Stefan Boltzmann Constant

Stefan’s Constant, often known as the Stefan-Boltzmann Constant, is a physical constant used in physics. It is the proportionality constant in the Stefan-Boltzmann law of Blackbody radiation. Stefan Boltzmann Constant is represented by the Greek letter. This physical constant was hypothesised by Josef Stefan in 1879, and it was determined by Ludwig Boltzmann in 1884. 

“The emission of electromagnetic waves, which convey energy away from the generating item, is known as thermal radiation. The radiation is in the infrared portion of the electromagnetic spectrum for ordinary temperatures (less than red hot). The Stefan-Boltzmann law describes the relationship that governs net radiation from heated things.”

Stefan Boltzmann Equation

The same law was derived in 1884 by Austrian physicist Ludwig Boltzmann from thermodynamic considerations, and it was first proposed in 1879 by Austrian physicist Josef Stefan as a result of his experimental studies: if E is the radiant heat energy emitted from a unit area in one second (that is, the power from a unit area) and T is the absolute temperature (in kelvins), then E=σT⁴. The proportionality constant, known as the Stefan-Boltzmann constant, is represented by the Greek letter sigma (). The value of this constant is 5.670374419 10^–8 W m^-2 K^-4 .

By integrating over all wavelengths at a given temperature, which will constitute a small flat black body box, the equation can also be obtained from Planck’s law.  “With increasing temperatures, the amount of thermal radiation released grows quickly, and the primary frequency of the radiation increases.”

The Stefan–Boltzmann constant can be used to calculate the amount of heat emitted by a black body that absorbs and emits all radiant energy. The Stefan–Boltzmann constant also allows for the conversion of temperature (K) to intensity (Wm2), which is power per unit area.

Stefan Boltzmann Constant Value

The Stefan Boltzmann constant has a globally agreed value and is expressed in SI units as-

Constant Stefan Boltzmann σ=5.670367(13) x 10^-8W.m^-2.K^-4

The formula for the dimensions is [M]^-1[T]^-3[O]^-4

It can also be stated in different units. The Stefan Boltzmann constant value and related units can be found in the table below.

• Stefan’s law states that a black body’s total energy radiated per unit surface area per unit time is proportional to the fourth power of its absolute temperature at all wavelengths.
• A blackbody is the ideal light absorber and emitter. Any light that strikes it is absorbed. A perfect radiator is also a perfect blackbody.
• The more efficiently a thing absorbs light, the more efficiently it emits it. As a result, a perfect absorber should be the highest efficient radiator imaginable; nevertheless, because a perfect absorber does not reflect any radiation, it will seem black.
• The temperature of an object’s absolute temperature is measured on a scale with 0 as absolute zero. The absolute temperature scales are Kelvin, degree units Celsius, and Rankine degree unit Fahrenheit; this is also known as thermodynamic temperature.
• Absolute zero is the temperature at which a system has the lowest conceivable energy, i.e. it has the smallest amount of energy. Molecules’ motions slow down as they approach this temperature. A gas thermometer can only measure the lowest temperature. You’re well aware that electronic equipment will not function at this temperature. Finally, the molecules’ Kinetic Energy becomes insignificant or nil.

Applications

The Stefan Boltzmann constant has numerous uses in physics. The following are a few of them:

• It’s used to calculate how much heat the dark body radiates.
• It can be used to convert temperature (K) to intensity (W.m-2) measurements, which is basically power per square metre.

Conclusion

In terms of temperature, the Stefan–Boltzmann law explains the power radiated by a dark substance. The Stefan–Boltzmann equation says that the total energy radiated per unit surface area of a black body across all wavelengths per unit time jstar (also known as the black-body radiant emittance) is directly proportional to the black body’s thermodynamic temperature T:

j*=σT4.

Ludwig Boltzmann (1844–1906) gave a derivation of the law from theoretical considerations in 1884, based on Adolfo Bartoli’s work. [6] In 1876, Bartoli used thermodynamic concepts to prove the existence of radiation pressure. Boltzmann, following Bartoli, considered an ideal heat engine that used electromagnetic radiation as the working matter instead of an ideal gas.

The law was almost immediately tested in the lab. Although discrepancies at greater temperatures were noted by Heinrich Weber in 1888, full accuracy within measurement uncertainties was established by 1897 up to temperatures of 1535 K.