer by radiation to a loaf of bread in an oven at a uniform temperature of 177°C, if the emissivity of the surface of the loaf is 0.85. The total surface area and temperature of the loaf are respectively 0.0645 m2 and 100°C.

p = e σ A (T4 - T4)

p   = 0.0645 x 0.85 x 5.73 x 10-8 (4504- 3734)

p    = 68.0 J s-1.

 Alloy 24ST Polished 0.09 Alumina, Flame sprayed 0.8 Aluminum Commercial sheet 0.09 Aluminum Foil 0.04 Aluminum Commercial Sheet 0.09 Aluminum Heavily Oxidized 0.2 - 0.31 Aluminum Highly Polished 0.039 - 0.057 Aluminum Anodized 0.77 Aluminum Rough 0.07 Aluminum paint 0.27 - 0.67 Antimony, polished 0.28 - 0.31 Asbestos board 0.96 Asbestos paper 0.93 - 0.945 Asphalt 0.93 Basalt 0.72 Beryllium 0.18 Beryllium, Anodized 0.9 Bismuth, bright 0.34 Black Body Matt 1.00 Black lacquer on iron 0.875 Black Parson Optical 0.95 Black Silicone Paint 0.93 Black Epoxy Paint 0.89 Black Enamel Paint 0.80 Brass Dull Plate 0.22 Brass Rolled Plate Natural Surface 0.06 Brass Polished 0.03 Brass Oxidized 600oC 0.6 Brick, red rough 0.93 Brick, fireclay 0.75 Cadmium 0.02 Carbon, not oxidized 0.81 Carbon filament 0.77 Carbon pressed filled surface 0.98 Cast Iron, newly turned 0.44 Cast Iron, turned and heated 0.60 - 0.70 Chromium polished 0.058 Concrete 0.85 Concrete, rough 0.94 Concrete tiles 0.63 Cotton Cloth 0.77 Copper electroplated 0.03 Copper heated and covered with thick oxide layer 0.78 Copper Polished 0.023 - 0.052 Copper Nickel Alloy, polished 0.059 Glass smooth 0.92 - 0.94 Glass, pyrex 0.85 - 0.95 Gold not polished 0.47 Gold polished 0.025 Granite 0.45 Gypsum 0.85 Ice smooth 0.966 Ice rough 0.985 Inconel X Oxidized 0.71 Iron polished 0.14 - 0.38 Iron, plate rusted red 0.61 Iron, dark gray surface 0.31 Iron, rough ingot 0.87 - 0.95 Lampblack paint 0.96 Lead pure unoxidized 0.057 - 0.075 Lead Oxidized 0.43 Lime wash 0.91 Magnesium Oxide 0.20 - 0.55 Magnesium Polished 0.07 - 0.13 Marble White 0.95 Masonry Plastered 0.93 Mercury liquid 0.1 Mild Steel 0.20 - 0.32 Molybdenum polished 0.05 - 0.18 Nickel, elctroplated 0.03 Nickel, polished 0.072 Nickel, oxidized 0.59 - 0.86 Nichrome wire, bright 0.65 - 0.79 Oak, planed 0.89 Oil paints, all colors 0.92 - 0.96 Paper offset 0.55 Plaster 0.98 Platinum, polished plate 0.054 - 0.104 Porcelain, glazed 0.92 Paint 0.96 Paper 0.93 Plaster, rough 0.91 Plastics 0.91 Porcelain glazed 0.93 Quartz glass 0.93 Roofing paper 0.91 Rubber, hard glossy plate 0.94 Rubber Nat Hard 0.91 Rubber Nat Soft 0.86 Sand 0.76 Sawdust 0.75 Silicon Carbide 0.83 - 0.96 Silver Polished 0.02 - 0.03 Steel Oxidized 0.79 Steel Polished 0.07 Stainless Steel, weathered 0.85 Stainless Steel, polished 0.075 Stainless Steel, type 301 0.54 - 0.63 Steel Galvanized Old 0.88 Steel Galvanized New 0.23 Tile 0.97 Tin unoxidized 0.04 Titanium polished 0.19 Tungsten polished 0.04 Tungsten aged filament 0.032 - 0.35 Water 0.95 - 0.963 Wood Beech, planned 0.935 Wood Oak, planned 0.885 Wrought Iron 0.94 Zink Tarnished 0.25 Zink polished 0.045