Deriving Stefan-Boltzmann law from Planck distribution | Multilingual [CC]

In this video, we address Blackbody radiation and integrate the energy spectral distribution over all possible wavelengths to obtain the Total Energy Density.
This energy density results proportional to T^{4}, a.k.a. Stefan-Boltzmann law.
We also discuss some math-related strategies to approach these types of problems~!

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[stescottlover]

Just what I wanted to find....very clear explanation. Thank you!

[eli_margetts]

awesome video dude. Super well explained. And I had the same question as matei but see you answered that too! Great work.

[orwelgeorge]

Lovely work, fills a huge hole in my understanding

[mateihurba]

This video was very helpful! One question, isn't the factor of 8 in Plank's law supposed to be a 2? In that case, the alpha factor would be different.

[RF-fipt]

Very well explained, and your answer to @mateihurba8580 clarify more. One clarification i need if possible: σ=5.67x10^-8 W/(m^2.K^4) without steradian comes from that formula with 2 at numerator, and is from a Hemisphere blackbody (what i undestand from 2 sites: spectralcalc radiance: integrating planck equation and NASA TE Michels planck functions and integrals). Is σ or your α constants valids only to Hemispheres? Like to a sphere we need to multiply by 2? Because the Sun sphere is widely stated with a Power of 3.8x10^26 W, using P=4πr^2σT^4 gives that also (T=5780, r=700Mm), but maybe is wrong by a factor of 2, and is really 7.8x10^26W, by that fórmulas. But truly is 3.8x10^26W, by the independent measure of 1360W/m^2, at the Earth distance of 150MKm. I cannot understand why they talk to hemisphere.

[voidisyinyangvoidisyinyang]

fascinating. What if Planck was covering up the noncommutative calculus truth of reality? See Professor Basil J. Hiley for details. Wonder how that would change this analysis.

[lanomusambazi-txeg]

Mmmm you are too fast sir. I'm failing to follow through.