Browse Definitions :
Definition

Stefan-Boltzmann constant

What is the Stefan-Boltzmann constant?

The Stefan-Boltzmann constant, symbolized by the lowercase Greek letter sigma (σ), is a physical constant expressing the relationship between the heat radiation emitted by a black body and its absolute temperature. According to the Stefan-Boltzmann law, σ has a value of 5.670374419 × 10−8 watt per square meter per kelvin to the fourth (W / (m2 x K4).

σ represents the constant of proportionality between these two variables. The law itself only applies to black bodies, which are theoretical surfaces that absorb all incident heat radiation. In practice, such bodies do not exist.

However, the Stefan-Boltzmann law and constant are still useful to study radiation phenomena, such as in Planck's radiation law, and to establish the relationship between an object's temperature and the heat radiated by it.

Black bodies and Stefan-Boltzmann constant

The Stefan-Boltzmann constant is named after its two formulators, Austrian physicists Josef Stefan and Ludwig Boltzmann, who each formulated it in 1879 and 1884, respectively. σ is a constant value and involves black body radiation.

A black body -- sometimes spelled as blackbody -- is also called an ideal radiator. It is an object that radiates or absorbs all radiant energy falling on it with perfect efficiency. The word black refers to the fact that incident visible light gets absorbed into the body instead of being reflected, so the surface appears to be black. Although black bodies are purely theoretical, a box with a small hole and a blackened interior provides a good -- in fact, the best possible -- practical approximation of a black body.

The Stefan-Boltzmann constant defines the power per unit area emitted by a black body as a function of its thermodynamic temperature.

Energy radiated by an ideal radiator

The constant is based on Stefan-Boltzmann's law, which states that the radiant heat energy emitted from a unit area of the black body in one second (E) is directly proportional to the fourth power of its absolute temperature, or E = σ x T4.

E is distributed over a range of wavelengths of radiation. Further, as T increases, the wavelength for maximum energy emission shifts to shorter values, so high energy means short wavelengths and high frequency.

Illustration showing how to measure a wavelength
How to measure a wavelength

Deriving the Stefan-Boltzmann constant

The value of the Stefan-Boltzmann constant can be derived or determined experimentally, like Stefan and Boltzmann did. Using the Boltzmann constant, the formula to derive the constant is expressed as the following:

σ = (2 x π5 x kB4) / (15 x h3 x c2) = 5.670367 x 10-8 W / (m2 x K4)

Here:

According to the Committee on Data of the International Science Council, σ can also be derived from the gas constant as the following:

σ = (2 x π5 x R4) / (15 x h3 x c2 x NA4) = (32 x π5 x h x R4 x R4) / (15 x Ar(e)4 x Mu4 x c6 x α8)

Here:

  • R = universal gas constant = 8.3144598 J per mole per K (J x mol-1 x K-1)
  • NA = Avogadro constant = 6.02214076 x 1023 mol-1
  • R= Rydberg constant = 10,973,731.6 m-1
  • Ar(e) = relative atomic mass of the electron = 1/1,840 mass of the proton or neutron
  • Mu = molar mass constant = 1 gram per mol (g / mol)
  • α = fine structure constant = 1 / 137 = 0.0072973525

Expressing Stefan-Boltzmann constant in various unit systems

The dimensional formula for the Stefan-Boltzmann constant is expressed as M1 x T-3 x K-4, where M is mass.

σ can also be expressed in other systems as follows:

Unit system σ Units

Centimeter-gram-second

5.6704 x 105

erg x cm2 x s1 x K4

Thermochemistry

11.7 x 108

cal x cm2 x day1 x K4

U.S. customary units

1.714 x 109

BTU x hr1 x ft2 x ˚R4

Stefan-Boltzmann constant applications

The Stefan-Boltzmann constant is used in many practical applications in physics. In particular, the constant helps with the derivation of many physical quantities, such as the amount of heat a black body radiates. It is also used to calculate the temperature required to generate a particular amount of radiation by a black body over a specific area.

Other Stefan-Boltzmann constant applications are the following:

  • convert K to the units for intensity, or W / m2;
  • calculate how hot the sun is based on how much power strikes the Earth in a square meter;
  • predict how much heat the Earth radiates into space;
  • calculate the radii of stars; and
  • calculate the emissivity of an object, which is the ratio of its total emissive power to the total emissive power of a black body.

See also: table of physical constants.

This was last updated in August 2022

Continue Reading About Stefan-Boltzmann constant

Networking
  • network traffic

    Network traffic is the amount of data that moves across a network during any given time.

  • dynamic and static

    In general, dynamic means 'energetic, capable of action and/or change, or forceful,' while static means 'stationary or fixed.'

  • MAC address (media access control address)

    A MAC address (media access control address) is a 12-digit hexadecimal number assigned to each device connected to the network.

Security
  • Evil Corp

    Evil Corp is an international cybercrime network that uses malicious software to steal money from victims' bank accounts and to ...

  • Trojan horse

    In computing, a Trojan horse is a program downloaded and installed on a computer that appears harmless, but is, in fact, ...

  • quantum key distribution (QKD)

    Quantum key distribution (QKD) is a secure communication method for exchanging encryption keys only known between shared parties.

CIO
  • benchmark

    A benchmark is a standard or point of reference people can use to measure something else.

  • spatial computing

    Spatial computing broadly characterizes the processes and tools used to capture, process and interact with 3D data.

  • organizational goals

    Organizational goals are strategic objectives that a company's management establishes to outline expected outcomes and guide ...

HRSoftware
  • talent acquisition

    Talent acquisition is the strategic process employers use to analyze their long-term talent needs in the context of business ...

  • employee retention

    Employee retention is the organizational goal of keeping productive and talented workers and reducing turnover by fostering a ...

  • hybrid work model

    A hybrid work model is a workforce structure that includes employees who work remotely and those who work on site, in a company's...

Customer Experience
  • database marketing

    Database marketing is a systematic approach to the gathering, consolidation and processing of consumer data.

  • cost per engagement (CPE)

    Cost per engagement (CPE) is an advertising pricing model in which digital marketing teams and advertisers only pay for ads when ...

  • B2C (Business2Consumer or Business-to-Consumer)

    B2C -- short for business-to-consumer -- is a retail model where products move directly from a business to the end user who has ...

Close