# What is Stefan-boltzmann law: Definition and 28 Discussions

The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time

j

{\displaystyle j^{\star }}
(also known as the black-body radiant emittance) is directly proportional to the fourth power of the black body's thermodynamic temperature T:

j

=
σ

T

4

.

{\displaystyle j^{\star }=\sigma T^{4}.}
The constant of proportionality σ, called the Stefan–Boltzmann constant, is derived from other known physical constants. Since 2019, the value of the constant is

σ
=

2

π

5

k

4

15

c

2

h

3

=
5.670374

×

10

8

W

m

2

K

4

,

{\displaystyle \sigma ={\frac {2\pi ^{5}k^{4}}{15c^{2}h^{3}}}=5.670374\ldots \times 10^{-8}\,\mathrm {W\,m^{-2}\,K^{-4}} ,}
where k is the Boltzmann constant, h is Planck's constant, and c is the speed of light in a vacuum. The radiance from a specified angle of view (watts per square metre per steradian) is given by

L
=

j

π

=

σ
π

T

4

.

{\displaystyle L={\frac {j^{\star }}{\pi }}={\frac {\sigma }{\pi }}T^{4}.}
A body that does not absorb all incident radiation (sometimes known as a grey body) emits less total energy than a black body and is characterized by an emissivity,

ε
<
1

{\displaystyle \varepsilon <1}
:

j

=
ε
σ

T

4

.

{\displaystyle j^{\star }=\varepsilon \sigma T^{4}.}

j

{\displaystyle j^{\star }}
has dimensions of energy flux (energy per unit time per unit area), 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.

ε

{\displaystyle \varepsilon }
is the emissivity of the grey body; if it is a perfect blackbody,

ε
=
1

{\displaystyle \varepsilon =1}
. In the still more general (and realistic) case, the emissivity depends on the wavelength,

ε
=
ε
(
λ
)

{\displaystyle \varepsilon =\varepsilon (\lambda )}
.
To find the total power radiated from an object, multiply by its surface area,

A

{\displaystyle A}
:

P
=
A

j

=
A
ε
σ

T

4

.

{\displaystyle P=Aj^{\star }=A\varepsilon \sigma T^{4}.}
Wavelength- and subwavelength-scale particles, metamaterials, and other nanostructures are not subject to ray-optical limits and may be designed to exceed the Stefan–Boltzmann law.

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1. ### Power Radiated From a Copper Cube

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2. ### Question on how much intensity of light has been scattered

I actually am not sure what equations are relevant here but I thought these are the relevant ones. My Approach: By Stefan-Boltzman Law, the intensity absorbed by the Earth is given as ## I = e \sigma T^4## where e is the emissivity of Earth, ##\sigma## is Stefan-Boltzman constant and T is the...
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4. ### B Understanding the Stefan-Boltzmann Law (when the surroundings are hotter)

1.If so what would the law mean if ##T_{surroundings}>T##? 2. Stefan-Boltzmann Law is formulated as ##H = A\sigma T^4## where ##H## is the energy emitted per unit time, ##A## is the area of the object, ##T## is the absolute temperature of the object and (3.) I am unclear about whether...
5. ### I Why don't humans glow in the dark?

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6. ### B The Stefan-Boltzmann Law and Sunspots

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9. S

### B Understanding Stefan Boltzmann Law: Derivation and Simulation Guide

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In the energy balance of a system where a small object at T1 enclosed in a body at T2 given by the Stefan-Boltzmann equation q = A1ε1σT14 - A1α12σT24 shouldn't it be a differential equation since the small body could be absorbing/releasing sufficient net energy from the enclosing body that...
14. ### Stefan-Boltzmann law, luminosity, brightness and magnitude?

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15. ### Is Manipulating the Stefan-Boltzmann Law with Metamaterials Possible?

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19. ### Derivation of Stefan-Boltzmann Law from Wien's Law

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