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}.}
The radiant emittance
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.
##e## is emissivity
##\sigma## is the Stefan-Boltzmann constant, ##5.67*10^{-8} W m^{-2} K^{-4}##
A is the surface area
T is the temperature
##\frac{dQ}{dt}## is the rate of heat transfer or radiated power
At first glance this appeared to be an easy problem, just plug in the values and go, so...
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...
I have a question about the Second Law of Thermodynamics and the Stefan-Boltzmann law.
These quotes are from http://www.ces.fau.edu/nasa/module-2/correlation-between-temperature-and-radiation.php
“The Stefan-Boltzmann law, a fundamental law of physics, explains the relationship between an...
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...
Lets assume:
emissivity of a human=0.91
T=310K
Surface area body: 1.60 m^2
If we use the Stefan-Boltzmann Law we can find a value for the rate of emission of light by a human.
Rate emission=762 J/s
Given this rate of emission, why don't humans glow in the dark?
The Stefan-Boltzmann Law
Question: Is this law proven to be true? If so, then what about sunspots?
The surface of the sun is roughly double the temperature of an umbra which means it should be 16 times brighter according to this law. It isn't.
The luminosity of the photosphere is 10,000...
I am having a doubt of why is the radiative flux IvdvcosΘdw in equilibrium integrated for a spherical black body only from 0 to pi/2 not pi(e.g. For the entire surface for which it is zero),
v=frequency
dw= solid angle
Homework Statement
It's not a piece of homework, I'm doing a project and I've been wondering how I may be able to show it mathematically. I've covered the material before but it was a long long time ago...
Homework EquationsThe Attempt at a Solution
[/B]
A-Thinking about modelling my "ship"...
Hello, everyone, I was looking at this video () and I need to make a simulation for Stefan Boltzmann law calculating its constant. I didn't understand few things.
In the video, it shows that Stefan Boltzmann law is R = e*sigma*T^4vand then says that rate of net heat transferred
ΔQ/Δt =...
Homework Statement
A sphere of radius r_s is at the center of a spherical shell of inner radius r_i=10\, r_s and thickness s = 10\, {\rm cm}\ll r_i.
The sphere has a temperature T_s=1073\, {\rm K} and and an emissivity e=0.90.
The inner surface of the shell has a temperature T_i = 873...
Hello!
This is an old problem from the Estonian-Finnish open physics olympiad (2013) and I hope you will be able to lend me some help.
1. Homework Statement
Sun-rays are focused with a lens of diameter d = 10 cm and focal length f = 7 cm to a black thin plate. Behind the plate is a mirror...
I'm designing an oven and want to ensure that the insulation I specify has a low enough Thermal Conductivity (k) to resist excessive heat loss. I determine heat loss (Hout)with the following equation: Hout=A*U*(T1-T0). U is dependent on k (U=k/L). I omitted the heat transfer coefficient in...
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...
From what I understand, in the equation P=\sigma AT^4, P is the power output of the star which is the energy radiated per second in EM radiation of all frequencies, and I think luminosity is also defined as the energy radiated per second in EM radiation of all frequencies. Therefore luminosity...
So I saw some papers on arXiv that explore the notion of playing around with the Stefan-Boltzmann law using metamaterials:
http://arxiv.org/abs/1109.5444
http://arxiv.org/abs/1411.1360
I know enough physics that it looks rather interesting, but I don't know enough math to judge how credible it...
Hi, I have a few questions about Stefan-Boltzmann's law. Let's say that the temerature of an object increases for 2 degrees Celsius, that means that the emmited energy of a surface of that object will increase 16 times. Is this happening because the number of photons is increased 16 times or is...
Hi guys. I had a question concerning a pure proton plasma with a given temperature and its loss of energy due to the Stefan-Boltzmann law. From my understanding, the Stefan-Boltzmann law applies to objects that contain electrons. I don't think that's true but I would like to know if it is. If...
Homework Statement
Derive Stefan-Boltzmann law from Wien’s law
Hint: you can use (without proof) R(T) = -∞∫∞ R(λ,T)dλ , ρ(λ,T)=(4/c)*R(λ,T)
Homework Equations
wien's law: p(λ,T) = f(λ,T)/^5
Stefan's law : R(T) = σT^4
The Attempt at a Solution
Honestly I am having trouble just...
Homework Statement
Derive Stefan-Boltzmann Law from Wien's Law.
Hint: You can use (without proof) R(T)=∫(-∞ to ∞) R(λ,T)dλ, p(λ,T)= 4/c R(λ,T).
Homework Equations
Stefan-Boltzmann Law:P=AσT^4
Wien's Law: λmax=(2.898*10^-3 m*K)/T.
The Attempt at a Solution
Let λmax=(2.898*10^-3...
Hello, I am in DIRE need of help with my science fair project and am completely stuck. All/most relevant information should be able to be found here: http://sciencebuddies.org/science-fair-projects/project_ideas/Phys_p073.shtml?fave=no&isb=c2lkOjEsaWE6UGh5cyxwOjUscmlkOjEyNDE1MzMw&from=TSW
1. I...
Hello Physics Forum! There's an interesting experiment to verify the Stefan-Boltzmann law using an incandescent lamp. Which treats the filament as an approximate blackbody, approximates that the input power fully goes to the radiating channel (i.e. no conduction or gas loss), measures the...
Homework Statement
in about 6X10^7 y from now, the sun will be a red giant star with a temperature 1/2 its present value and a radius 100 times larger.
a) what will be the luminosity of the red giant sun be compared to its current value?
b) assume that the new luminosity gives you the...
I've been trying to derive the Stefan-Boltzmann law using thermodynamics, and have resorted to looking up the derivation in the feynman lectures and on wikipedia, and I'm confused by both. I think the wikipedia derivation is the best one to look at, it's here...
Homework Statement
Starting with the Planck distribution R(\lambda,T) for blackbody radiation.
(a) Derive the blackbody Stefan-Boltzmann law (ie total flux is proportional to T4) by integrating the above expression over all wavelengths. Thus show that
R(T) =...
Hi!
I'm wondering if anybody can recommend me a book where it's explained how to solve (analytically) integral that appears in Stefan-Boltzmann's law:
\int_0^\infty \frac{x^n}{(e^x-1)^m}dx
Thanx!
Homework Statement
A person is standing outdoors in the shade where the temperature is 27°C.
(a) What is the radiant energy absorbed per second by his head when it is covered with hair? The surface area of the hair (assumed to be flat) is 160 cm2 and its emissivity is 0.85.
(b) What...
I've looked all over the internet, and can't find a decent explanation.
Could someone please explain why the stefan-boltzmann radiation law of I = oT^4 be explained in classical mechanics rather then quantum?
It's urgent, sorry to be pushy.
Cheers.
I've been reading about the Stefan-Boltzmann law, but there is one thing that I don't understand. Why is it T^4? I can't think of anywhere that the 4 is coming from and can't find anything about this with Google searches.