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

On Tue, 26 Nov 2024 20:50:43 +0000, ProkaryoticCaspaseHomolog wrote:

On Tue, 26 Nov 2024 18:29:11 +0000, rhertz wrote:
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On Tue, 26 Nov 2024 8:27:15 +0000, ProkaryoticCaspaseHomolog wrote:
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On Mon, 25 Nov 2024 21:54:34 +0000, rhertz wrote:
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This means that half of the accumulated 955 Joules remain within the
cavity.

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477.5 Joules of energy in a volume of 5.236e-4 m^3 implies a energy
energy density u (assumed to be black body) within the shell of
9.12e4 J/m^3
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u = 4 σ T^4/c
9.12e4 = 4 * 5.67e^-8 T^4/3.0e^8
T^4 = 120,634,920,634,920,634,920
T = 1.05e5 K temperature of the black body radiation
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Your numbers don't make sense.

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Your entire post don't make sense.
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1) Your u value is wrong by 10 times. It should be u = 9.12e5 J/m^3.

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Yes, I dropped a digit.
So things are even WORSE for you.
The effective black body temperature corresponding to that radiation
density is 1.86e5 K
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2) You applied incorrectly how the radiation is spread within the
cavity.
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P = uc/4 is the radiative FLUX of energy being radiated in 3D, traveling
at the speed of light. The factor 4 is due to the integration of energy
moving omnidirectionally and being radiated toward infinity, which IS
NOT THE CASE HERE, INSIDE THE CAVITY.
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The 477.5 Joules ARE CONFINED in the cavity, and the radiation keeps
bouncing within its volume.
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At any case, it would give a radiative flux P = 6.84E+13 J m^-2/sec.

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Read that out loud and ask yourself if that is reasonable.
68.4 trillion watts per square meter.
From a 5 watts of input power.
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When you modify the Stefan-Boltzmann law by writing u = 4 σ T^4/c,
you're assuming that the energy propagates spherically without
attenuation. At any case, T =  186,364 K, a value that HAS NO MEANING
AT ALL.

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It has a very definite meaning.
See the discussion in "Energy density"
https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law#Energy_density
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3) Using correctly the influence of energy within the cavity filled with
air (behaving as an ideal gas), you have:
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E = 3/2 nRT
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n = PV/RT , moles of air in the volume
R = 8.3145 kJ/kmol K (ideal gas)
R = 0.287 kJ/kg K (air)
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ΔT = 2E/(3 PV) = 6 K , the increase above room temperature.

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What type of numerology are you using?
Where did you get a value of E to plug into that?
Check your units. PV has dimensions of energy, so 2E(3 PV) is a
dimensionless number.
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As you can see, this is a much more reasonable value.
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What would you expect if you use a 5 W incandescent lamp heating the
cavity?
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Only 6"C increase in the inner temperature after a couple of minutes.

Yet you claim that that 5 watt incandescent lamp will raise the
temperature to 707 K.

I didn't claim that! ChatGPT made the calculations, which seemed to me
excessively high.
THAT'S WHY I copied the four questions for you TO REPLICATE my chat, as
it was impossible to transcript the extensive formulae.
In that way, I thought, you could have had A DUPLICATE of my chat.
But YOU REFUSED TO DO IT, even when I wanted that you checked it.
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.
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.
***********************************************
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.
Here: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/raddens.html
WATCH THIS CALCULATION, DONE AT THAT SITE:
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.
You are mixing different concepts of the theories around BBC.
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.
Thermal Radiation, Black Body Theory and the Birth of Quantum Physics
https://physictheories.blogspot.com/2019/
Read the last part, about RADIOMETRY, and the definitions of:
Spectral Radiant Energy inside a cavity: The original formulae u and E
from Planck. THESE ARE THE ORIGINAL PLANCK'S FORMULAE INSIDE THE BBC.
Spectral Radiant Exitance Me(𝜆,T) at the aperture in the cavity: THIS IS
WHAT YOU USED. 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).
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.