Share
Explore BrainMass

Blackbody Radiation

Black-body radiation is a type of electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment or emitted by a black body held at constant, uniform temperature. The radiation has a specific spectrum and intensity that depends only on the temperature of the body.

A perfectly insulated enclosure that is in thermal equilibrium internally contains black-body radiation and will emit it through a hole made in its wall, provided that hole is small enough to have negligible effect upon that equilibrium.

A black-body at room temperature appears black, as most of the energy it radiates is infra-red and cannot be perceived by the human eye. At higher temperature, it glows with increasing intensity and colors that will range from dull red to blindingly blue-white as the temperature increases.
Planck’s law of black-body radiation states

I(v,T)= (2hv^3)/c^2 1/(e^(hv/kT)-1)

Where I(v,T) is the energy per unit time radiated per unit area of emitting surface in the normal direction per unit soli angle per unit frequency by a black body at temperature T
H is the Planck constant
C is the speed of light in a vacuum
K is the Boltzmann constant
V is the frequency of the electromagnetic radiation
T is the absolute temperature of the body

Wien’s displacement law shows how the spectrum of black-body radiation at any temperature is related to the spectrum at any other temperature. A consequence of Wien’s displacement law is that the wavelength at which the intensity per unit wavelength of the radiation produced by a black body is at a maximum λmax which is a function of only temperature as seen below:

λ_max=b/T

Where b is the Wien’s displacement constant.

The Stefan-Boltzmann Law states that the power emitted per unit area of the surface of a black body is directly proportional to the fourth power of its absolute temperature as seen below:

j^*= σT^4

Where j* is the total power radiated per unit area, T is the absolute temperature and σ is the Stefan-Boltzmann constant

Calculation involving Radiation View Factors

A cross section through a tunnel containing two long parallel straight pipes of diameter, D, and distance, L, between their centers. The direct radiation factor between two such pipes is given by the equation in the attached file. Find the rate of heat loss per meter run from each pipe if pipe 1 has a temperature of 450 K and em

Electricity of a Piece of Metals

A piece of metal is heated from a temperature of 27 oC to a temperature of 590 oC. How many more times the energy (amount) does the metal emit as blackbody radiation at the higher temperature than at the lower temperature

Blackbody radiation curve

What is the wavelength (in μm or 10^-6m) of the peak of the blackbody radiation curve for an emitter at temperature 180 K? You will need to write your answer in scientific notation and enter only the decimal part of the answer. Remember to write your answer as the number x 10^-6 and enter only the decimal number before the

Planck's formula for spectral distribution

Planck's formula for spectral distribution of the flux emitted by a blackbody is: S_v = [(2*pi*h)/(c^2)][(v^3)/((e^hv/kT)-1)] a) from this formula deduce that the totl flux is proportional to the fourth power of the temperture, that is: integral from 0 to infinity S_v dv (proportionality symbo

Quantum Mechanics: Example Problems

Which of the following statements are true about quantum theory? 1.(T/F)photoelectric effect shows the particle-like nature of light 2.(T/F) in addition to light, matter may also display wave-like properties 3.(T/F) the energy of a quantum of light is related to its wavelength 4.(T/F) a particle of light is calle

Absorbing Blackbody Radiation

A perfect blackbody is one that absorbs all the radiation, light that falls on it. Since there is energy in radiation there is a certain energy density in the cavity, u = U/V, where U is the energy, V is the volume and u is the energy density. From electromagnetic theory, the pressure exerted by the radiation is p=1/3u, and expe

Radiation Wavelength as a Function of Temperature

Calculate the wavelengths at which the photosphere, chromospheres, and corona emit the most radiation. Explain how your calculation results suggest the best way to observe these regions of the solar atmosphere. (Treat each part of the atmosphere as a perfect blackbody. Assume average temperatures of 50,000 K and 1.5 x 10 K for t

Modern Physics

See attached file for full problem description. 1. The distribution of energy density for black body or cavity radiation as a function of frequency in a neighborhood of df about f is given by: Integrate this function between 0 and infinity to find the total energy density. 2. In an experiment to study the photoelectric ef

Classical theory is energy radiated by a blackbody approached

Please see attached for all questions. 1. According to the classical theory of physics, the energy radiated by a blackbody approached infinity as the wavelength of the emitted light approaches zero. a) Why is this considered a problem for classical physics? b) Max Planck solved this problem is 1990. What was the key to th

Planck's Law for Blackbody Radiation vs. The Rayleigh-Jeans Law

Given: f(lambda) = 8pi*kt(lambda^4) Where lambda is measured in meters, T is the temperature in kelvins, k is Boltzmann's constant. The Rayleigh-Jeans Law agrees with experimental measurements for long wavelengths but disagrees drastically for short wavelengths. [The law predicts that f(lambda) -> 0 as f(lambda) --> infinity

Black Body Radiation and Venetian Blinds

Consider venetian blinds that are painted black on one side and white on the other. Assume that the blinds are installed between two panes of glass, with a vacuum inbetween so that air and its convection have no effect on the problem. Assume that the reflectivity of the white side is 90% and that of the black side is 10%. How we