Re: Want to prove E=mc²? University labs should try this!

On Tue, 26 Nov 2024 22:07:31 +0000, rhertz wrote:

I didn't claim that! ChatGPT made the calculations, which seemed to me
excessively high.

It was ridiculously high. You should not have repeated the numbers
that it provided, ESPECIALLY if you are as expert in the topic as
you claim to be.
ChatGPT knows how to put sentences together that, on a probabilistic
basis, correspond with other sentences generally accepted as well-
constructed. It does not actually understand the meaning of those
sentences, which is why ChatGPT often spouts bullshit.

THAT'S WHY I copied the four questions for you TO REPLICATE my chat, as
it was impossible to transcript the extensive formulae.
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In that way, I thought, you could have had A DUPLICATE of my chat.
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But YOU REFUSED TO DO IT, even when I wanted that you checked it.

I prefer to learn about a subject so that I can answer on my own.
AI tools are a useful crutch PROVIDED you understand the subject.

Regarding ΔT = 2E/(3 PV), n is missing. And it comes from E = 3/2 nRT,
derived from the equation for ideal gas  PV = nRT.

n does not have units of temperature. It is also dimensionless.
Your calculation was hence totally senseless.

The 3/2R part of this equation comes from the fact that the molar
internal energy of a monatomic ideal gas at temperature T is the molar
heat capacity of that gas at constant volume V.
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Regarding your INCORRECT USE of the formula u = 4 σ T^4/c, I only can
repeat what I wrote: YOU CAN'T USE THIS FORMULA FOR A SMALL CAVITY. It
was thought as Radiation Energy Density in open space, for uses in
astronomy and astrophysics, NOT WITHIN A SMALL ALUMINUM CAVITY.

It is correct for black body radiation. It is not correct for other
scenarios such as, say, an intense beam of collimated, monochromatic
light (laser light). Its applicability does not depend on the volume
of space.

Here: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/raddens.html
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WATCH THIS CALCULATION, DONE AT THAT SITE:
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For A REGION OF SPACE where the temperature is T = 186,500 K, the
RADIATION ENERGY DENSITY is 0.9146125157872499 x 10^6 J/m^3.

Why the all-caps?
Except for my factor-of-ten fumble, 0.9146125157872499 x 10^6 J/m^3
is practically the same my previous calculation of 9.12e4 J/m^3
(which should have been 9.12e5 J/m^3). The only difference is a bit of
round-off error in the third place.
In other words, their online calculator agrees with my Windows
calculator computation.

You are mixing different concepts of the theories around BBC.
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I invite you to read the history of developments in BBC radiation, which
I wrote in 2019, and that end with Planck's discovery of h.
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Thermal Radiation, Black Body Theory and the Birth of Quantum Physics
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https://physictheories.blogspot.com/2019/
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Read the last part, about RADIOMETRY, and the definitions of:
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Spectral Radiant Energy inside a cavity: The original formulae u and E
from Planck. THESE ARE THE ORIGINAL PLANCK'S FORMULAE INSIDE THE BBC.
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Spectral Radiant Exitance Me(𝜆,T) at the aperture in the cavity: THIS IS
WHAT YOU USED.

No, I was calculating energy density, assuming the black body nature
of the radiation. Read again that section of the Wikipedia article
that I provided you a link for.

IT'S THE ENERGY THAT FLOWS OUT OF THE BBC, THROUGH A
HOLE. This was what was ACTUALLY MEASURED at the BPT, whose physicists
provided ESSENTIAL INFORMATION to Planck in October 1900. He had two
months left to present his paper at the German Physics Society on
December 14, 1900 (date considered the birth of quantum physics).
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IRRADIANCE is measured outside the BBC, and the factor c/4 allowed the
use of Planck's formula to measurements and calculations in astronomy.
NOR HIM NEITHER WIEN DERIVED SUCH EQUATION. It was derived AFTER THEM,
by physicists working in RADIOMETRY.