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:


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

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

Heat Transfer: Thermal conduction and radiation, Stefan's law

An iPod is left running inside a thin insulating case 2.5mm thick with thermal condoctivity of 0.02WK^-1 m^-1 The case is black and at 25 degrees Celsius and exchanges energy with it's surroundings, all of which are at 20 degrees Celsius, by radiation alone. What is the temperature inside the case?

Blackbody Radition in Flatland

Blackbody Radition in Flatland a) Carry out the derivation of u(v,t), the energy per unit area per unit frequency in the electromagnetic field, for the 2-dimentional case, i.e. inside a square cavity of side L held at temperature T. Find the total energy in the square and show that it's of the form: U(T) = (L^2)a(T^n) and det

The energy of photons is examined.

1) The temperature of the surface of the Sun is 5800 K. Using Wein's Law, compute the wavelength of the color of light at which the Sun has its greatest Emissive Power. Describe this color verbally. 2) Use Planck's quantum equation to compute the energy of the "photons" of the light for the color whose wavelength was identi

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