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Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure p and volume V is proportional to the product of amount of substance n and absolute temperature T: pV=nRT,where R is the molar gas constant (8.31446261815324 J⋅K−1⋅mol−1).[3] Introducing the Boltzmann constant as the gas constant per molecule[4] k = R/NA transforms the ideal gas law into an alternative form: pV=NkT,where N is the number of molecules of gas.
kB derives from classical statistical mechanics.
Of course it's needed. How else can you describe the Boltzmann distribution, rationalise the gas laws, or do thermodynamics? Quantum mechanics doesn't displace classical mechanics, any more than relativity displaces newtonian physics. The test of both is that they degenerate to the classical formula for large or slow systems.
Planck's formula and Wien's approximation both attempt to describe the spectrum of black body radiation, the characteristic energy distribution emitted by an ideal perfect absorber at a given temperature. However, they differ in their accuracy and underlying assumptions....In conclusion, Planck's formula is the more general and accurate description of black body radiation, thanks to its inclusion of energy quantization. Wien's approximation provides a useful simplification for shorter wavelengths but is not sufficient for the entire spectrum.
Planck's Formula B(ν, T) = (2 * h * ν^3) / (c^2 * (e^(h * ν / (k_B * T)) - 1))Wien's Approximation B(ν, T) = (2 * h * ν^3) / (c^2 * e^(h * ν / (k_B * T)))
You're right, at first glance, the equations might seem very similar, with Planck's formula just adding a -1 term to Wien's approximation. However, that seemingly small addition has a profound impact:The -1 term accounts for quantization: This term incorporates the revolutionary idea that energy can only be emitted or absorbed in discrete packets. This concept of quantized energy levels was a major breakthrough in physics and went beyond the classical framework used in Wien's approximation.
Just shows why you shouldn't use ChatGPT as a source of scientific information. It displays all the insight and understanding of a politician.
Quote from: alancalverd on 08/03/2024 08:42:26Just shows why you shouldn't use ChatGPT as a source of scientific information. It displays all the insight and understanding of a politician.It reflects the quality of training data sources. It seems like it hasn't been equipped with the tools to filter out incorrect statements.
anything from an AI source may be infected by untruth
But humans tend to conduct experiments or simply ask "does that seem reasonable?" AI just goes on regurgitating any old rubbish because it doesn't care about the consequences of its output.
The model may be 100% accurate and quote Donald Trump's authoritative speech to the letter, but I wouldn't want anyone to inject themselves with hydrochloroquinone.
If all the previously accumulated information is the Bible, AI will reject any scientific statement as unreliable and the world will regress to the intellectual level of the Republican Party.
It was once. Similar problems have been found where all the permitted truth was all in Mao's Little Red Book, or Lysenko's state-approved botany papers.Problem with the internet as a source is that there is only one right answer to scientific question, but an infinite number of wrong ones, and the internet grants allows them equal weight.